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状态i,j,k为已经有i行，j列放满，放了k个棋子的概率，转移分四种情况（只增加行，只增加列，行列都增加，行列都不增加）讨论即可。
#include #include #include #include #include #include #include #include #include #include using namespace std; #define MP make_pair#define PB push_backtypedef long long LL;typedef unsigned long long ULL;typedef vector VI;typedef pair PII;typedef pair PDD;const int INF = INT_MAX / 3;const double eps = 1e-8;const LL LINF = 1e17;const double DINF = 1e60;const int maxn = 60;double f[maxn][maxn][maxn * maxn];bool vis[maxn][maxn][maxn * maxn];int n, m;double dfs(int i, int j, int k) { int pi = n - i, pj = m - j; if(i < 0 || j < 0 || k > pi * pj) return 0; if(i == 0 && j == 0) return k; if(i == n && j == m) return dfs(i - 1, j - 1, k + 1); if(vis[i][j][k]) return f[i][j][k]; double rest = n * m - k; double ret = dfs(i - 1, j - 1, k + 1) * i * j / rest + dfs(i, j, k + 1) * (pi * pj - k) / rest + dfs(i - 1, j, k + 1) * pj * i / rest + dfs(i, j - 1, k + 1) * pi * j / rest; vis[i][j][k] = true; return f[i][j][k] = ret;}int main() { int T; scanf("%d", &T); while(T--) { scanf("%d%d", &n, &m); memset(vis, 0, sizeof(vis)); printf("%.13f\n", dfs(n, m, 0)); } return 0;}
转载于:https://www.cnblogs.com/rolight/p/4031906.html