Given an array consisting of n integers, find the contiguous subarray whose length is greater than or equal to k that has the maximum average value. And you need to output the maximum average value.
Example 1: Input: [1,12,-5,-6,50,3], k = 4 Output: 12.75 Explanation: when length is 5, maximum average value is 10.8, when length is 6, maximum average value is 9.16667. Thus return 12.75. Note: 1 <= k <= n <= 10,000. Elements of the given array will be in range [-10,000, 10,000]. The answer with the calculation error less than 10-5 will be accepted.
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9024,235,3007,2399,6724,5573,1501,4841,7225,251,7492,9845,9428,1067,6976,7058,6805,1057,5260,1021,59,212,4762,9925,824,9318,9082,6096,6563,8244,9633,1939,8479,2640,4338,1555,8214,2191,6397,1791,8795,241,1636,8223,7661,8613,1634,4466,9670,3246,1840,6081,3458,6602,6007,634,5921,1441,6731,8836,9686,2716,775,4517,5357,1466,2425,9923,9,8822,8066,5156,5415,9703,3380,3076,4668,5014,7543,690,4612,5735,6771,4423,2337,9130,5057,4610,572,8140,9798,258,857,6926,1127,6214,4744,3552,2489,4753,8726,555,9910,4142,6610,9642,3570,1278,1008,7465,1968,5620,3200,8740,43,1890,7870,1453,6500,8442,9593,2651,5052,450,9577,6180,3016,4321,9732,1857,5426,8459,2413,1688,8953,9023,1330,2523,6654,8690,9989,8622,663,9541,7362,706,1431,1585,8511,7932,6379,8105,6935,1432,4907,6512,7612,7924,7185,3696,9781,2611,8507,8546,652,7460,3922,8334,6336,576,7025,2677,9198,7688,2218,2913,4746,2,850,3258,7934,7229,7715,1221,8661,2622,7733,2625,6898,1270,6322,6680,233,1181,1578,885,8642,5500,9220,1330,2428,6245,359,7979,285,8929,7244,5031,8931,8094,4641,3217,5323,2356,4438,337,1331,8523,2962,8229,9793,5636,1261,27,6818,9192,912,1812,4692,132,9494,3473,2729,9853,1452,3014,8782,8696,4398,7714,3142,9039,931,8465,7748,5370,5154,5431,245,8117,3660,39,105,1274,66,3275,466,7330,5087,1510,3815,933,4983,6544,786,6435,5911,5921,1483,6661,9987,4625,5700,7270,9443,9800,8992,4597,5231,9238,9066,5244,9277,5524,6518,5695,8799,6984,3025,239,8494,6840,1172,9830,9737,8311,6265,2000,584,4101,8661,571,5078,713,7841,4521,514,6834,5471,2097,6072,4537,7341,5349,6413,3859,7396,5213,7195,421,5452,2042,3614,2976,1872,9703,7639,4489,1703,8223,8590,6716,8794,3669,7429,2988,8190,4295,9822,13,2745,2246,903,86,3947,7316,298,1343,2529,3845,1764,4333,5887,1730,3662,7759,1433,1301,2249,3136,9525,839,6204,8319,860,9986,1307,5403,4281,7481,5416,3378,9727,6319,3465,3674,9988,115,1369,8869,3960,3134,3203,9848,4864,6865,7607,2650,4518,6208,2138,4043,3400,8343,8715,4260,8329,6374,6015,8962,3856,1432,2341,9935,4103,5806,9962,4091,5921,1331,2961,6233,817,2516,6081,2034,5733,41,4684,251,6249,6822,647,6001,5165,9362,6614,3494,5736,2629,2457,5944,413,1150,5880,4517,6956,5842,4960,9229,3525,4273,5462,4343,3141,7896,6377,5226,7937,1061,1830,538,7883,2477,2892,9401,1839,9506,9247,3927,2135,8056,9872,8901,9206,2104,9770,2514,4298,4730,1743,7823,5356,3558,2166,8497,1454,8543,76,5743,5956,1906,2633,192,4383,5525,9593,2574,5031,8840,2853,3519,3249,2725,2420,2455,1181,2190,4970,5479,3272,3065,9655,8628,2975,1821,3478,781,6717,3554,6524,2673,5460,9158,9217,6195,4683,8810,8769,6067,4003,1622,9586,7252,700,8358,6059,8233,548,1029,65,3820,447,9720,8801,3422,1541,2279,4204,4610,2185,7080,7284,3997,2590,2853,192,3626,1664,5313,9693,2019,3287,5631,5623,339,3989,1682,4925,4537,9064,4990,4709,9511,4710,9862,9285,2603,8493,9841,7214,678,6922,850,1027,9512,3703,7571,3138,1719,2884,2831,3738,2524,4814,9361,9215,8803,7396,4140,9692,6460,9130,4402,2323,3840,4264,1608,2796,9110,1450,10,9788,4724,7212,7168,4236,915,4739,3727,8987,3976,2910,2725,6500,7725,8439,5715,6528,2187,6208,6221,8647,5338,6975,7322,5531,7591,5282,8327,6701,3084,4689,2842,7808,1901,10,8397,9168,4749,2124,8155,8725,5034,7233,1577,9111,2024,3645,1992,4211,9853,8213,9210,5191,1540,6532,7074,5483,8166,5401,8537,1251,6442,1379,9059,4695,7741,7456,216,8842,5932,4723,7568,7319,1956,5497,6430,332,9142,8422,4543,8995,2987,105,539,879,2989,7613,6363,1156,9367,4900,2407,5809,2631,7818,6857,372,5275,7073,9214,7559,1796,3134,4878,105,8632,1309,6789,4126,6083,7685,3122,9071,7790,13,9950,780,7626,2665,1936,6993,7565,695,9155,196,8513,6012,6920,140,9437,6135,7700,1233,5621,2578,7690,605,239,832,4732,2675,8517,4206,8098,6307,4219,4400,3439,1845,7066,5375,5191,4631,2422,4346,1180,936,6710,8100,1076,6147,587,8776,3732,6209,7707,7775,6814,4298,8607,7898,3325,7124,2104,1423,9783,6323,5824,3223,4521,2890,8598,9712,3873,1021,410,1405,8309,7120,9506,9385,3267,6445,4514,3351,2654,8573,1126,5821,9223,9733,3719,2549,6857,2176,324,6641,4851,6148,6216,9372,5390,4814,5436,5616,2187,2198,7021,6848,5670,2879,2586,8937,5677,7100,8641,8331,2025,9767,504,7600,9501,576,149,2710,2752,6826,5703,7603,9326,1919,3328,4717,3086,5116,6685,1625,7315,58,8474,2985,2938,1060,8275,8615,4512,6916,3298,2889,3035,155,489,2536,731,6991,1599,3483,3817,3654,7438,3143,1926,766,4212,5012,2235,7249,2989,9550,7308,7815,8887,6598,5227,7162,1565,6091,430,1215,8980,3466,1370,5822,2354,8453,2813,305,8288,2982,3960,5727,2477,5886,2845,3042,7250,5080,291,6591,982,3951,759,9870,549,5986,3384,8466,8430,167,9682,7410,3633,7404,3232,5987,5858,2397,6293,4146,5379,6605,6225,4209,8843,5423,7251,2445,6855,3894,9036,4190,7846,9795,412,8395,2134,3796,3214,564,3963,2896,7974,3948,6652,7559,6288,8862,6308,8933,9361,8040,5538,5586,2249,4381,7361,9500,6826,4217,3394,2214,8407,7592,2010,8819,5988,496,8967,5554,1060,9283,8450,5386,3231,1454,2945,9519,317,5606,4804,9678,3646,342,1616,5895,1075,8978,1747,4253,9547,1493,2820,4306,9086,1182,9477,1426,1678,8444,6980,2738,4079,1782,8124,7311,9588,7422,3182,9905,3028,4339,9583,6674,468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01,1552,4669,4438,9061,8362,9561,3696,6712,8840,7562,9117,5203,6966,8500,3009,1055,3210,7963,3846,1977,6628,1723,8658,3157,7496,664,5399,4111,451,2053,7764,8355,3074,2202,7417,1436,1764,1113,8148,6956,5027,7266,2160,1993,2118,5169,9400,5328,9485,9598,7305,2465,1321,2315,1975,5169,9332,7374,5632,9783,9427,3396,8138,2501,5599,5555,3937,3715,3020,8438,671,8047,2056,9183,6392,526,4353,2145,5854,190,1743,9512,2655,9417,8179,4630,4586,7511,8356,219,7294,7783,3615,1785,284,5566,7340,574,9281,6713,5364,9953,4760,3772,9136,7505,4298,9841,9650,152,6383,1393,6016,9039,810,4196,21,5397,1707,8378,1968,5354,6161,1935,7139,2798,7502,831,9724,6783,7544,5088,3088,2305,8860,2225,9810,3158,8418,5812,9662,4802,7205,5679,193,8016,9875,214,9765,7934,4944,1733,3288,7458,20,6779,6608,7522,7611,6332,4306,5155,1420,7394,3812,6632,5971,9974,6142,4390,5786,5804,5544,2992,7835,5737,7360,4062,2303,3477,8349,7248,1562,7989,1058,1582,4769,7666,9105,2380,3998,9763,3887,1770,7157,7700,4754,9481,4026,896,3871,9813,3052,5767,9157,7240,1504,2869,7654,159,6346,6003,3759,7908,3993,4817,5842,8762,8835,4947,7494,9185,4710,1381,7307,8220,5433,2061,7701,9460,9309,7924,5625,8714,3691,1134,2306,1547,4003,9960,1706,6701,5964,5466,961,9957,6635,6803,8719,5471,1751,6213,1008,2813,3946,8316,1033,9380,6729,8734,8840,2391,3010,817,1105,6701,1951,3411,8248,5954,3371,6307,2655,9335,8125,9968,5644,4760,6771,715,6583,8522,6928,7592,7688,7227,5908,8721,6607,8989,3808,1799,1380,6818,2616,8837,9872,4567,2248,4472,6873,1972,779,5880,7659,5256,5848,3304,17,2619,4019,2952,7494,7300,544,1534,879,2804,6607,7486,8146,415,9285,9526,3586,8253,8364,3458,9172,6964,4282,6045,8936,1414,8277,2948,6670,477,6252,3039,9448,6623,5992,3294,275,2888,4828,1154,2045,1436,4992,191,8203,629,9717,1789,8882,4433,1599,8054,1398,2234,451,6686,3648,5080,9634,318,5557,2238,9710,5006,5214,5702,4652,1841,4942,9481,2996,6987,7269,4340,3530,5472,4970,3248,3614,3852,4033,5213,8259,5431,7447,5062,8470,7447,143,8104,4118,2052,6695,3828,3410,1909,5882,8063,3750,7176,7544,3098,4164,4813,7439,7694,6637,8761,7294,251,2613,7680,1817,7224,3111,5616,2287,7933,3064,8782,6038,7182,834,2733,7362,4245,994,9596,8660,4744,6772,6204,4195,936,7369,1634,4983,4006,395,8629,610,9360,6309,2427,2937,5773,8043,1576,3706,7459,358,6096,993,7544,8829,8355,8141,9823,7951,6801,920,4724,9357,5115,2012,3078,3101,3347,3437,9848,1977,4047,5560,4638,2826,8497,411,7221,73,4118,4681,6783,214,5674,680,5396,382,5173,1571,8333,8327,8843,9409,7684,3958,7774,7115,3411,1121,552,3259,3098,951,8820,7737,3777,3669,4500,998,3743,4970,5679,6878,5185,7706,3910,6933,8088,9084,4856,2773,7411,3700,2183,1447,7658,9957,8562,7422,7430,9114,681,6881,65,5853,970,194,9523,5470,1193,9618,441,3224,2848,1978,930,6759,8911,5370,5843,3767,8144,9606,3819,6679,1053,7830,2988,9616,5252,418,5082,2285,7299,5148,8139,8269,5342,4014,3740,2887,9984,533,6112,2832,2511,3394,5943,7774,5117,8138,7893,3261,7744,1713,9940,5150,9543,2928,1118,4795,3346,6200,3432,6998,7700,1571,5267,9395,1937,9007,2282,1921,9540,4746,1106,8403,8141,3401,2529,3258,1540,423,2871,5636,8488,9163,786,8031,8443,8256,9178,1789,4457,2610,5139,2157,534,407,1552,8823,5766,187,745,1659,4933,8203,62,9426,1604,2592,9036,9496,9367,1907,1485,7855,1070,8623,2238,9513,6880,7768,7655,1337,378,2794,9846,7264,9553,1399,6088,5320,1586,3185,6979,2871,7740,7041,2298,5696,5985,1334,5193,5352,3242,6678,9559,664,1653,1797,6530,8533,9565,537,9870,6296,9683,9717,9912,5589,7468,6000,909,5406,9185,7888,8277,6925,1281,575,8974,3619,1910,4167,5323,1504,7197,4883,8520,5202,3032,1402,3736,8950,8291,9958,1598,4327,9675,1510,9916,3495,7511,825,8901,3048,5065,3531,6326,2698,4106,5300,6317,2368,5819,1641,224,9368,2876,5097,4570,2260,2851,8306,1210,1143,8265,2808,1822,4292,671,1738,4140,8182,8915,9393,7582,3980,2924,3908,3030,3383,5560,9348,2103,1379,7341,8680,7099,6569,129,1670,8829,2980,6328,6392,475,945,9200,2297] 9
/* binary search
any range avg should be between minA and maxA, we check whether there will be any range avg >= midA,
then narrow down the range continuely
n = j - i + 1
minA <= (A[i] + A[i+1] + A[j])/n <= maxA
=> whether the avg > some_value?
=> (A[i] + A[i+1] + A[j])/n > X
=> (A[i] + A[i+1] + A[j]) > n*X
=> (A[i] + A[i+1] + A[j]) - n*X > n*X - n*X
=> (A[i] - x) + (A[i+1] - x) + ... (A[j] - x) > 0
*/
// 120ms, 50%
class Solution {
public:
double findMaxAverage(vector<int>& nums, int k) {
if (nums.empty() || nums.size() < k) return 0;
double minv = *min_element(nums.begin(), nums.end());
double maxv = *max_element(nums.begin(), nums.end());
const double EPSILON = 0.000005;
while (minv <= maxv) {
double mid = minv + (maxv-minv)/2.0;
if (maxExists(nums, k, mid)) {
minv = mid + EPSILON;
} else {
maxv = mid - EPSILON;
}
}
return maxv;
}
bool maxExists(const vector<int>& nums, int k, double target) {
double sum = 0.0, pre_sum = 0.0;
for (int i = 0; i < k; i++) {
sum += nums[i] - target;
}
for (int i = k; i < nums.size(); i++) {
if (sum >= 0) return true;
sum += nums[i] - target;
pre_sum += nums[i-k] - target;
if (pre_sum < 0) {
sum -= pre_sum;
pre_sum = 0;
}
}
return sum >= 0;
}
};
// 816ms, 6%
// only need to check 2k range
class Solution {
public:
double findMaxAverage(vector<int>& nums, int k) {
vector<int> psums;
psums.reserve(nums.size());
partial_sum(nums.begin(), nums.end(), back_inserter(psums));
double res = INT_MIN;
for (int i = 0; i <= nums.size()-k; i++) {
//for (int j = i + k-1; j < nums.size(); j++) {
for (int m = k; m < 2*k; m++) {
int j = i + m - 1;
if (j >= nums.size()) break;
double sum = i > 0? psums[j] - psums[i-1] : psums[j];
res = max(res, sum/(j-i+1));
}
}
return res;
}
};
// TLE
class Solution {
public:
double findMaxAverage(vector<int>& nums, int k) {
vector<int> psums;
psums.reserve(nums.size());
partial_sum(nums.begin(), nums.end(), back_inserter(psums));
double res = INT_MIN;
for (int i = 0; i <= nums.size()-k; i++) {
for (int j = i + k-1; j < nums.size(); j++) {
double sum = i > 0? psums[j] - psums[i-1] : psums[j];
res = max(res, sum/(j-i+1));
}
}
return res;
}
};