http://acm.hdu.edu.cn/showproblem.php?pid=1220
一开始的做法是，先暴力算出一个面，就是n * n的面，能有多少对。记作face
然后从上开始算下来，最上一层，face个，然后第二层，有n * n * (up - 1)个。
递推下去，up是在第i层上面有多少个。
#include <cstdio> #include <cstdlib> #include <cstring> #include <cmath> #include <algorithm> #define IOS ios::sync_with_stdio(false) using namespace std; #define inf (0x3f3f3f3f) typedef long long int LL; #define MY "H:/CodeBlocks/project/CompareTwoFile/DataMy.txt", "w", stdout #define ANS "H:/CodeBlocks/project/CompareTwoFile/DataAns.txt", "w", stdout #include <iostream> #include <sstream> #include <vector> #include <set> #include <map> #include <queue> #include <string> const int maxn = 1e3 + 20; int e[maxn][maxn]; int a[maxn][maxn]; int tonext[5][2] = {{0, 0}, {0, 1}, {1, 0}, {0, -1}, {-1, 0}}; int n; void work() { int to = 0; memset(e, 0, sizeof e); memset(a, 0, sizeof a); for (int i = 1; i <= n; ++i) { for (int j = 1; j <= n; ++j) { a[i][j] = ++to; } } // for (int i = 1; i <= n; ++i) { // for (int j = 1; j <= n; ++j) { // cout << a[i][j] << " "; // } // cout << endl; // } int ans = 0; for (int i = 1; i <= n; ++i) { for (int j = 1; j <= n; ++j) { int t = ans; for (int k = 1; k <= n; ++k) { for (int h = 1; h <= n; ++h) { bool flag = true; if (e[a[i][j]][a[k][h]]) continue; for (int oo = 0; oo < 5; ++oo) { int tx = i + tonext[oo][0]; int ty = j + tonext[oo][1]; if (k == tx && h == ty) { int dis = abs(a[tx][ty] - a[i][j]); if (dis == 1 || dis == n || dis == 0) { flag = false; break; } } } if (!flag) continue; e[a[i][j]][a[k][h]] = e[a[k][h]][a[i][j]] = 1; ans++; } } //// cout << ans - t << " "; } // cout << endl; } // cout << ans << endl; int per = n * n * n; int toans = ans; int up = n * n; for (int i = 2; i <= n; ++i) { toans += ans; toans += (n * n) * (up - 1); up += n * n; } cout << toans << endl; } int main() { #ifdef local freopen("data.txt","r",stdin); #endif IOS; while (cin >> n) work(); return 0; }
逆向思维。
一共有C(n * n * n, 2)对。然后减去4个面的。
一行有n - 1对4个面的，有n行，同样，有n列。然后还有n竖，所以是三种。
每一种，在一个面上，有(n - 1) * n，一个体上，有(n - 1) * n * n，所以减去3 * all
#include <cstdio> #include <cstdlib> #include <cstring> #include <cmath> #include <algorithm> #define IOS ios::sync_with_stdio(false) using namespace std; #define inf (0x3f3f3f3f) typedef long long int LL; #define MY "H:/CodeBlocks/project/CompareTwoFile/DataMy.txt", "w", stdout #define ANS "H:/CodeBlocks/project/CompareTwoFile/DataAns.txt", "w", stdout #include <iostream> #include <sstream> #include <vector> #include <set> #include <map> #include <queue> #include <string> int C(int n, int m) { int ans = 1; for (int i = 1; i <= m; ++i) { ans = ans * (n - i + 1) / i; } return ans; } int n; void work() { cout << C(n * n * n, 2) - (n - 1) * n * n * 3 << endl; } int main() { #ifdef local freopen("data.txt","r",stdin); #endif IOS; while (cin >> n) work(); return 0; }