Leet Code #1793

1793. Maximum Score of a Good Subarray

Link to Problem.

Lessons will be learned, and things will get easier

Iteration One

Goals

• Working Solution for all edge cases

Notes

from typing import List

# pre: nums are all positive numbers
class Solution:
    def scoreSubarray(self, nums: List[int], i: int, j: int) -> int:
        if i == j:
            return nums[i]
        else:
            return min(nums[i:j]) * (j - i)
    
    def maximumScore(self, nums: List[int], k: int) -> int:
        n : int = len(nums)
        res : int = self.scoreSubarray(nums, k, k)

        for i in range(k,-1,-1):
            for j in range(k + 1,n+1,1):
                tmp = self.scoreSubarray(nums, i, j)
                if tmp > res:
                    res = tmp
                res = max(res, self.scoreSubarray(nums, i, j))
                
        return res


# Lets test the solution defined above
inputs = [
    {"nums" : [1,4,3,7,4,5], "k" : 3, "output" : 15},
    {"nums" : [8182,1273,9847,6230,52,1467,6062,726,4852,4507,2460,2041,500,1025,5524], "k" : 8, "output" : 9014},
    {"nums" : [6569,9667,3148,7698,1622,2194,793,9041,1670,1872], "k" : 5, "output" : 9732},
    {"nums" : [529,7655,4113,7929,7745,6149,2691,435,7858,978,5467,8761,2881,4175,359,9711,7157,1740,5214,7660,1113,614,4077,2859,2954,1170,3997,4526,2771,4046,3174,7126,3866,7603,5596,9587,1826,9228,9983,2487,7018,1130,1299,1389,5914,2926,5679,5781,5770,8705,9053,3449,9893,6042,4349,2008,2959,9730,5639,8813,5206,747,460,149,2553,4006,2012,8966,2245,2635,9089,7962,5879,9785,1069,7122,7926,9546,4557,5719,6926,2353,1887,2744,2240,472,7559,824,4320,8267,7210,4764,8368,3071,8973,7849,8704,2375,5130,5092,8311,6147,7692,6794,8280,4863,4932,4863,946,4243,7307,5061,3752,426,6352,1978,818,5604,3306,9034,9805,7900,8462,4473,1914,8449,113,8566,7671,9518,693,730,8064,2004,9584,8725,4392,468,3013,502,6472,4185,6380,471,4258,3424,8435,7470,5109,7228,486,8925,3130,1574,4454,9048,5824,679,5364,3804,5143,6714,5695,2806,7653,9153,26,3195,2856,4303,6914,270,9011,3325,7835,1770,8668,3395,1756,6702,743,2618,6841,7492,6068,9150,8852,5004,9610,6716,7053,4937,6209,2772,4454,3988,432,8097,9400,3194,5565,6266,2821,4769,5019,164,443,8620,695,8173,7705,5081,1376,6573,9364,7328,2513,8020,2361,4915,5346,7410,2379,5538,7560,9431,1049,9069,9616,9368,3998,3240,8006,3177,4380,794,8668,4685,3456,2257,2645,7269,2424,5209,4198,3086,6821,7598,3764,7505,6191,9018,7019,338,5606,1484,1962,1415,8423,6988,9140,8305,6196,2299,3397,8634,3855,2139,4924,7102,4662,6713,1056,5418,5982,940,3149,9245,637,8873,7651,2975,6447,5539,291,9119,7773,9287,4286,858,9111,5012,9499,1595,4408,918,5742,5134,9475,8427,9556,8422,4825,9747,522,266,9267,7351,5413,7374,8556,8014,6194,6076,3011,1612,217,6101,7673,5623,6757,5038,2615,3711,8296,7453,408,868,4090,1038,6549,7307,7886,3571,6450,1947,5236,8943,5827,1325,1278,9292,1930,7778,6039,3935,623,7886,256,1194,833,4219,3641,1047,2543,4442,9242,150,8148,1460,9650,5882,9647,431,7709,714,6345,6104,3240,6151,6310,7220,216,6452,3271,3368,1247,7870,8492,2124,1932,3524,5515,2911,8798,7242,1019,8154,3942,5654,5994,8323,449,1914,5680,2821,8399,1904,6356,8538,298,7418,2339,1672,2948,584,4877,2702,36,8044,1528,3815,799,8865,7043,5846,3204,4238,3012,2060,8169,9422,8049,8871,1517,819,6066,4821,7262,6131,9774,9210,9683,338,3573,3812,4398,5022,1313,9705,792,3644,3397,529,8340,2683,524,5635,6653,9852,8619,39,6060,4273,3026,7680,6861,4470,8,4094,4720,388,9344,7749,394,3603,8406,8713,9328,4423,3074,9966,694,4094,3627,6926,3558,4322,1720,3814,7277,5770,7077,9871,7872,4016,1196,7425,8843,8631,2500,142,991,9472,1603,7433,2955,5213,3083,9960,3993,8940,2675,5442,8308,6653,2105,4640,2020,8924,8918,2949,4949,5442,9580,2811,5205,7078,9779,5049,4455,3420,5586,6315,1629,101,5384,4917,7629,2731,8121,2852,9260,8445,2896,8075,4667,2164,7085,3616,3177,9104,5318,8728,2332,3943,2388,4352,8537,199,1655,3881,7058,3912,7027,5721,9737,6031,3265,2699,8285,7835],
     "k" : 314,
     "output" : 36150 },
    {"nums" : [5,5,4,5,4,1,1,1], "k" : 0, "output" : 20}
]

tmp = Solution()

for input in inputs:
    output = tmp.maximumScore(nums = input["nums"], k = input["k"])
    assert output == input["output"], f'Test failed for:\nnums = {input["nums"]},\nk = {input["k"]}\nExpected = {input["output"]}, Returned = {output}'

Results

Not sure I really learned much here. Clearly dynamic programming is an area of growth for me, but this problem was tricky in how you used a deque and contructed the solution.

If it isn’t clear, I copied this solution from a refernce answer. I was getting close, but this solution is so elegant.

Summary

• Time Limit Exceeded
• 23/72 testcases passed

Clearly this is an O(n^2) solution, so lets work on getting something a little more eficient

Iteration Two

Goals

All testcases passing with no time limit exceeded.

Open Question: How can I enforce time-limit constraints on my testcases?

from typing import List

# pre: nums are all positive numbers
class Solution:
    def scoreSubarray(self, nums: List[int], i: int, j: int) -> int:
        if i == j:
            return nums[i]
        else:
            return min(nums[i:j]) * (j - i)
    
    def maximumScore(self, nums: List[int], k: int) -> int:
        n : int = len(nums)
        res : int = self.scoreSubarray(nums, k, k)
        max_j : int = n

        # res starts as nums[k]
        curr_min : int = res
        new_ele : int = 0

        for i in range(k,-1,-1):
            for j in range(k + 1,max_j + 1,1):

                # If we are adding a new minimum, 
     
                new_ele = nums[j - 1]
                if (new_ele < curr_min):
                    curr_min = new_ele
                    # and it's not possible to beat prev max
                    if new_ele * max_j < res:
                        # Cap j here for future iterations
                        max_j = j
                        break

                res = max(res, self.scoreSubarray(nums, i, j))

            # If we are adding a new minimum, 
            # and it's not possible to beat prev max
            new_ele = nums[i]
            if new_ele < curr_min:
                curr_min = new_ele
                if new_ele * max_j < res:
                    break

            res = max(res, self.scoreSubarray(nums, i, j))
                
        return res


# Lets test the solution defined above
inputs = [
    {"nums" : [1,4,3,7,4,5], "k" : 3, "output" : 15},
    {"nums" : [8182,1273,9847,6230,52,1467,6062,726,4852,4507,2460,2041,500,1025,5524], "k" : 8, "output" : 9014},
    {"nums" : [6569,9667,3148,7698,1622,2194,793,9041,1670,1872], "k" : 5, "output" : 9732},
    {"nums" : [529,7655,4113,7929,7745,6149,2691,435,7858,978,5467,8761,2881,4175,359,9711,7157,1740,5214,7660,1113,614,4077,2859,2954,1170,3997,4526,2771,4046,3174,7126,3866,7603,5596,9587,1826,9228,9983,2487,7018,1130,1299,1389,5914,2926,5679,5781,5770,8705,9053,3449,9893,6042,4349,2008,2959,9730,5639,8813,5206,747,460,149,2553,4006,2012,8966,2245,2635,9089,7962,5879,9785,1069,7122,7926,9546,4557,5719,6926,2353,1887,2744,2240,472,7559,824,4320,8267,7210,4764,8368,3071,8973,7849,8704,2375,5130,5092,8311,6147,7692,6794,8280,4863,4932,4863,946,4243,7307,5061,3752,426,6352,1978,818,5604,3306,9034,9805,7900,8462,4473,1914,8449,113,8566,7671,9518,693,730,8064,2004,9584,8725,4392,468,3013,502,6472,4185,6380,471,4258,3424,8435,7470,5109,7228,486,8925,3130,1574,4454,9048,5824,679,5364,3804,5143,6714,5695,2806,7653,9153,26,3195,2856,4303,6914,270,9011,3325,7835,1770,8668,3395,1756,6702,743,2618,6841,7492,6068,9150,8852,5004,9610,6716,7053,4937,6209,2772,4454,3988,432,8097,9400,3194,5565,6266,2821,4769,5019,164,443,8620,695,8173,7705,5081,1376,6573,9364,7328,2513,8020,2361,4915,5346,7410,2379,5538,7560,9431,1049,9069,9616,9368,3998,3240,8006,3177,4380,794,8668,4685,3456,2257,2645,7269,2424,5209,4198,3086,6821,7598,3764,7505,6191,9018,7019,338,5606,1484,1962,1415,8423,6988,9140,8305,6196,2299,3397,8634,3855,2139,4924,7102,4662,6713,1056,5418,5982,940,3149,9245,637,8873,7651,2975,6447,5539,291,9119,7773,9287,4286,858,9111,5012,9499,1595,4408,918,5742,5134,9475,8427,9556,8422,4825,9747,522,266,9267,7351,5413,7374,8556,8014,6194,6076,3011,1612,217,6101,7673,5623,6757,5038,2615,3711,8296,7453,408,868,4090,1038,6549,7307,7886,3571,6450,1947,5236,8943,5827,1325,1278,9292,1930,7778,6039,3935,623,7886,256,1194,833,4219,3641,1047,2543,4442,9242,150,8148,1460,9650,5882,9647,431,7709,714,6345,6104,3240,6151,6310,7220,216,6452,3271,3368,1247,7870,8492,2124,1932,3524,5515,2911,8798,7242,1019,8154,3942,5654,5994,8323,449,1914,5680,2821,8399,1904,6356,8538,298,7418,2339,1672,2948,584,4877,2702,36,8044,1528,3815,799,8865,7043,5846,3204,4238,3012,2060,8169,9422,8049,8871,1517,819,6066,4821,7262,6131,9774,9210,9683,338,3573,3812,4398,5022,1313,9705,792,3644,3397,529,8340,2683,524,5635,6653,9852,8619,39,6060,4273,3026,7680,6861,4470,8,4094,4720,388,9344,7749,394,3603,8406,8713,9328,4423,3074,9966,694,4094,3627,6926,3558,4322,1720,3814,7277,5770,7077,9871,7872,4016,1196,7425,8843,8631,2500,142,991,9472,1603,7433,2955,5213,3083,9960,3993,8940,2675,5442,8308,6653,2105,4640,2020,8924,8918,2949,4949,5442,9580,2811,5205,7078,9779,5049,4455,3420,5586,6315,1629,101,5384,4917,7629,2731,8121,2852,9260,8445,2896,8075,4667,2164,7085,3616,3177,9104,5318,8728,2332,3943,2388,4352,8537,199,1655,3881,7058,3912,7027,5721,9737,6031,3265,2699,8285,7835],
     "k" : 314,
     "output" : 36150 },
    {"nums" : [3135,245,9277,2315,2945,7091,281,1242,6725,1544,2364,7756,7908,3272,3358,1851,3096,8914,1835,5922,1479,6028,2541,2284,4979,571,1700,6434,62,5378,9973,3997,2880,9307,277,8486,2374,6135,7181,5942,3870,1986,2382,9229,1429,3274,4933,8707,3151,6328,6374,3921,8578,260,7540,304,7441,6931,4160,7894,7486,572,6882,7664,887,4945,2517,7416,2258,5316,1078,9260,9866,9741,8001,1146,5318,2397,1808,4934,3480,3992,6079,1545,764,6841,6900,9452,9575,3076,9535,5559,9289,192,124,7681,6602,1979,3867,8333,3049,3739,1812,1795,7687,5635,4624,7012,913,9680,3012,1286,9490,4001,1238,7961,1492,2559,5897,3661,1665,2976,1448,6901,9761,5762,4156,3341,8422,2810,3574,3751,8130,8719,4145,7881,9438,2332,25,8968,676,4668,1108,8456,4335,4627,6961,8516,7091,9051,6092,9834,2732,3623,5324,2043,6833,5639,4004,1780,2946,3501,60,3395,9217,3304,7444,616,6929,6576,724,4138,6198,8560,638,9182,7067,4431,7138,8623,98,9259,3379,8451,6353,4599,1990,5979,5802,9079,8500,5795,194,6180,68,2157,8181,5961,9229,7840,2645,8624,1112,5115,5146,6301,1202,4813,8123,8005,799,9593,3700,3178,7775,4141,4908,7944,4617,6401,2743,9803,9092,8303,3705,9195,6594,9755,3687,6797,507,8679,2077,4597,2287,7658,5964,5487,9429,4648,836,7128,3295,1030,5782,8829,4700,5287,8155,3356,8283,5881,88,4196,5108,4551,6153,9088,4594,6358,5537,8300,4002,333,9792,6861,8098,7262,7663,2517,4023,726,4036,4711,8529,5610,8088,408,143,2227,2526,8651,7918,4747,7283,599,6717,3426,1149,9063,1243,815,3145,2751,4639,413,6607,6700,7102,1559,3911,8077,900,7035,1025,7278,6835,7413,8743,7598,3347,6002,3644,4171,9132,5199,6822,3531,6499,7653,1797,6960,3358,3508,1082,7217,1136,2561,8878,7968,6292,2419,4412,2790,3472,1299,9502,8683,3884,1757,2812,7986,2932,8056,6798,7043,3556,2001,2306,585,511,7680,7973,5934,1519,4203,3232,7724,9619,4934,9866,3046,5755,1637,4709,6935,5095,4746,430,4568,4865,2085,4528,2480,6035,8693,2862,9894,5058,1190,3860,9664,4704,514,5775,4851,6029,941,104,428,6859,9759,9206,7749,670,5661,9032,855,957,6636,8864,6320,2488,9585,194,5352,7224,4197,4509,8311,8188,9072,1998,8117,1097,4229,2878,3638,3649,3503,7591,8391,5579,9863,2074,1711,9725,6628,8432,2603,519,5654,3709,2207,6495,7253,5108,1868,6546,9414,8191,7970,9928,5387,4961,3428,6480,9465,7879,2844,741,6613,5743,3004,3486,4517,7113,6868,7717,1242,9030,6578,9138,2630,5704,7045,9650,5506,9544,5875,2364,2483,8957,6823,8705,4145,7628,2382,9381,4178,5277,6323,7292,6782,7147,7032,4691,4242,52,424,6754,9593,2274,735,1638,3514,5510,2537,2775,8064,2111,1232,9090,6265,9750,7263,247,7184,1273,761,4605,9283,4302,4169,2338,3786,6029,9243,6093,9875,7110,3074,8735,8104,3297,5565,7784,7797,8757,2056,1346,6658,4878,9409,9656,8444,2785,7681,379,7575,7819,366,5206,7734,951,9744,2063,7775,8048,7634,8553,9339,4710,1870,1839,6745,344,3099,453,9065,8066,6632,9913,4556,4666,5394,1849,7716,5321,9727,3652,2340,1264,4562,9690,7183,5823,8395,8196,5910,8080,8309,6599,1475,7063,5161,4698,5726,3971,7788,1092,8527,9565,8063,9759,5597,3286,5623,206,9149,3803,1066,2018,2439,9598,6791,6509,5173,845,1152,3494,4792,8811,4416,8019,2033,9350,6536,7345,808,1807,8276,2377,4588,8603,5331,9468,5663,9249,4997,2963,7717,9259,8085,8132,271,9713,1013,277,421,6122,420,4682,8017,3029,1415,7755,1421,9961,237,4411,4627,7895,1027,2316,3441,7867,9000,273,8471,8743,8002,5213,9896,4536,5576,6009,1752,6508,6786,9410,8248,3963,245,9068,4968,1513,6055,7128,3294,4431,1832,9327,1897,6065,4889,8725,979,7244,2937,4121,7568,5363,4788,2495,5785,8991,1327,6730,5931,3010,41,5468,6774,5925,7371,7943,6058,1948,4325,4202,9461,6293,124,8849,3288,5880,1904,5329,1672,1576,1862,5221,4430,8550,352,9149,6707,9426,3852,6388,132,4586,2243,697,9454,8983,4364,9189,3909,7312,7454,7796,9570,2452,2495,9527,6927,7032,5911,8172,1634,2997,6923,4962,9583,5118,1391,6836,9540,883,7076,8095,1622,4672,6592,7617,9987,8477,6981,5393,2471,1517,6620,706,2323,6763,3744,8217,8682,2301,4875,2473,9446,610,2169,2527,4583,1050,6901,3495,1269,1794,702,2355,3627,2645,9724,3422,7950,2206,3336,5242,4547,9773,51,9481,8834,2596,1535,9365,438,2162,3791,7470,5298,4055,6696,7885,6951,614,1519,4117,7778,1768,1485,4679,9496,8940,9237,6553,5725,5308,2928,9188,2838,1340,7994,659,8944,6633,2764,3430,5994,8771,2585,2792,4022,7036,1672,1885,9983,748,7559,3328,5970,2283,3495,7246,3296,3402,5162,6617,9752],
     "k" : 400,
     "output" : 29725 },
    # New test case takes for-ever to run... Basically does not complete
    # {"nums" : 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759,2670,4980,733,72,1314,8551,8233,1078,250,1913,1821,8249,445,1934,5487,3468,420,8013,1745,4696,5337,5649,7013,908,2440,281,1778,4288,5052,1625,395,4091,9945,4058,3111,6575,3529,963,564,5206,6266,988,5176,9275,7309,590,3526,4692,4031,8010,489,6297,7147,1029,9506,713,9345,5736,6574,6637,7787,5447,8955,8641,8379,2703,4847,2954,9671,9871,3143,3730,1006,7175,19,3591,1846,9160,9532,1817,9061,9352,6982,3709,3599,6094,2668,8017,749,200,915,7801,5585,8015,477,4621,4205,8023,2302,470,3398,6189,7261,7770,3477,8887,8325,1647,9402,2798,2444,2200,7810,3184,7807,8703,3255,5909,617,9663,2070,3924,2920,7166,5227,3403,609,5992,8768,8238,2379,3307,3238,8013,5622,420,1965,5189,4249,7177,8930,781,8147,3080,7215,9366,7081,2856,4542,5767,2355,243,4058,7869,4078,1433,8539,2730,5353,3883,951,1356,2431,1973,6546,3292,4189,7795,7113,5853,7438,318,2198,6705,9555,8567,3012,2374,7655,6879,6657,1698,1259,6488,6969,9950,75,8496,6546,2992,1547,1584,8430,3178,9784,1666,2889,4593,8191,2118,1942,4111,1063,946,6890,6225,6099,3445,6960,7989,7572,8386,3754,5299,1031,5720,3978,7394,1511,9173,478,6411,3296,3798,7257,8289,8851,5250,9887,3255,64,9493,2485,7454,1653,1289,9296,1002,3019,3117,7382,1829,2612,772,9198,8345,6925,7418,4717,4391,3267,161,8682,3361,3332,1456,2382,809,2937,2581,9789,8456,3640,4429,4668,3138,3164,2874,1466,7990,7224,1038,1670,4267,919,6906,7582,2779,4442,8412,1432,94,7258,2400,743,1252,5907,1987,2567,7449,7138,9681,5524,139,721,8418,8860,7370,5995,7692,3460,6997,1314,6732,3493,5277,242,6652,7472,2003,1449,6762,2818,1487,9878,2166,4967,2879,6974,2422,9891,5365,8035,7377,8540,1297,2473,9851,5120,1592,2356,9064,5626,2343,4917,8670,5345,3081,3890,8313,1779,6552,7437,6116,6902,6385,1096,2779,7829,4123,3003,514,4189,9715,8138,4597,58,7691,8834,581,9343,7392,2569,4174,4692,8835,9484,5340,1889,8901,2706,7751,5132,4806,1586,4729,3846,9246,1658,7059,6467,3455,3463,5513,4903,284,1071,6682,3600,9750,1211,2544,4906,2165,5968,7359,9071,4038,2675,7599,2738,1533,1394,1187,5485,6844,9839,4352,1584,5462,4774,9890,7398,1153,2597,1869,9386,9400,6338,8149,9960,435,4973,4313,6207,5923,1159,7157,987,3494,6966,795,3475,5887,4817,6174,7899,6350,5312,3741,8352,3969,3178,2713,7606,8185,56,9585,3546,395,7171,8414,4532,2983,1819,1950,5193,9727,3716,9507,5975,5559,6165,8886,3516,7442,5093,2113,3499,3585,820,2951,4148,7453,4039,4686,5199,7455,6422,4583,3699,9824,5759,4148,6397,6784,3314,418,7105,6750,8724,9623,1133,2856,5954,9424,4089,216,1101,4577,8349,9698,4499,452,3248,8755,9306,1995,1168,6481,4943,5326,7537,3464,8394,8457,1571,5757,4534,4896,3216,7011,704,1325,5029,3974,3181,7027,8028,6652,8796,251,6169,5703,2014,791,7883,8389,581,8196,3178,9085,1999,2773,923,1222,4378,7565,6362,1033,607,5883,2957,3921,9102,701,6088,7758,1632,120,4658,8848,9964,5661,5998,3806,7918,4725,8217,967,6430,5748,4930,1314,3533,5388,4957,1481,4822,1682,5172,9611,6526,217,242,4333,4288,7756,2151,1893,2030,2719,113,7256,2446,3931,9689,4941,4719,3382,7188,6983,1777,2817,1314,1757,5806,1522,9626,9856,8906,3391,2516,1894,2022,566,5258,6324,6989,6914,7014,5950,9721,8548,3162,1924,5196,7653,6203,4405,1521,4313,5116,470,9517,7413,1052,9174,8234,9233,2402,4688,7531,9137,2815,2082,6708,6702,3332,2314,6816,5517,6109,5359,2914,9285,7821,9638,600,8466,1389,6126,1372,8314,2560,5627,1131,5520,3110,4346,7301,4687,3226,6247,7846,1651,886,9163,1959,5738,3789,792,7237,7062,8240,6624,7006,8572,5963,1769,6523,2506,2147,3246,5009,8047,9750,6545,4991,3675,7831,5557,2603,7776,1099,818,5663,7458,7314,9749,4520,3147,1343,9225,4454,4344,4796,5088,2651,3797,1924,6559,1638,5918,1624,6219,3655,9747,2478,6897,5144,9694,9377,3170,4895,4085,8557,5052,8164,3999,4570,7237,2231,8303,944,7939,5282,7265,3526,8025,717,6876,546,3825,4176,804,6611,6053,7305,6462,8990,9400,5112,5446,2116,2689,5433,8938,8394,7456,8456,9486,3568,3200,5860,7824,1745,6389,1605,2816,1201,4941,1932,998,481,2376,1268,4558,5700,6300,318,8984,4931,4083,3696,7750,3331,3588,3964,1916,356,4500,4353,1124,9440,8420,4351,391,8238,6654,3526,1003,2391,7551,2290,5876,9688,7356,40,6740,7920,7789,780,3046,3868,6018,4218,2341,4921,1989,4073,2012,3193,8007,7883,5445,4849,7046,1742,3858,9928,5119,2981,3933,1074,2084,561,5920,3105,3604,4192,93,454,1825,3832,1691,483,986,3292,1056,4855,619,3770,1424,379,616,1555,8319,6864,3905,5898,6076,9943,783,6029,5414,9414,1382,4031,9795,6107,7847,2402,2047,1363,4865,7659,4194,3757,9823,9823,9912,4278,9221,6265,7613,4509,6053,562,254,8241,424,9570,1703,9946,9518,3117,5671,8676,7958,6244,5911,4729,9504,2395,4262,9257,5023,1589,4752,4476,8487,8029,5047,6856,2763,6227,5757,6612,2272,2158,565,5195,7723,6310,8446,7040,8033,8653,8291,9766,6246,6112,8812,5770,985,5938,4105,4691,3279,4509,5329,7574,6206,1856,2949],
    # "k" : 4362,
    # "output" : 29725 },
    {"nums" : [5,5,4,5,4,1,1,1], "k" : 0, "output" : 20}
]

tmp = Solution()

for input in inputs:
    output = tmp.maximumScore(nums = input["nums"], k = input["k"])
    assert output == input["output"], f'Test failed for:\nnums = {input["nums"]},\nk = {input["k"]}\nExpected = {input["output"]}, Returned = {output}'

Results

• 36 / 72 testcases passed
• Commented out test case causes program to run for 2+ minutes… There should be an easy way to catch this

Iteration Three

• With new timing out test, we should find a way to enforce a timeout time. TBD what a reasonable time is
• Will just add code to enforce some sort of test locally

from typing import List
import multiprocessing
from functools import partial, wraps

class TimeExceededException(Exception):
    pass

def function_runner(*args, **kwargs):
    """Used as a wrapper function to handle
    returning results on the multiprocessing side"""

    send_end = kwargs.pop("__send_end")
    function = kwargs.pop("__function")
    try:
        result = function(*args, **kwargs)
    except Exception as e:
        send_end.send(e)
        return
    send_end.send(result)

def _run_with_timer(func, max_execution_time) -> int:
    @wraps(func)
    def wrapper(*args, **kwargs) -> int:
        recv_end, send_end = multiprocessing.Pipe(False)
        kwargs["__send_end"] = send_end
        kwargs["__function"] = func
        
        p = multiprocessing.Process(target=function_runner, args=args, kwargs=kwargs)
        p.start()
        p.join(max_execution_time)
        if p.is_alive():
            p.terminate()
            p.join()
            raise TimeExceededException("Exceeded Execution Time")
        
        result = recv_end.recv()

        if isinstance(result, Exception):
            raise result

        return result

    return wrapper

# Defines the real wrapper and time limit
enforce_time_limit = partial(_run_with_timer, max_execution_time=2)

# pre: nums are all positive numbers
class Solution:
    def scoreSubarray(self, nums: List[int], i: int, j: int) -> int:
        if i == j:
            return nums[i]
        else:
            return min(nums[i:j]) * (j - i)
        
    # Enforces time-limit on func
    @enforce_time_limit
    def maximumScore(self, nums: List[int], k: int) -> int:
        n : int = len(nums)
        res : int = self.scoreSubarray(nums, k, k + 1)
        max_j : int = n

        # res starts as nums[k]
        curr_min : int = res
        new_ele : int = 0

        for i in range(k, -1, -1):
            # k + 1 already covered in itial calc
            for j in range(k + 1, max_j + 1, 1):

                # If we are adding a new minimum, 
     
                new_ele = nums[j - 1]
                if (new_ele < curr_min):
                    curr_min = new_ele
                    # and it's not possible to beat prev max
                    if new_ele * max_j < res:
                        # Cap j here for future iterations
                        max_j = j
                        break

                res = max(res, self.scoreSubarray(nums, i, j))

            # If we are adding a new minimum, 
            # and it's not possible to beat prev max
            new_ele = nums[i]
            if new_ele < curr_min:
                curr_min = new_ele
                if new_ele * max_j < res:
                    break

        return res


# Lets test the solution defined above
inputs = [
    {"nums" : [1,4,3,7,4,5], "k" : 3, "output" : 15},
    {"nums" : [8182,1273,9847,6230,52,1467,6062,726,4852,4507,2460,2041,500,1025,5524], "k" : 8, "output" : 9014},
    {"nums" : [6569,9667,3148,7698,1622,2194,793,9041,1670,1872], "k" : 5, "output" : 9732},
    {"nums" : [529,7655,4113,7929,7745,6149,2691,435,7858,978,5467,8761,2881,4175,359,9711,7157,1740,5214,7660,1113,614,4077,2859,2954,1170,3997,4526,2771,4046,3174,7126,3866,7603,5596,9587,1826,9228,9983,2487,7018,1130,1299,1389,5914,2926,5679,5781,5770,8705,9053,3449,9893,6042,4349,2008,2959,9730,5639,8813,5206,747,460,149,2553,4006,2012,8966,2245,2635,9089,7962,5879,9785,1069,7122,7926,9546,4557,5719,6926,2353,1887,2744,2240,472,7559,824,4320,8267,7210,4764,8368,3071,8973,7849,8704,2375,5130,5092,8311,6147,7692,6794,8280,4863,4932,4863,946,4243,7307,5061,3752,426,6352,1978,818,5604,3306,9034,9805,7900,8462,4473,1914,8449,113,8566,7671,9518,693,730,8064,2004,9584,8725,4392,468,3013,502,6472,4185,6380,471,4258,3424,8435,7470,5109,7228,486,8925,3130,1574,4454,9048,5824,679,5364,3804,5143,6714,5695,2806,7653,9153,26,3195,2856,4303,6914,270,9011,3325,7835,1770,8668,3395,1756,6702,743,2618,6841,7492,6068,9150,8852,5004,9610,6716,7053,4937,6209,2772,4454,3988,432,8097,9400,3194,5565,6266,2821,4769,5019,164,443,8620,695,8173,7705,5081,1376,6573,9364,7328,2513,8020,2361,4915,5346,7410,2379,5538,7560,9431,1049,9069,9616,9368,3998,3240,8006,3177,4380,794,8668,4685,3456,2257,2645,7269,2424,5209,4198,3086,6821,7598,3764,7505,6191,9018,7019,338,5606,1484,1962,1415,8423,6988,9140,8305,6196,2299,3397,8634,3855,2139,4924,7102,4662,6713,1056,5418,5982,940,3149,9245,637,8873,7651,2975,6447,5539,291,9119,7773,9287,4286,858,9111,5012,9499,1595,4408,918,5742,5134,9475,8427,9556,8422,4825,9747,522,266,9267,7351,5413,7374,8556,8014,6194,6076,3011,1612,217,6101,7673,5623,6757,5038,2615,3711,8296,7453,408,868,4090,1038,6549,7307,7886,3571,6450,1947,5236,8943,5827,1325,1278,9292,1930,7778,6039,3935,623,7886,256,1194,833,4219,3641,1047,2543,4442,9242,150,8148,1460,9650,5882,9647,431,7709,714,6345,6104,3240,6151,6310,7220,216,6452,3271,3368,1247,7870,8492,2124,1932,3524,5515,2911,8798,7242,1019,8154,3942,5654,5994,8323,449,1914,5680,2821,8399,1904,6356,8538,298,7418,2339,1672,2948,584,4877,2702,36,8044,1528,3815,799,8865,7043,5846,3204,4238,3012,2060,8169,9422,8049,8871,1517,819,6066,4821,7262,6131,9774,9210,9683,338,3573,3812,4398,5022,1313,9705,792,3644,3397,529,8340,2683,524,5635,6653,9852,8619,39,6060,4273,3026,7680,6861,4470,8,4094,4720,388,9344,7749,394,3603,8406,8713,9328,4423,3074,9966,694,4094,3627,6926,3558,4322,1720,3814,7277,5770,7077,9871,7872,4016,1196,7425,8843,8631,2500,142,991,9472,1603,7433,2955,5213,3083,9960,3993,8940,2675,5442,8308,6653,2105,4640,2020,8924,8918,2949,4949,5442,9580,2811,5205,7078,9779,5049,4455,3420,5586,6315,1629,101,5384,4917,7629,2731,8121,2852,9260,8445,2896,8075,4667,2164,7085,3616,3177,9104,5318,8728,2332,3943,2388,4352,8537,199,1655,3881,7058,3912,7027,5721,9737,6031,3265,2699,8285,7835],
     "k" : 314,
     "output" : 36150 },
    {"nums" : [3135,245,9277,2315,2945,7091,281,1242,6725,1544,2364,7756,7908,3272,3358,1851,3096,8914,1835,5922,1479,6028,2541,2284,4979,571,1700,6434,62,5378,9973,3997,2880,9307,277,8486,2374,6135,7181,5942,3870,1986,2382,9229,1429,3274,4933,8707,3151,6328,6374,3921,8578,260,7540,304,7441,6931,4160,7894,7486,572,6882,7664,887,4945,2517,7416,2258,5316,1078,9260,9866,9741,8001,1146,5318,2397,1808,4934,3480,3992,6079,1545,764,6841,6900,9452,9575,3076,9535,5559,9289,192,124,7681,6602,1979,3867,8333,3049,3739,1812,1795,7687,5635,4624,7012,913,9680,3012,1286,9490,4001,1238,7961,1492,2559,5897,3661,1665,2976,1448,6901,9761,5762,4156,3341,8422,2810,3574,3751,8130,8719,4145,7881,9438,2332,25,8968,676,4668,1108,8456,4335,4627,6961,8516,7091,9051,6092,9834,2732,3623,5324,2043,6833,5639,4004,1780,2946,3501,60,3395,9217,3304,7444,616,6929,6576,724,4138,6198,8560,638,9182,7067,4431,7138,8623,98,9259,3379,8451,6353,4599,1990,5979,5802,9079,8500,5795,194,6180,68,2157,8181,5961,9229,7840,2645,8624,1112,5115,5146,6301,1202,4813,8123,8005,799,9593,3700,3178,7775,4141,4908,7944,4617,6401,2743,9803,9092,8303,3705,9195,6594,9755,3687,6797,507,8679,2077,4597,2287,7658,5964,5487,9429,4648,836,7128,3295,1030,5782,8829,4700,5287,8155,3356,8283,5881,88,4196,5108,4551,6153,9088,4594,6358,5537,8300,4002,333,9792,6861,8098,7262,7663,2517,4023,726,4036,4711,8529,5610,8088,408,143,2227,2526,8651,7918,4747,7283,599,6717,3426,1149,9063,1243,815,3145,2751,4639,413,6607,6700,7102,1559,3911,8077,900,7035,1025,7278,6835,7413,8743,7598,3347,6002,3644,4171,9132,5199,6822,3531,6499,7653,1797,6960,3358,3508,1082,7217,1136,2561,8878,7968,6292,2419,4412,2790,3472,1299,9502,8683,3884,1757,2812,7986,2932,8056,6798,7043,3556,2001,2306,585,511,7680,7973,5934,1519,4203,3232,7724,9619,4934,9866,3046,5755,1637,4709,6935,5095,4746,430,4568,4865,2085,4528,2480,6035,8693,2862,9894,5058,1190,3860,9664,4704,514,5775,4851,6029,941,104,428,6859,9759,9206,7749,670,5661,9032,855,957,6636,8864,6320,2488,9585,194,5352,7224,4197,4509,8311,8188,9072,1998,8117,1097,4229,2878,3638,3649,3503,7591,8391,5579,9863,2074,1711,9725,6628,8432,2603,519,5654,3709,2207,6495,7253,5108,1868,6546,9414,8191,7970,9928,5387,4961,3428,6480,9465,7879,2844,741,6613,5743,3004,3486,4517,7113,6868,7717,1242,9030,6578,9138,2630,5704,7045,9650,5506,9544,5875,2364,2483,8957,6823,8705,4145,7628,2382,9381,4178,5277,6323,7292,6782,7147,7032,4691,4242,52,424,6754,9593,2274,735,1638,3514,5510,2537,2775,8064,2111,1232,9090,6265,9750,7263,247,7184,1273,761,4605,9283,4302,4169,2338,3786,6029,9243,6093,9875,7110,3074,8735,8104,3297,5565,7784,7797,8757,2056,1346,6658,4878,9409,9656,8444,2785,7681,379,7575,7819,366,5206,7734,951,9744,2063,7775,8048,7634,8553,9339,4710,1870,1839,6745,344,3099,453,9065,8066,6632,9913,4556,4666,5394,1849,7716,5321,9727,3652,2340,1264,4562,9690,7183,5823,8395,8196,5910,8080,8309,6599,1475,7063,5161,4698,5726,3971,7788,1092,8527,9565,8063,9759,5597,3286,5623,206,9149,3803,1066,2018,2439,9598,6791,6509,5173,845,1152,3494,4792,8811,4416,8019,2033,9350,6536,7345,808,1807,8276,2377,4588,8603,5331,9468,5663,9249,4997,2963,7717,9259,8085,8132,271,9713,1013,277,421,6122,420,4682,8017,3029,1415,7755,1421,9961,237,4411,4627,7895,1027,2316,3441,7867,9000,273,8471,8743,8002,5213,9896,4536,5576,6009,1752,6508,6786,9410,8248,3963,245,9068,4968,1513,6055,7128,3294,4431,1832,9327,1897,6065,4889,8725,979,7244,2937,4121,7568,5363,4788,2495,5785,8991,1327,6730,5931,3010,41,5468,6774,5925,7371,7943,6058,1948,4325,4202,9461,6293,124,8849,3288,5880,1904,5329,1672,1576,1862,5221,4430,8550,352,9149,6707,9426,3852,6388,132,4586,2243,697,9454,8983,4364,9189,3909,7312,7454,7796,9570,2452,2495,9527,6927,7032,5911,8172,1634,2997,6923,4962,9583,5118,1391,6836,9540,883,7076,8095,1622,4672,6592,7617,9987,8477,6981,5393,2471,1517,6620,706,2323,6763,3744,8217,8682,2301,4875,2473,9446,610,2169,2527,4583,1050,6901,3495,1269,1794,702,2355,3627,2645,9724,3422,7950,2206,3336,5242,4547,9773,51,9481,8834,2596,1535,9365,438,2162,3791,7470,5298,4055,6696,7885,6951,614,1519,4117,7778,1768,1485,4679,9496,8940,9237,6553,5725,5308,2928,9188,2838,1340,7994,659,8944,6633,2764,3430,5994,8771,2585,2792,4022,7036,1672,1885,9983,748,7559,3328,5970,2283,3495,7246,3296,3402,5162,6617,9752],
     "k" : 400,
     "output" : 29725 },
    # New test case takes for-ever to run... Basically does not complete
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759,2670,4980,733,72,1314,8551,8233,1078,250,1913,1821,8249,445,1934,5487,3468,420,8013,1745,4696,5337,5649,7013,908,2440,281,1778,4288,5052,1625,395,4091,9945,4058,3111,6575,3529,963,564,5206,6266,988,5176,9275,7309,590,3526,4692,4031,8010,489,6297,7147,1029,9506,713,9345,5736,6574,6637,7787,5447,8955,8641,8379,2703,4847,2954,9671,9871,3143,3730,1006,7175,19,3591,1846,9160,9532,1817,9061,9352,6982,3709,3599,6094,2668,8017,749,200,915,7801,5585,8015,477,4621,4205,8023,2302,470,3398,6189,7261,7770,3477,8887,8325,1647,9402,2798,2444,2200,7810,3184,7807,8703,3255,5909,617,9663,2070,3924,2920,7166,5227,3403,609,5992,8768,8238,2379,3307,3238,8013,5622,420,1965,5189,4249,7177,8930,781,8147,3080,7215,9366,7081,2856,4542,5767,2355,243,4058,7869,4078,1433,8539,2730,5353,3883,951,1356,2431,1973,6546,3292,4189,7795,7113,5853,7438,318,2198,6705,9555,8567,3012,2374,7655,6879,6657,1698,1259,6488,6969,9950,75,8496,6546,2992,1547,1584,8430,3178,9784,1666,2889,4593,8191,2118,1942,4111,1063,946,6890,6225,6099,3445,6960,7989,7572,8386,3754,5299,1031,5720,3978,7394,1511,9173,478,6411,3296,3798,7257,8289,8851,5250,9887,3255,64,9493,2485,7454,1653,1289,9296,1002,3019,3117,7382,1829,2612,772,9198,8345,6925,7418,4717,4391,3267,161,8682,3361,3332,1456,2382,809,2937,2581,9789,8456,3640,4429,4668,3138,3164,2874,1466,7990,7224,1038,1670,4267,919,6906,7582,2779,4442,8412,1432,94,7258,2400,743,1252,5907,1987,2567,7449,7138,9681,5524,139,721,8418,8860,7370,5995,7692,3460,6997,1314,6732,3493,5277,242,6652,7472,2003,1449,6762,2818,1487,9878,2166,4967,2879,6974,2422,9891,5365,8035,7377,8540,1297,2473,9851,5120,1592,2356,9064,5626,2343,4917,8670,5345,3081,3890,8313,1779,6552,7437,6116,6902,6385,1096,2779,7829,4123,3003,514,4189,9715,8138,4597,58,7691,8834,581,9343,7392,2569,4174,4692,8835,9484,5340,1889,8901,2706,7751,5132,4806,1586,4729,3846,9246,1658,7059,6467,3455,3463,5513,4903,284,1071,6682,3600,9750,1211,2544,4906,2165,5968,7359,9071,4038,2675,7599,2738,1533,1394,1187,5485,6844,9839,4352,1584,5462,4774,9890,7398,1153,2597,1869,9386,9400,6338,8149,9960,435,4973,4313,6207,5923,1159,7157,987,3494,6966,795,3475,5887,4817,6174,7899,6350,5312,3741,8352,3969,3178,2713,7606,8185,56,9585,3546,395,7171,8414,4532,2983,1819,1950,5193,9727,3716,9507,5975,5559,6165,8886,3516,7442,5093,2113,3499,3585,820,2951,4148,7453,4039,4686,5199,7455,6422,4583,3699,9824,5759,4148,6397,6784,3314,418,7105,6750,8724,9623,1133,2856,5954,9424,4089,216,1101,4577,8349,9698,4499,452,3248,8755,9306,1995,1168,6481,4943,5326,7537,3464,8394,8457,1571,5757,4534,4896,3216,7011,704,1325,5029,3974,3181,7027,8028,6652,8796,251,6169,5703,2014,791,7883,8389,581,8196,3178,9085,1999,2773,923,1222,4378,7565,6362,1033,607,5883,2957,3921,9102,701,6088,7758,1632,120,4658,8848,9964,5661,5998,3806,7918,4725,8217,967,6430,5748,4930,1314,3533,5388,4957,1481,4822,1682,5172,9611,6526,217,242,4333,4288,7756,2151,1893,2030,2719,113,7256,2446,3931,9689,4941,4719,3382,7188,6983,1777,2817,1314,1757,5806,1522,9626,9856,8906,3391,2516,1894,2022,566,5258,6324,6989,6914,7014,5950,9721,8548,3162,1924,5196,7653,6203,4405,1521,4313,5116,470,9517,7413,1052,9174,8234,9233,2402,4688,7531,9137,2815,2082,6708,6702,3332,2314,6816,5517,6109,5359,2914,9285,7821,9638,600,8466,1389,6126,1372,8314,2560,5627,1131,5520,3110,4346,7301,4687,3226,6247,7846,1651,886,9163,1959,5738,3789,792,7237,7062,8240,6624,7006,8572,5963,1769,6523,2506,2147,3246,5009,8047,9750,6545,4991,3675,7831,5557,2603,7776,1099,818,5663,7458,7314,9749,4520,3147,1343,9225,4454,4344,4796,5088,2651,3797,1924,6559,1638,5918,1624,6219,3655,9747,2478,6897,5144,9694,9377,3170,4895,4085,8557,5052,8164,3999,4570,7237,2231,8303,944,7939,5282,7265,3526,8025,717,6876,546,3825,4176,804,6611,6053,7305,6462,8990,9400,5112,5446,2116,2689,5433,8938,8394,7456,8456,9486,3568,3200,5860,7824,1745,6389,1605,2816,1201,4941,1932,998,481,2376,1268,4558,5700,6300,318,8984,4931,4083,3696,7750,3331,3588,3964,1916,356,4500,4353,1124,9440,8420,4351,391,8238,6654,3526,1003,2391,7551,2290,5876,9688,7356,40,6740,7920,7789,780,3046,3868,6018,4218,2341,4921,1989,4073,2012,3193,8007,7883,5445,4849,7046,1742,3858,9928,5119,2981,3933,1074,2084,561,5920,3105,3604,4192,93,454,1825,3832,1691,483,986,3292,1056,4855,619,3770,1424,379,616,1555,8319,6864,3905,5898,6076,9943,783,6029,5414,9414,1382,4031,9795,6107,7847,2402,2047,1363,4865,7659,4194,3757,9823,9823,9912,4278,9221,6265,7613,4509,6053,562,254,8241,424,9570,1703,9946,9518,3117,5671,8676,7958,6244,5911,4729,9504,2395,4262,9257,5023,1589,4752,4476,8487,8029,5047,6856,2763,6227,5757,6612,2272,2158,565,5195,7723,6310,8446,7040,8033,8653,8291,9766,6246,6112,8812,5770,985,5938,4105,4691,3279,4509,5329,7574,6206,1856,2949],
    "k" : 4362,
    "output" : 29725 },
    {"nums" : [5,5,4,5,4,1,1,1], "k" : 0, "output" : 20}
]

tmp = Solution()

for input in inputs:
    try: 
        output = tmp.maximumScore(nums = input["nums"], k = input["k"])
        if output != input["output"]:
            print(f'Test failed for:\nnums = {input["nums"]},\nk = {input["k"]}\nExpected = {input["output"]}, Returned = {output}')
    except TimeExceededException as e: print(f'Time Limit error for:\nnums = {input["nums"]},\nk = {input["k"]}')

Iteration 3.5

Now that we have a way to enforce a time limit, lets try and improve our algorithm

from typing import List
import multiprocessing
from functools import partial, wraps

class TimeExceededException(Exception):
    pass

def function_runner(*args, **kwargs):
    """Used as a wrapper function to handle
    returning results on the multiprocessing side"""

    send_end = kwargs.pop("__send_end")
    function = kwargs.pop("__function")
    try:
        result = function(*args, **kwargs)
    except Exception as e:
        send_end.send(e)
        return
    send_end.send(result)

def _run_with_timer(func, max_execution_time) -> int:
    @wraps(func)
    def wrapper(*args, **kwargs) -> int:
        recv_end, send_end = multiprocessing.Pipe(False)
        kwargs["__send_end"] = send_end
        kwargs["__function"] = func
        
        p = multiprocessing.Process(target=function_runner, args=args, kwargs=kwargs)
        p.start()
        p.join(max_execution_time)
        if p.is_alive():
            p.terminate()
            p.join()
            raise TimeExceededException("Exceeded Execution Time")
        
        result = recv_end.recv()

        if isinstance(result, Exception):
            raise ValueError

        return result

    return wrapper

# Defines the real wrapper and time limit
enforce_time_limit = partial(_run_with_timer, max_execution_time=2)

# pre: nums are all positive numbers
class Solution:
    # Enforces time-limit on func
    # If you are debugging simpler test case errors, remove this
    # @enforce_time_limit
    def maximumScore(self, nums: List[int], k: int) -> int:
        n : int = len(nums)
        curr_min : int = nums[k]
        result : int = curr_min

        # If we track when a new min happens (and it's value), we can just skip through and test vals quickly
        i_mins : List[(int, int)] = [(k, curr_min)]
        j_mins : List[(int, int)] = [(k, curr_min)]
        i_min : int = curr_min
        j_min : int = curr_min

        for idx, ele in enumerate(nums[k:]):
            if ele < j_min:
                j_min = ele
                j_mins.append((idx + k, ele))
        
        if j_mins[-1][0] != n - 1:
            j_mins.append((n - 1, j_min))
        
        for idx, ele in reversed(list(enumerate(nums[0:k + 1]))):
            if ele < i_min:
                i_min = ele
                i_mins.append((idx, ele))
        
        if i_mins[-1][0] != 0:
            i_mins.append((0, i_min))

        min1 : int = 0
        min2 : int = 0

        j_len : int = len(j_mins)
        i_len : int = len(i_mins)

        print(f'{i_mins}')
        print(f'{j_mins}')
        
        
        for i_key, (i_idx, i_ele) in reversed(list(enumerate(i_mins))):
            for j_key, (j_idx, j_ele) in reversed(list(enumerate(j_mins))):
                if i_key == i_len and j_key == j_len:
                    result = max(result, min(i_ele, j_ele) * (j_idx - i_idx + 1))
                if i_key != 0 and j_key != 0:
                    min1 = min(i_mins[i_key - 1][1], j_ele)
                    min2 = min(i_ele, j_mins[j_key - 1][1])
                    if min1 > min2:
                        if j_key != j_len - 1:
                            result = max(result, min1 * (j_mins[j_key + 1][0] - i_idx - 1))
                        else:
                            result = max(result, min1 * (j_idx - i_idx))
                    elif min2 > min1:
                        if i_key != i_len - 1:
                            result = max(result, min2 * (j_idx - i_mins[i_key + 1][0] - 1))
                        else:
                            result = max(result, min2 * (j_idx - i_idx))
                    else:
                        result = max(result, min1 * (j_idx - i_idx + 1))
                elif i_key == 0:
                    min1 = min(i_ele, j_mins[j_key - 1][1])
                    if i_len != 1:
                        result = max(result, min1 * (j_idx - i_mins[i_key + 1][0] - 1))
                    else:
                        result = max(result, min1 * (j_idx - i_idx))
                elif j_key == 0:
                    min1 = min(i_mins[i_key - 1][1], j_ele)
                    if j_len != 1:
                        result = max(result, min1 * (j_mins[j_key + 1][0] - i_idx - 1))
                    else:
                        result = max(result, min1 * (j_idx - i_idx))
                else:
                    # We are just looking at nums[k]...
                    pass

        return result


# Lets test the solution defined above
inputs = [
    {"nums" : [1,4,3,7,4,5], "k" : 3, "output" : 15},
    {"nums" : [8182,1273,9847,6230,52,1467,6062,726,4852,4507,2460,2041,500,1025,5524], "k" : 8, "output" : 9014},
    {"nums" : [6569,9667,3148,7698,1622,2194,793,9041,1670,1872], "k" : 5, "output" : 9732},
    {"nums" : [5868,4839,3608,4826,2829,2871,3224,3579,9860,6453,458,1617,2201,2906,8334,8410,3104,1385,5462,4287,2960,5417,2640,2287,6331,4494,773,1178,1426,5271,3221,7606,1091,9043,7008,7218,6004,4636,6253,5628,9533,2204,6903,6912,9736,793,8529,190,1302,4140,3212,2589,2735,109,9090,8351,332,8693,2461,6274,7233,2689,7255,3894,3855,1037,7385,3874],
     "k" : 38,
     "output" : 37088 },
    {"nums" : [3135,245,9277,2315,2945,7091,281,1242,6725,1544,2364,7756,7908,3272,3358,1851,3096,8914,1835,5922,1479,6028,2541,2284,4979,571,1700,6434,62,5378,9973,3997,2880,9307,277,8486,2374,6135,7181,5942,3870,1986,2382,9229,1429,3274,4933,8707,3151,6328,6374,3921,8578,260,7540,304,7441,6931,4160,7894,7486,572,6882,7664,887,4945,2517,7416,2258,5316,1078,9260,9866,9741,8001,1146,5318,2397,1808,4934,3480,3992,6079,1545,764,6841,6900,9452,9575,3076,9535,5559,9289,192,124,7681,6602,1979,3867,8333,3049,3739,1812,1795,7687,5635,4624,7012,913,9680,3012,1286,9490,4001,1238,7961,1492,2559,5897,3661,1665,2976,1448,6901,9761,5762,4156,3341,8422,2810,3574,3751,8130,8719,4145,7881,9438,2332,25,8968,676,4668,1108,8456,4335,4627,6961,8516,7091,9051,6092,9834,2732,3623,5324,2043,6833,5639,4004,1780,2946,3501,60,3395,9217,3304,7444,616,6929,6576,724,4138,6198,8560,638,9182,7067,4431,7138,8623,98,9259,3379,8451,6353,4599,1990,5979,5802,9079,8500,5795,194,6180,68,2157,8181,5961,9229,7840,2645,8624,1112,5115,5146,6301,1202,4813,8123,8005,799,9593,3700,3178,7775,4141,4908,7944,4617,6401,2743,9803,9092,8303,3705,9195,6594,9755,3687,6797,507,8679,2077,4597,2287,7658,5964,5487,9429,4648,836,7128,3295,1030,5782,8829,4700,5287,8155,3356,8283,5881,88,4196,5108,4551,6153,9088,4594,6358,5537,8300,4002,333,9792,6861,8098,7262,7663,2517,4023,726,4036,4711,8529,5610,8088,408,143,2227,2526,8651,7918,4747,7283,599,6717,3426,1149,9063,1243,815,3145,2751,4639,413,6607,6700,7102,1559,3911,8077,900,7035,1025,7278,6835,7413,8743,7598,3347,6002,3644,4171,9132,5199,6822,3531,6499,7653,1797,6960,3358,3508,1082,7217,1136,2561,8878,7968,6292,2419,4412,2790,3472,1299,9502,8683,3884,1757,2812,7986,2932,8056,6798,7043,3556,2001,2306,585,511,7680,7973,5934,1519,4203,3232,7724,9619,4934,9866,3046,5755,1637,4709,6935,5095,4746,430,4568,4865,2085,4528,2480,6035,8693,2862,9894,5058,1190,3860,9664,4704,514,5775,4851,6029,941,104,428,6859,9759,9206,7749,670,5661,9032,855,957,6636,8864,6320,2488,9585,194,5352,7224,4197,4509,8311,8188,9072,1998,8117,1097,4229,2878,3638,3649,3503,7591,8391,5579,9863,2074,1711,9725,6628,8432,2603,519,5654,3709,2207,6495,7253,5108,1868,6546,9414,8191,7970,9928,5387,4961,3428,6480,9465,7879,2844,741,6613,5743,3004,3486,4517,7113,6868,7717,1242,9030,6578,9138,2630,5704,7045,9650,5506,9544,5875,2364,2483,8957,6823,8705,4145,7628,2382,9381,4178,5277,6323,7292,6782,7147,7032,4691,4242,52,424,6754,9593,2274,735,1638,3514,5510,2537,2775,8064,2111,1232,9090,6265,9750,7263,247,7184,1273,761,4605,9283,4302,4169,2338,3786,6029,9243,6093,9875,7110,3074,8735,8104,3297,5565,7784,7797,8757,2056,1346,6658,4878,9409,9656,8444,2785,7681,379,7575,7819,366,5206,7734,951,9744,2063,7775,8048,7634,8553,9339,4710,1870,1839,6745,344,3099,453,9065,8066,6632,9913,4556,4666,5394,1849,7716,5321,9727,3652,2340,1264,4562,9690,7183,5823,8395,8196,5910,8080,8309,6599,1475,7063,5161,4698,5726,3971,7788,1092,8527,9565,8063,9759,5597,3286,5623,206,9149,3803,1066,2018,2439,9598,6791,6509,5173,845,1152,3494,4792,8811,4416,8019,2033,9350,6536,7345,808,1807,8276,2377,4588,8603,5331,9468,5663,9249,4997,2963,7717,9259,8085,8132,271,9713,1013,277,421,6122,420,4682,8017,3029,1415,7755,1421,9961,237,4411,4627,7895,1027,2316,3441,7867,9000,273,8471,8743,8002,5213,9896,4536,5576,6009,1752,6508,6786,9410,8248,3963,245,9068,4968,1513,6055,7128,3294,4431,1832,9327,1897,6065,4889,8725,979,7244,2937,4121,7568,5363,4788,2495,5785,8991,1327,6730,5931,3010,41,5468,6774,5925,7371,7943,6058,1948,4325,4202,9461,6293,124,8849,3288,5880,1904,5329,1672,1576,1862,5221,4430,8550,352,9149,6707,9426,3852,6388,132,4586,2243,697,9454,8983,4364,9189,3909,7312,7454,7796,9570,2452,2495,9527,6927,7032,5911,8172,1634,2997,6923,4962,9583,5118,1391,6836,9540,883,7076,8095,1622,4672,6592,7617,9987,8477,6981,5393,2471,1517,6620,706,2323,6763,3744,8217,8682,2301,4875,2473,9446,610,2169,2527,4583,1050,6901,3495,1269,1794,702,2355,3627,2645,9724,3422,7950,2206,3336,5242,4547,9773,51,9481,8834,2596,1535,9365,438,2162,3791,7470,5298,4055,6696,7885,6951,614,1519,4117,7778,1768,1485,4679,9496,8940,9237,6553,5725,5308,2928,9188,2838,1340,7994,659,8944,6633,2764,3430,5994,8771,2585,2792,4022,7036,1672,1885,9983,748,7559,3328,5970,2283,3495,7246,3296,3402,5162,6617,9752],
     "k" : 400,
     "output" : 29725 },
    # New test case takes for-ever to run... Basically does not complete
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759,2670,4980,733,72,1314,8551,8233,1078,250,1913,1821,8249,445,1934,5487,3468,420,8013,1745,4696,5337,5649,7013,908,2440,281,1778,4288,5052,1625,395,4091,9945,4058,3111,6575,3529,963,564,5206,6266,988,5176,9275,7309,590,3526,4692,4031,8010,489,6297,7147,1029,9506,713,9345,5736,6574,6637,7787,5447,8955,8641,8379,2703,4847,2954,9671,9871,3143,3730,1006,7175,19,3591,1846,9160,9532,1817,9061,9352,6982,3709,3599,6094,2668,8017,749,200,915,7801,5585,8015,477,4621,4205,8023,2302,470,3398,6189,7261,7770,3477,8887,8325,1647,9402,2798,2444,2200,7810,3184,7807,8703,3255,5909,617,9663,2070,3924,2920,7166,5227,3403,609,5992,8768,8238,2379,3307,3238,8013,5622,420,1965,5189,4249,7177,8930,781,8147,3080,7215,9366,7081,2856,4542,5767,2355,243,4058,7869,4078,1433,8539,2730,5353,3883,951,1356,2431,1973,6546,3292,4189,7795,7113,5853,7438,318,2198,6705,9555,8567,3012,2374,7655,6879,6657,1698,1259,6488,6969,9950,75,8496,6546,2992,1547,1584,8430,3178,9784,1666,2889,4593,8191,2118,1942,4111,1063,946,6890,6225,6099,3445,6960,7989,7572,8386,3754,5299,1031,5720,3978,7394,1511,9173,478,6411,3296,3798,7257,8289,8851,5250,9887,3255,64,9493,2485,7454,1653,1289,9296,1002,3019,3117,7382,1829,2612,772,9198,8345,6925,7418,4717,4391,3267,161,8682,3361,3332,1456,2382,809,2937,2581,9789,8456,3640,4429,4668,3138,3164,2874,1466,7990,7224,1038,1670,4267,919,6906,7582,2779,4442,8412,1432,94,7258,2400,743,1252,5907,1987,2567,7449,7138,9681,5524,139,721,8418,8860,7370,5995,7692,3460,6997,1314,6732,3493,5277,242,6652,7472,2003,1449,6762,2818,1487,9878,2166,4967,2879,6974,2422,9891,5365,8035,7377,8540,1297,2473,9851,5120,1592,2356,9064,5626,2343,4917,8670,5345,3081,3890,8313,1779,6552,7437,6116,6902,6385,1096,2779,7829,4123,3003,514,4189,9715,8138,4597,58,7691,8834,581,9343,7392,2569,4174,4692,8835,9484,5340,1889,8901,2706,7751,5132,4806,1586,4729,3846,9246,1658,7059,6467,3455,3463,5513,4903,284,1071,6682,3600,9750,1211,2544,4906,2165,5968,7359,9071,4038,2675,7599,2738,1533,1394,1187,5485,6844,9839,4352,1584,5462,4774,9890,7398,1153,2597,1869,9386,9400,6338,8149,9960,435,4973,4313,6207,5923,1159,7157,987,3494,6966,795,3475,5887,4817,6174,7899,6350,5312,3741,8352,3969,3178,2713,7606,8185,56,9585,3546,395,7171,8414,4532,2983,1819,1950,5193,9727,3716,9507,5975,5559,6165,8886,3516,7442,5093,2113,3499,3585,820,2951,4148,7453,4039,4686,5199,7455,6422,4583,3699,9824,5759,4148,6397,6784,3314,418,7105,6750,8724,9623,1133,2856,5954,9424,4089,216,1101,4577,8349,9698,4499,452,3248,8755,9306,1995,1168,6481,4943,5326,7537,3464,8394,8457,1571,5757,4534,4896,3216,7011,704,1325,5029,3974,3181,7027,8028,6652,8796,251,6169,5703,2014,791,7883,8389,581,8196,3178,9085,1999,2773,923,1222,4378,7565,6362,1033,607,5883,2957,3921,9102,701,6088,7758,1632,120,4658,8848,9964,5661,5998,3806,7918,4725,8217,967,6430,5748,4930,1314,3533,5388,4957,1481,4822,1682,5172,9611,6526,217,242,4333,4288,7756,2151,1893,2030,2719,113,7256,2446,3931,9689,4941,4719,3382,7188,6983,1777,2817,1314,1757,5806,1522,9626,9856,8906,3391,2516,1894,2022,566,5258,6324,6989,6914,7014,5950,9721,8548,3162,1924,5196,7653,6203,4405,1521,4313,5116,470,9517,7413,1052,9174,8234,9233,2402,4688,7531,9137,2815,2082,6708,6702,3332,2314,6816,5517,6109,5359,2914,9285,7821,9638,600,8466,1389,6126,1372,8314,2560,5627,1131,5520,3110,4346,7301,4687,3226,6247,7846,1651,886,9163,1959,5738,3789,792,7237,7062,8240,6624,7006,8572,5963,1769,6523,2506,2147,3246,5009,8047,9750,6545,4991,3675,7831,5557,2603,7776,1099,818,5663,7458,7314,9749,4520,3147,1343,9225,4454,4344,4796,5088,2651,3797,1924,6559,1638,5918,1624,6219,3655,9747,2478,6897,5144,9694,9377,3170,4895,4085,8557,5052,8164,3999,4570,7237,2231,8303,944,7939,5282,7265,3526,8025,717,6876,546,3825,4176,804,6611,6053,7305,6462,8990,9400,5112,5446,2116,2689,5433,8938,8394,7456,8456,9486,3568,3200,5860,7824,1745,6389,1605,2816,1201,4941,1932,998,481,2376,1268,4558,5700,6300,318,8984,4931,4083,3696,7750,3331,3588,3964,1916,356,4500,4353,1124,9440,8420,4351,391,8238,6654,3526,1003,2391,7551,2290,5876,9688,7356,40,6740,7920,7789,780,3046,3868,6018,4218,2341,4921,1989,4073,2012,3193,8007,7883,5445,4849,7046,1742,3858,9928,5119,2981,3933,1074,2084,561,5920,3105,3604,4192,93,454,1825,3832,1691,483,986,3292,1056,4855,619,3770,1424,379,616,1555,8319,6864,3905,5898,6076,9943,783,6029,5414,9414,1382,4031,9795,6107,7847,2402,2047,1363,4865,7659,4194,3757,9823,9823,9912,4278,9221,6265,7613,4509,6053,562,254,8241,424,9570,1703,9946,9518,3117,5671,8676,7958,6244,5911,4729,9504,2395,4262,9257,5023,1589,4752,4476,8487,8029,5047,6856,2763,6227,5757,6612,2272,2158,565,5195,7723,6310,8446,7040,8033,8653,8291,9766,6246,6112,8812,5770,985,5938,4105,4691,3279,4509,5329,7574,6206,1856,2949],
     "k" : 4362,
     "output" : 43821 },
    {"nums" : [5,5,4,5,4,1,1,1], "k" : 0, "output" : 20},
    {"nums" : [1301,5849,5714,435,8962,239,2942,8905,7984,981,9091,2069,2775,5874,1226,2347,8145,9079,5433,6498,343,6507,841,9491,4870,476,2687,1254,3517,3316,1910,6489,1787,6203,6232,7959,8301,7448,6103,9374,2071,3800,4737,3869,4090,4619,9828,766,3283,231,4338,7233,799,7350,1451,8605,1666,6833,4553,7334,2070,2518,230,5928,2209,4298,1139,4122,7585,8888,3121,2130,2993,3853,5131,8078,5368,8946,3724,9279,4481,298,5224,6415,4909,2682,8430,2064,6281,4901,2271,1860,415,1472,5705,7580,5543,3401,9397,489,6701,1114,6139,8706,3241,1308,2021,8154,1471,4119,488,8084,5665,8409,7233,5282,3067,3491,3632,6908,9559,6028,8498,9553,6831,6719,2365,5103,4520,4110,1936,1677,5730,9310,9431,2079,3516,3876,7384,4650,3250,7319,6812,1181,3594,4778,4630,3004,2429,1066,9527,9449,1897,3306,7134,2909,5390,703,4688,7166,6821,2743,239,4174,1652,8981,4796,6429,5594,785,8850,6284,8347,2432,1376,3075,2718,2097,556,5213,6821,4514,3407,1706,3865,7415,8069,9943,592,3621,6210,9302,3514,8313,3211,5458,6363,9878,4968,7258,6175,2221,7335,2462,5887,5074,8463,345,9110,5265,2781,8067,8880,1751,7798,6738,3966,3667,1992,5654,1935,1134,117,4273,3606,4436,8603,7905,2769,6900,2220,3302,5852,4861,6438,2764,4073,5406,8659,5834,1253,3731,7325,1849,2747,3896,8358,772,338,3658,7578,8017,3358,1776,4913,9817,6467,8681,8451,6363,5655,9981,5661,3761,8867,3320,4245,4616,969,9447,7619,2982,3211,1376,5733,8959,6327,3316,6725,8011,9467,6818,1156,7794,8221,1080,1191,2068,3046,5775,1118,7709,1910,289,7499,8814,7555,3877,4117,9825,1740,9947,3473,7632,8937,5553,3034,554,312,4545,4374,3495,5911,6369,7002,4071,5943,3172,8237,5628,2175,6177,9064,8292,1270,9214,5248,925,446,6229,7880,7817,115,9306,3316,3329,1339,5223,5066,9164,8159,7429,9496,8176,6847,9256,1779,4156,8389,2620,1926,2393,6185,6700,7000,9959,1238,490,9701,9640,1841,2701,1563,1915,9404,9272,9418,6297,5650,7845,5816,3149,1563,6038,912,6078,5854,3162,7876,5622,8591,7788,5521,1609,9122,2235,1882,5471,574,1627,5930,6728,4465,4309,644,4489,1915,1241,2125,5782,2866,3245,9445,8560,5039,7179,9345,6563,650,6501,6992,9528,1534,2531,7547,6402,336,7522,7509,2728,8992,844,932,6659,8961,8338,8683,8865,7471,6325,8538,5122,514,6270,4885,9206,2983,690,569,9841,3919,8301,8409,9214,2510,10000,7483], 
     "k" : 240, 
     "output" : 51405}
]
tmp = Solution()
for input in inputs:
    try: 
        # print(f'Trying {input["nums"]} with k = {input["k"]}')
        output = tmp.maximumScore(nums = input["nums"], k = input["k"])
        if output != input["output"]:
            print(f'Test failed for:\nnums = {input["nums"]},\nk = {input["k"]}\nExpected = {input["output"]}, Returned = {output}')
    except TimeExceededException as e: print(f'Time Limit error for:\nnums = {input["nums"]},\nk = {input["k"]}')

[(3, 7), (2, 3), (0, 1)]
[(3, 7), (4, 4), (5, 4)]
[(8, 4852), (7, 726), (4, 52), (0, 52)]
[(8, 4852), (9, 4507), (10, 2460), (11, 2041), (12, 500), (14, 500)]
[(5, 2194), (4, 1622), (0, 1622)]
[(5, 2194), (6, 793), (9, 793)]
[(38, 6253), (37, 4636), (32, 1091), (26, 773), (10, 458), (0, 458)]
[(38, 6253), (39, 5628), (41, 2204), (45, 793), (47, 190), (53, 109), (67, 109)]
[(400, 8864), (399, 6636), (398, 957), (397, 855), (394, 670), (389, 428), (388, 104), (252, 88), (194, 68), (162, 60), (138, 25), (0, 25)]
[(400, 8864), (401, 6320), (402, 2488), (404, 194), (488, 52), (701, 41), (863, 41)]
[(4362, 3694), (4358, 3688), (4357, 1456), (4354, 1044), (4332, 421), (4297, 332), (4292, 123), (4167, 81), (3912, 20), (3841, 10), (2923, 3), (0, 3)]
[(4362, 3694), (4364, 710), (4373, 240), (4436, 176), (4454, 31), (4515, 2), (9125, 2)]
[(0, 5)]
[(0, 5), (2, 4), (5, 1), (7, 1)]
[(240, 1253), (222, 117), (0, 117)]
[(240, 1253), (247, 772), (248, 338), (293, 289), (332, 115), (446, 115)]

Results:

• 65/72 test cases passed
• Frustrating that I still didn’t figure out why my alogirthm was doing so poorly…

This iteration seems to catch most issues, but runtime is creeping back in as an issue.

Iteration 4

Decided to look at a reference solution, as I was pulling my hair out, and wanted it to be over.

Turns out there are three things I was missing: - The greedy approach worked - Two other algorithms I would never have thought of

See editorial

class Solution:
    def maximumScore(self, nums: List[int], k: int) -> int:
        n : int = len(nums)
        left : int = k
        right : int = k
        ans : int = nums[k]
        curr_min : int = nums[k]
        
        while left > 0 or right < n - 1:
            if (0 if left == 0 else nums[left - 1]) < (0 if right >= n - 1 else nums[right + 1]):
                right += 1
                curr_min = min(curr_min, nums[right])
            else:
                left -= 1
                curr_min = min(curr_min, nums[left])

            ans = max(ans, curr_min * (right - left + 1))
        
        return ans

# Lets test the solution defined above
inputs = [
    {"nums" : [1,4,3,7,4,5], "k" : 3, "output" : 15},
    {"nums" : [8182,1273,9847,6230,52,1467,6062,726,4852,4507,2460,2041,500,1025,5524], "k" : 8, "output" : 9014},
    {"nums" : [6569,9667,3148,7698,1622,2194,793,9041,1670,1872], "k" : 5, "output" : 9732},
    {"nums" : [5868,4839,3608,4826,2829,2871,3224,3579,9860,6453,458,1617,2201,2906,8334,8410,3104,1385,5462,4287,2960,5417,2640,2287,6331,4494,773,1178,1426,5271,3221,7606,1091,9043,7008,7218,6004,4636,6253,5628,9533,2204,6903,6912,9736,793,8529,190,1302,4140,3212,2589,2735,109,9090,8351,332,8693,2461,6274,7233,2689,7255,3894,3855,1037,7385,3874],
     "k" : 38,
     "output" : 37088 },
    {"nums" : [3135,245,9277,2315,2945,7091,281,1242,6725,1544,2364,7756,7908,3272,3358,1851,3096,8914,1835,5922,1479,6028,2541,2284,4979,571,1700,6434,62,5378,9973,3997,2880,9307,277,8486,2374,6135,7181,5942,3870,1986,2382,9229,1429,3274,4933,8707,3151,6328,6374,3921,8578,260,7540,304,7441,6931,4160,7894,7486,572,6882,7664,887,4945,2517,7416,2258,5316,1078,9260,9866,9741,8001,1146,5318,2397,1808,4934,3480,3992,6079,1545,764,6841,6900,9452,9575,3076,9535,5559,9289,192,124,7681,6602,1979,3867,8333,3049,3739,1812,1795,7687,5635,4624,7012,913,9680,3012,1286,9490,4001,1238,7961,1492,2559,5897,3661,1665,2976,1448,6901,9761,5762,4156,3341,8422,2810,3574,3751,8130,8719,4145,7881,9438,2332,25,8968,676,4668,1108,8456,4335,4627,6961,8516,7091,9051,6092,9834,2732,3623,5324,2043,6833,5639,4004,1780,2946,3501,60,3395,9217,3304,7444,616,6929,6576,724,4138,6198,8560,638,9182,7067,4431,7138,8623,98,9259,3379,8451,6353,4599,1990,5979,5802,9079,8500,5795,194,6180,68,2157,8181,5961,9229,7840,2645,8624,1112,5115,5146,6301,1202,4813,8123,8005,799,9593,3700,3178,7775,4141,4908,7944,4617,6401,2743,9803,9092,8303,3705,9195,6594,9755,3687,6797,507,8679,2077,4597,2287,7658,5964,5487,9429,4648,836,7128,3295,1030,5782,8829,4700,5287,8155,3356,8283,5881,88,4196,5108,4551,6153,9088,4594,6358,5537,8300,4002,333,9792,6861,8098,7262,7663,2517,4023,726,4036,4711,8529,5610,8088,408,143,2227,2526,8651,7918,4747,7283,599,6717,3426,1149,9063,1243,815,3145,2751,4639,413,6607,6700,7102,1559,3911,8077,900,7035,1025,7278,6835,7413,8743,7598,3347,6002,3644,4171,9132,5199,6822,3531,6499,7653,1797,6960,3358,3508,1082,7217,1136,2561,8878,7968,6292,2419,4412,2790,3472,1299,9502,8683,3884,1757,2812,7986,2932,8056,6798,7043,3556,2001,2306,585,511,7680,7973,5934,1519,4203,3232,7724,9619,4934,9866,3046,5755,1637,4709,6935,5095,4746,430,4568,4865,2085,4528,2480,6035,8693,2862,9894,5058,1190,3860,9664,4704,514,5775,4851,6029,941,104,428,6859,9759,9206,7749,670,5661,9032,855,957,6636,8864,6320,2488,9585,194,5352,7224,4197,4509,8311,8188,9072,1998,8117,1097,4229,2878,3638,3649,3503,7591,8391,5579,9863,2074,1711,9725,6628,8432,2603,519,5654,3709,2207,6495,7253,5108,1868,6546,9414,8191,7970,9928,5387,4961,3428,6480,9465,7879,2844,741,6613,5743,3004,3486,4517,7113,6868,7717,1242,9030,6578,9138,2630,5704,7045,9650,5506,9544,5875,2364,2483,8957,6823,8705,4145,7628,2382,9381,4178,5277,6323,7292,6782,7147,7032,4691,4242,52,424,6754,9593,2274,735,1638,3514,5510,2537,2775,8064,2111,1232,9090,6265,9750,7263,247,7184,1273,761,4605,9283,4302,4169,2338,3786,6029,9243,6093,9875,7110,3074,8735,8104,3297,5565,7784,7797,8757,2056,1346,6658,4878,9409,9656,8444,2785,7681,379,7575,7819,366,5206,7734,951,9744,2063,7775,8048,7634,8553,9339,4710,1870,1839,6745,344,3099,453,9065,8066,6632,9913,4556,4666,5394,1849,7716,5321,9727,3652,2340,1264,4562,9690,7183,5823,8395,8196,5910,8080,8309,6599,1475,7063,5161,4698,5726,3971,7788,1092,8527,9565,8063,9759,5597,3286,5623,206,9149,3803,1066,2018,2439,9598,6791,6509,5173,845,1152,3494,4792,8811,4416,8019,2033,9350,6536,7345,808,1807,8276,2377,4588,8603,5331,9468,5663,9249,4997,2963,7717,9259,8085,8132,271,9713,1013,277,421,6122,420,4682,8017,3029,1415,7755,1421,9961,237,4411,4627,7895,1027,2316,3441,7867,9000,273,8471,8743,8002,5213,9896,4536,5576,6009,1752,6508,6786,9410,8248,3963,245,9068,4968,1513,6055,7128,3294,4431,1832,9327,1897,6065,4889,8725,979,7244,2937,4121,7568,5363,4788,2495,5785,8991,1327,6730,5931,3010,41,5468,6774,5925,7371,7943,6058,1948,4325,4202,9461,6293,124,8849,3288,5880,1904,5329,1672,1576,1862,5221,4430,8550,352,9149,6707,9426,3852,6388,132,4586,2243,697,9454,8983,4364,9189,3909,7312,7454,7796,9570,2452,2495,9527,6927,7032,5911,8172,1634,2997,6923,4962,9583,5118,1391,6836,9540,883,7076,8095,1622,4672,6592,7617,9987,8477,6981,5393,2471,1517,6620,706,2323,6763,3744,8217,8682,2301,4875,2473,9446,610,2169,2527,4583,1050,6901,3495,1269,1794,702,2355,3627,2645,9724,3422,7950,2206,3336,5242,4547,9773,51,9481,8834,2596,1535,9365,438,2162,3791,7470,5298,4055,6696,7885,6951,614,1519,4117,7778,1768,1485,4679,9496,8940,9237,6553,5725,5308,2928,9188,2838,1340,7994,659,8944,6633,2764,3430,5994,8771,2585,2792,4022,7036,1672,1885,9983,748,7559,3328,5970,2283,3495,7246,3296,3402,5162,6617,9752],
     "k" : 400,
     "output" : 29725 },
    # New test case takes for-ever to run... Basically does not complete
    {"nums" : 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759,2670,4980,733,72,1314,8551,8233,1078,250,1913,1821,8249,445,1934,5487,3468,420,8013,1745,4696,5337,5649,7013,908,2440,281,1778,4288,5052,1625,395,4091,9945,4058,3111,6575,3529,963,564,5206,6266,988,5176,9275,7309,590,3526,4692,4031,8010,489,6297,7147,1029,9506,713,9345,5736,6574,6637,7787,5447,8955,8641,8379,2703,4847,2954,9671,9871,3143,3730,1006,7175,19,3591,1846,9160,9532,1817,9061,9352,6982,3709,3599,6094,2668,8017,749,200,915,7801,5585,8015,477,4621,4205,8023,2302,470,3398,6189,7261,7770,3477,8887,8325,1647,9402,2798,2444,2200,7810,3184,7807,8703,3255,5909,617,9663,2070,3924,2920,7166,5227,3403,609,5992,8768,8238,2379,3307,3238,8013,5622,420,1965,5189,4249,7177,8930,781,8147,3080,7215,9366,7081,2856,4542,5767,2355,243,4058,7869,4078,1433,8539,2730,5353,3883,951,1356,2431,1973,6546,3292,4189,7795,7113,5853,7438,318,2198,6705,9555,8567,3012,2374,7655,6879,6657,1698,1259,6488,6969,9950,75,8496,6546,2992,1547,1584,8430,3178,9784,1666,2889,4593,8191,2118,1942,4111,1063,946,6890,6225,6099,3445,6960,7989,7572,8386,3754,5299,1031,5720,3978,7394,1511,9173,478,6411,3296,3798,7257,8289,8851,5250,9887,3255,64,9493,2485,7454,1653,1289,9296,1002,3019,3117,7382,1829,2612,772,9198,8345,6925,7418,4717,4391,3267,161,8682,3361,3332,1456,2382,809,2937,2581,9789,8456,3640,4429,4668,3138,3164,2874,1466,7990,7224,1038,1670,4267,919,6906,7582,2779,4442,8412,1432,94,7258,2400,743,1252,5907,1987,2567,7449,7138,9681,5524,139,721,8418,8860,7370,5995,7692,3460,6997,1314,6732,3493,5277,242,6652,7472,2003,1449,6762,2818,1487,9878,2166,4967,2879,6974,2422,9891,5365,8035,7377,8540,1297,2473,9851,5120,1592,2356,9064,5626,2343,4917,8670,5345,3081,3890,8313,1779,6552,7437,6116,6902,6385,1096,2779,7829,4123,3003,514,4189,9715,8138,4597,58,7691,8834,581,9343,7392,2569,4174,4692,8835,9484,5340,1889,8901,2706,7751,5132,4806,1586,4729,3846,9246,1658,7059,6467,3455,3463,5513,4903,284,1071,6682,3600,9750,1211,2544,4906,2165,5968,7359,9071,4038,2675,7599,2738,1533,1394,1187,5485,6844,9839,4352,1584,5462,4774,9890,7398,1153,2597,1869,9386,9400,6338,8149,9960,435,4973,4313,6207,5923,1159,7157,987,3494,6966,795,3475,5887,4817,6174,7899,6350,5312,3741,8352,3969,3178,2713,7606,8185,56,9585,3546,395,7171,8414,4532,2983,1819,1950,5193,9727,3716,9507,5975,5559,6165,8886,3516,7442,5093,2113,3499,3585,820,2951,4148,7453,4039,4686,5199,7455,6422,4583,3699,9824,5759,4148,6397,6784,3314,418,7105,6750,8724,9623,1133,2856,5954,9424,4089,216,1101,4577,8349,9698,4499,452,3248,8755,9306,1995,1168,6481,4943,5326,7537,3464,8394,8457,1571,5757,4534,4896,3216,7011,704,1325,5029,3974,3181,7027,8028,6652,8796,251,6169,5703,2014,791,7883,8389,581,8196,3178,9085,1999,2773,923,1222,4378,7565,6362,1033,607,5883,2957,3921,9102,701,6088,7758,1632,120,4658,8848,9964,5661,5998,3806,7918,4725,8217,967,6430,5748,4930,1314,3533,5388,4957,1481,4822,1682,5172,9611,6526,217,242,4333,4288,7756,2151,1893,2030,2719,113,7256,2446,3931,9689,4941,4719,3382,7188,6983,1777,2817,1314,1757,5806,1522,9626,9856,8906,3391,2516,1894,2022,566,5258,6324,6989,6914,7014,5950,9721,8548,3162,1924,5196,7653,6203,4405,1521,4313,5116,470,9517,7413,1052,9174,8234,9233,2402,4688,7531,9137,2815,2082,6708,6702,3332,2314,6816,5517,6109,5359,2914,9285,7821,9638,600,8466,1389,6126,1372,8314,2560,5627,1131,5520,3110,4346,7301,4687,3226,6247,7846,1651,886,9163,1959,5738,3789,792,7237,7062,8240,6624,7006,8572,5963,1769,6523,2506,2147,3246,5009,8047,9750,6545,4991,3675,7831,5557,2603,7776,1099,818,5663,7458,7314,9749,4520,3147,1343,9225,4454,4344,4796,5088,2651,3797,1924,6559,1638,5918,1624,6219,3655,9747,2478,6897,5144,9694,9377,3170,4895,4085,8557,5052,8164,3999,4570,7237,2231,8303,944,7939,5282,7265,3526,8025,717,6876,546,3825,4176,804,6611,6053,7305,6462,8990,9400,5112,5446,2116,2689,5433,8938,8394,7456,8456,9486,3568,3200,5860,7824,1745,6389,1605,2816,1201,4941,1932,998,481,2376,1268,4558,5700,6300,318,8984,4931,4083,3696,7750,3331,3588,3964,1916,356,4500,4353,1124,9440,8420,4351,391,8238,6654,3526,1003,2391,7551,2290,5876,9688,7356,40,6740,7920,7789,780,3046,3868,6018,4218,2341,4921,1989,4073,2012,3193,8007,7883,5445,4849,7046,1742,3858,9928,5119,2981,3933,1074,2084,561,5920,3105,3604,4192,93,454,1825,3832,1691,483,986,3292,1056,4855,619,3770,1424,379,616,1555,8319,6864,3905,5898,6076,9943,783,6029,5414,9414,1382,4031,9795,6107,7847,2402,2047,1363,4865,7659,4194,3757,9823,9823,9912,4278,9221,6265,7613,4509,6053,562,254,8241,424,9570,1703,9946,9518,3117,5671,8676,7958,6244,5911,4729,9504,2395,4262,9257,5023,1589,4752,4476,8487,8029,5047,6856,2763,6227,5757,6612,2272,2158,565,5195,7723,6310,8446,7040,8033,8653,8291,9766,6246,6112,8812,5770,985,5938,4105,4691,3279,4509,5329,7574,6206,1856,2949],
     "k" : 4362,
     "output" : 43821 },
    {"nums" : [5,5,4,5,4,1,1,1], "k" : 0, "output" : 20},
    {"nums" : [1301,5849,5714,435,8962,239,2942,8905,7984,981,9091,2069,2775,5874,1226,2347,8145,9079,5433,6498,343,6507,841,9491,4870,476,2687,1254,3517,3316,1910,6489,1787,6203,6232,7959,8301,7448,6103,9374,2071,3800,4737,3869,4090,4619,9828,766,3283,231,4338,7233,799,7350,1451,8605,1666,6833,4553,7334,2070,2518,230,5928,2209,4298,1139,4122,7585,8888,3121,2130,2993,3853,5131,8078,5368,8946,3724,9279,4481,298,5224,6415,4909,2682,8430,2064,6281,4901,2271,1860,415,1472,5705,7580,5543,3401,9397,489,6701,1114,6139,8706,3241,1308,2021,8154,1471,4119,488,8084,5665,8409,7233,5282,3067,3491,3632,6908,9559,6028,8498,9553,6831,6719,2365,5103,4520,4110,1936,1677,5730,9310,9431,2079,3516,3876,7384,4650,3250,7319,6812,1181,3594,4778,4630,3004,2429,1066,9527,9449,1897,3306,7134,2909,5390,703,4688,7166,6821,2743,239,4174,1652,8981,4796,6429,5594,785,8850,6284,8347,2432,1376,3075,2718,2097,556,5213,6821,4514,3407,1706,3865,7415,8069,9943,592,3621,6210,9302,3514,8313,3211,5458,6363,9878,4968,7258,6175,2221,7335,2462,5887,5074,8463,345,9110,5265,2781,8067,8880,1751,7798,6738,3966,3667,1992,5654,1935,1134,117,4273,3606,4436,8603,7905,2769,6900,2220,3302,5852,4861,6438,2764,4073,5406,8659,5834,1253,3731,7325,1849,2747,3896,8358,772,338,3658,7578,8017,3358,1776,4913,9817,6467,8681,8451,6363,5655,9981,5661,3761,8867,3320,4245,4616,969,9447,7619,2982,3211,1376,5733,8959,6327,3316,6725,8011,9467,6818,1156,7794,8221,1080,1191,2068,3046,5775,1118,7709,1910,289,7499,8814,7555,3877,4117,9825,1740,9947,3473,7632,8937,5553,3034,554,312,4545,4374,3495,5911,6369,7002,4071,5943,3172,8237,5628,2175,6177,9064,8292,1270,9214,5248,925,446,6229,7880,7817,115,9306,3316,3329,1339,5223,5066,9164,8159,7429,9496,8176,6847,9256,1779,4156,8389,2620,1926,2393,6185,6700,7000,9959,1238,490,9701,9640,1841,2701,1563,1915,9404,9272,9418,6297,5650,7845,5816,3149,1563,6038,912,6078,5854,3162,7876,5622,8591,7788,5521,1609,9122,2235,1882,5471,574,1627,5930,6728,4465,4309,644,4489,1915,1241,2125,5782,2866,3245,9445,8560,5039,7179,9345,6563,650,6501,6992,9528,1534,2531,7547,6402,336,7522,7509,2728,8992,844,932,6659,8961,8338,8683,8865,7471,6325,8538,5122,514,6270,4885,9206,2983,690,569,9841,3919,8301,8409,9214,2510,10000,7483], 
     "k" : 240, 
     "output" : 51405}
]
tmp = Solution()
for input in inputs:
    try: 
        # print(f'Trying {input["nums"]} with k = {input["k"]}')
        output = tmp.maximumScore(nums = input["nums"], k = input["k"])
        if output != input["output"]:
            print(f'Test failed for:\nnums = {input["nums"]},\nk = {input["k"]}\nExpected = {input["output"]}, Returned = {output}')
    except TimeExceededException as e: print(f'Time Limit error for:\nnums = {input["nums"]},\nk = {input["k"]}')