70 lines
2.3 KiB
C++
70 lines
2.3 KiB
C++
#include <cstdio>
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#include <cstdlib>
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#include <cmath>
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#include <cstring>
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#include <string>
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#include <queue>
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#include <stack>
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#include <iostream>
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#include <algorithm>
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using namespace std;
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#define RD(x) scanf("%d",&x)
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#define RD2(x,y) scanf("%d%d",&x,&y)
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#define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)
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#define clr0(x) memset(x,0,sizeof(x))
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typedef long long LL;
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const int maxn = 20;
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int n, m;
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double p[maxn][maxn],h[maxn][maxn],f[maxn][maxn][maxn],g[maxn][maxn][maxn];
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int main() {
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while (~RD2(m,n)) {
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for (int i = 1; i <= m; i++) {
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scanf("%lf", &p[i][1]);
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p[i][0] = 1.0;
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for (int j = 2; j <= n; j++) {
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p[i][j] = p[i][j - 1] * p[i][1];
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}
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}
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for (int i = 1; i <= m; i++) {
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for (int j = 1; j <= n; j++) {
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scanf("%lf", &h[i][j]);
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}
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}
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clr0(f),clr0(g);
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double ans = 0;
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for (int i = 2; i <= n; i++) {
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f[i][0][0] = 1;
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for (int j = 1; j <= m; j++) {
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for (int x = m; x >= 0; x--) {
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for (int y = x; y >= 0; y--) {
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f[i][x][y] *= (1.0 - p[j][i - 2]);
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if (x > 0) {
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f[i][x][y] += f[i][x - 1][y] * p[j][i - 2] * (1.0 - p[j][1]);
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if (y > 0) {
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f[i][x][y] += f[i][x - 1][y - 1] * p[j][i - 1];
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}
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}
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g[i][x][y] *= (1.0 - p[j][i - 2]);
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if (x > 0) {
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g[i][x][y] += g[i][x - 1][y] * p[j][i - 2] * (1.0 - p[j][1]);
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if (y > 0) {
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g[i][x][y] += (g[i][x - 1][y - 1] + f[i][x - 1][y - 1] * h[j][i]) * p[j][i - 1];
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}
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}
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}
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}
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}
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for (int x = 1; x <= m; x++) {
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for (int y = 1; y <= x; y++) {
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ans += g[i][x][y] * ((double)y / x + 1.0);
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}
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}
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}
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for (int i = 1; i <= m; i++) {
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ans += h[i][1];
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}
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printf("%.10f\n", ans);
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}
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return 0;
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}
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