題目

a ^ 3 = b ^ 3 + c ^ 3 + d ^ 3
求有多少a, b, c, d滿足a ^ 3 = b ^ 3 + c ^ 3 + d ^ 3，其中a, b, c, d滿足1 <= a, b, c, d <= n

輸入格式:

一個正整數n，含義見題目描述

n <= 1000

輸出格式:

一個正整數表示答案

限制:

空間限制：128MByte 時間限制：1秒

樣例:

輸入：10 輸出：12

O(n^4):

#include<bits/stdc++.h> using namespace std; int main() {int ans = 0;int a,b,c,d;for(a=6;a<201;a++){for(b=2;b<a;b++){for(c=b;c<a;c++){for(d=c;d<a;d++){if(a*a*a==b*b*b+c*c*c+d*d*d){ans++;}}}}}cout << ans;return 0; }

O(n ^ 2logn):?

#include <iostream> #include <map> using namespace std; const int N = 1e3 + 100; int pow3[N]; map <int,int> vis; int main() {int n;cin >> n;int ans = 0;for(int i = 1; i <= n; i++){pow3[i] = i * i * i;}for(int a = 1; a <= n; a++){for(int b = 1; b <= a; b++){vis[pow3[a] - pow3[b]]++;}}for(int c = 1; c <= n; c++){for(int d = 1; d <= n; d++){if(vis[pow3[c] + pow3[d]]){ans += vis[pow3[c] + pow3[d]];}}}cout << ans << endl;return 0; }

O(n ^ 2):

#include <iostream> #include <map> #include <algorithm> using namespace std; const int N = 1e6 + 100; int pow3[1100]; int val1[N], cnt1; int val2[N], cnt2; int main() {int n;cin >> n;int ans = 0;for(int w = 1; w <= n; w++){pow3[w] = w * w * w;}for(int a = 1; a <= n; a++){for(int b = 1; b <= a; b++){val1[cnt1 ++] = pow3[a] - pow3[b];}}for(int c = 1; c <= n; c++){for(int d = 1; d <= n; d++){val2[cnt2 ++] = pow3[c] + pow3[d];}}sort(val1, val1 + cnt1);sort(val2 , val2 + cnt2);val1[cnt1] = -1;val2[cnt2] = -1;int i = 0, j = 0;while(i < cnt1 && j < cnt2){if(val1[i] == val2[j]){int a = 1, b = 1;while(val1[i + 1] == val1[i]){i++;a++;}while(val2[j + 1] == val2[j]){j++;b++;}i++, j++;ans += a * b;}else if (val1[i] < val2[j]){i++;}else{j++;}}cout << ans << endl;return 0; }

最暴力：

#include <iostream> using namespace std; long long n[10010] = {0,0,0,0,0,6,6,6,12,12,12,18,18,18,18,18,18,30,36,42,42,42,42,48,54,54,60,66,72,78,78,78,78,78,78,90,90,96,96,102,114,120,120,126,132,144,144,150,150,156,156,156,162,180,180,186,192,204,204,216,216,216,222,222,222,228,234,234,240,246,252,270,270,270,282,294,294,300,300,306,318,336,336,354,360,360,384,402,408,432,432,444,450,450,456,468,474,474,480,492,492,498,504,504,510,516,516,546,546,552,558,564,570,582,588,606,612,612,612,630,636,642,660,660,666,684,690,690,696,696,696,714,720,732,738,738,744,768,774,792,798,810,810,834,846,846,852,852,852,876,882,894,900,900,900,912,912,912,924,936,936,966,966,990,990,990,996,1014,1014,1026,1050,1056,1056,1098,1104,1128,1134,1146,1152,1182,1188,1188,1188,1200,1212,1230,1236,1242,1254,1266,1272,1290,1296,1302,1302,1308,1314,1338,1344,1356,1368,1380,1392,1398,1416,1434,1446,1446,1464,1488,1488,1494,1506,1518,1518,1554,1560,1572,1596,1614,1614,1626,1626,1632,1656,1662,1662,1686,1698,1716,1734,1758,1758,1776,1794,1794,1794,1800,1812,1830,1836,1842,1854,1866,1866,1902,1908,1908,1914,1920,1926,1956,1956,1968,1974,1992,1992,2010,2010,2022,2052,2058,2058,2088,2094,2106,2112,2124,2136,2172,2172,2172,2172,2178,2190,2214,2214,2220,2244,2262,2268,2286,2286,2304,2310,2310,2328,2364,2370,2394,2400,2418,2430,2442,2448,2448,2460,2466,2466,2496,2496,2520,2532,2544,2550,2562,2568,2580,2604,2604,2610,2622,2622,2622,2634,2634,2646,2664,2670,2682,2694,2706,2718,2778,2784,2790,2808,2832,2832,2850,2856,2862,2874,2886,2898,2922,2922,2922,2928,2952,2952,2982,2982,2994,3006,3012,3012,3060,3066,3084,3096,3132,3132,3156,3168,3198,3198,3204,3204,3246,3258,3270,3282,3294,3300,3312,3312,3336,3372,3384,3390,3420,3426,3438,3450,3456,3462,3504,3510,3534,3546,3558,3564,3600,3606,3618,3630,3648,3654,3660,3672,3684,3690,3708,3714,3768,3768,3774,3780,3804,3804,3834,3834,3846,3858,3888,3894,3924,3924,3954,3966,3990,3990,4020,4026,4026,4044,4062,4074,4116,4116,4122,4140,4146,4170,4206,4206,4224,4224,4230,4242,4296,4296,4302,4338,4356,4368,4404,4404,4440,4452,4452,4452,4464,4476,4482,4494,4500,4500,4548,4560,4566,4596,4614,4614,4638,4638,4656,4680,4710,4716,4740,4740,4770,4788,4788,4794,4818,4824,4842,4854,4866,4866,4872,4896,4914,4938,4962,4980,5028,5028,5040,5046,5064,5076,5106,5112,5130,5142,5148,5154,5232,5250,5262,5274,5280,5286,5304,5310,5334,5340,5346,5358,5394,5412,5430,5436,5460,5466,5484,5484,5502,5538,5544,5562,5598,5622,5622,5634,5646,5652,5700,5706,5712,5730,5742,5748,5790,5796,5802,5832,5856,5868,5886,5892,5916,5928,5946,5946,6006,6018,6018,6024,6024,6030,6036,6054,6060,6066,6084,6096,6132,6132,6138,6156,6162,6168,6210,6210,6228,6252,6264,6264,6294,6318,6318,6342,6360,6366,6390,6390,6396,6420,6444,6468,6516,6552,6558,6570,6606,6606,6618,6630,6648,6654,6678,6690,6720,6726,6738,6750,6750,6750,6786,6792,6804,6822,6834,6840,6882,6888,6900,6918,6948,6960,7020,7020,7032,7062,7086,7086,7104,7116,7134,7158,7182,7188,7236,7242,7254,7284,7290,7296,7314,7332,7332,7350,7350,7356,7404,7410,7416,7440,7458,7470,7494,7494,7512,7536,7560,7560,7602,7608,7638,7644,7656,7668,7746,7752,7758,7770,7782,7800,7842,7848,7878,7908,7908,7908,7956,7962,7980,7986,8004,8022,8040,8064,8100,8106,8148,8154,8190,8196,8208,8238,8244,8250,8274,8286,8316,8316,8322,8322,8370,8394,8400,8412,8424,8430,8466,8478,8484,8514,8514,8520,8586,8598,8616,8622,8658,8664,8694,8712,8754,8784,8784,8790,8820,8826,8850,8862,8898,8910,8922,8922,8946,8970,8982,8982,9036,9054,9078,9090,9114,9132,9150,9150,9162,9192,9198,9210,9240,9252,9252,9270,9294,9300,9360,9366,9384,9390,9402,9402,9444,9456,9468,9492,9510,9510,9540,9546,9552,9558,9570,9588,9654,9660,9678,9684,9714,9720,9750,9750,9768,9792,9804,9804,9858,9864,9882,9888,9900,9906,9936,9942,9960,9966,9990,10014,10044,10050,10080,10116,10134,10134,10164,10170,10188,10188,10194,10200,10278,10284,10296,10320,10332,10338,10362,10368,10404,10434,10452,10458,10494,10506,10506,10524,10536,10536,10590,10590,10632,10650,10656,10674,10704,10716,10716,10728,10782,10788,10818,10818,10854,10884,10884,10890,10938,10944,10968,10986,10986,10992,11028,11046,11076,11100,11136,11136,11190,11196,11202,11220,11226,11226,11286,11292,11304,11310,11340,11346,11406,11412,11424,11454,11472,11472,11478,11484,11502,11526,11550,11562,11634,11640,11646,11664,11676,11682,11760,11766,11790,11802,11826,11832,11886,11904,11904,11928,11970,11970,12000,12000,12000,12030,12036,12042,12054,12060,12090,12120,12132,12150,12186,12198,12216,12228,12240,12258,12318,12324,12348,12360,12372,12378,12444,12456,12480,12510,12522,12534,12558,12558,12558,12582,12618,12618,12660,12672,12702,12720,12732,12738,12786,12804,12816,12858,12888,12894,12930,12942,12948,12978,12984,13002,13032,13050,13062,13068,13104,13104,13128,13146,13170,13188,13194,13194,13206,13206,13242,13260,13290,13290,13326,13332,13356,13392,13410,13422,13476,13482,13482,13500,13530,13536,13572,13578,13626,13656,13680,13686,13752,13764,13770,13794,13818,13836,13878,13902,13920,13944,13950,13962,14052,14070,14100,14112,14130,14130,14196,14202,14220,14232,14244,14256,14286,14286,14292,14304,14346 }; int main() {int m;cin >> m;cout << n[m - 1];return 0; }

總結

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