hdu 4118 Time travel

概率dp求期望，高斯消元解多元式

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#include <CSTDIO>#include <QUEUE>using namespace std;// hdu 4118// http://www.cnblogs.com/kuangbin/archive/2012/10/02/2710606.html/*高斯消元 求期望e[x] = Σ(e[(x+i)%n]+i)*p[i]e[x] - p1*e[x+1] - p2*e[x+2] - p3*e[x+3] - ... - pm*e[x+m] = p1*1 + p2*2 + p3*3 + ... + pm*m*/const int MAXN = 250;const double _inf = 1e-9;double a[MAXN][MAXN], x[MAXN]; // 方程左边的矩阵和等式右边的值， x存放最后结果int equ, val;// 方程数 未知数个数inline double mabs(double _X){return _X<0?-_X:_X;}int gauss(){int i,j,k,col,max_r;    for(k=0,col=0;k<equ&&col<val;k++,col++)    {        max_r=k;        for(i=k+1;i<equ;i++)if(mabs(a[i][col])>mabs(a[max_r][col]))max_r=i;if(mabs(a[max_r][col])<_inf) return 0;if(k!=max_r){for(j=col;j<val;j++)swap(a[k][j],a[max_r][j]);swap(x[k],x[max_r]);}x[k]/=a[k][col];for(j=col+1;j<val;j++)a[k][j]/=a[k][col];a[k][col]=1;for(i=0;i<equ;i++)if(i!=k){x[i]-=x[k]*a[i][k];for(j=col+1;j<val;j++)a[i][j]-=a[k][j]*a[i][col];a[i][col]=0;}    }    return 1;}int n, m, _n;double p[MAXN];int num[MAXN], cnt;void bfs(int s){memset(num, -1, sizeof num);queue<int> q;cnt = 0;num[s] = cnt++;q.push(s);int t, i;while (!q.empty()){t = q.front(); q.pop();for ( i = 1; i<= m; ++i){if ( mabs(p[i] < _inf)) continue;int tmp = (t+i)%n;if ( num[tmp] == -1){num[tmp] = cnt++;q.push(tmp);}}}}int main()   {#ifndef ONLINE_JUDGE    freopen("in.txt", "r", stdin);#endifint t, i, j, k;;int s, e, d;scanf("%d", &t);while (t--){scanf("%d%d%d%d%d", &_n, &m, &e, &s, &d);for (i = 1; i<= m; i++)scanf("%lf", p+i), p[i]/=100.0;if ( e == s) {printf("0.00\n"); continue;}n = _n * 2 - 2;//  翻转 0 1 2 3 2 1 0if (d == 1)s = n - s; // 始终保持正向向右bfs(s);if (num[e] == -1 && num[n-e] == -1)// 排除不可能达到的点{printf("Impossible !\n" );continue;}equ = val = cnt;memset(a, 0, sizeof a);memset(x, 0, sizeof x);for (i = 0; i< n; ++i){if (num[i] != -1){if (i == e || i == n-e){a[num[i]][num[i]] = 1;x[num[i]] = 0;continue;}a[num[i]][num[i]] = 1;for (j = 1; j<= m; ++j){k = (i+j)%n;if (num[k] != -1){a[num[i]][num[k]] -= p[j];x[num[i]] += j*p[j];}}}}if (gauss()) printf("%.2lf\n", x[num[s]]);else printf("Impossible !\n" );}return 0;}