HDU 5245 Joyful (期望)
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题意:进行K次染色,每次染色会随机选取一个以(x1,y1),(x2,y2)为一组对角的子矩阵进行染色,求K次染色后染色面积的期望值(四舍五入)。
析:我们可以先求出每个格子的期望,然后再加起来即可。我们可以把格子进行划分,然后再求概率。
代码如下:
#pragma comment(linker, "/STACK:1024000000,1024000000") #include <cstdio> #include <string> #include <cstdlib> #include <cmath> #include <iostream> #include <cstring> #include <set> #include <queue> #include <algorithm> #include <vector> #include <map> #include <cctype> #include <cmath> #include <stack> #include <sstream> #define debug() puts("++++"); #define gcd(a, b) __gcd(a, b) #define lson l,m,rt<<1 #define rson m+1,r,rt<<1|1 #define freopenr freopen("in.txt", "r", stdin) #define freopenw freopen("out.txt", "w", stdout) using namespace std; typedef long long LL; typedef unsigned long long ULL; typedef pair<int, int> P; const int INF = 0x3f3f3f3f; const LL LNF = 1e16; const double inf = 0x3f3f3f3f3f3f; const double PI = acos(-1.0); const double eps = 1e-8; const int maxn = 1e5 + 10; const int mod = 1e9 + 7; const int dr[] = {-1, 0, 1, 0}; const int dc[] = {0, 1, 0, -1}; const char *de[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"}; int n, m; const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; inline bool is_in(int r, int c){ return r >= 0 && r < n && c >= 0 && c < m; } int main(){ int T; cin >> T; for(int kase = 1; kase <= T; ++kase){ int k; cin >> n >> m >> k; double ans = 0.0; for(int i = 1; i <= n; ++i) for(int j = 1; j <= m; ++j){ double p = m * n; p += 1.0 * (i-1) * (j-1) * (n-i+1) * (m-j+1); p += 1.0 * (i-1) * (m-j) * (n-i+1) * j; p += 1.0 * (j-1) * (n-i) * (m-j+1) * i; p += 1.0 * (n-i) * (m-j) * i * j; p += 1.0 * (i-1) * m * (n-i+1); p += 1.0 * (m-j) * n * j; p += 1.0 * (n-i) * m * i; p += 1.0 * (j-1) * n * (m-j+1); p = p / (1.0*n*n*m*m); ans += 1.0 - (pow(1.0-p, k)); } printf("Case #%d: %.f\n", kase, ans); } return 0; }
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