POJ3311(状态压缩DP+Floyd)

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不知道为什么min写成#define min(x,y) ((x)<(y)?(x):(y))用G++交就一直WA，用C++交就过了。

最后还是写成函数的形式好了。

因为顶点可以重复通过要先做Floyd处理一遍。

#include <iostream>#include <cstring>#include <cstdio>#define INF 0xffffffusing namespace std;int dis[11][11];int dp[1<<11][11];int n;int min(int x,int y){return x<y?x:y;}void floyd(){int i,j,k;for (k=0;k<=n;k++)for (i=0;i<=n;i++)for (j=0;j<=n;j++)if (dis[i][k]+dis[k][j]<dis[i][j])dis[i][j]=dis[i][k]+dis[k][j];}int main(){int i,j;while (1){scanf("%d",&n);if (!n) break;for (i=0;i<=n;i++)for (j=0;j<=n;j++)scanf("%d",&dis[i][j]);floyd();int state;for (state=1;state<1<<n;state++)      for (i=1;i<=n;i++)      {      dp[state][i]=INF;      if (state&(1<<(i-1)))      {      if ( state == 1<<(i-1))      dp[state][i]=dis[0][i];      else      {for (j=1;j<=n;j++)if (i!=j && (state&(1<<(j-1))))dp[state][i]=min(dp[state^(1<<(i-1))][j]+dis[j][i],dp[state][i]);      }      }      }int ans=INF;for (i=1;i<=n;i++)ans=min(dp[state-1][i]+dis[i][0],ans);printf("%d\n",ans);}}

为什么不用维护dp[state][0]呢？

因为dp[state][0]表示从0开始经过state中的那些点又回到0，dp[state][i](1<=i<=n)的更新不会用到dp[state^(1<<(i-1))][0]，如果可以通过0更新，则说明可以通过路径x->0->i更新（x是state^(1<<(i-1))中的某个点），而实际上我们已经用floyd处理过了，dis[x][i]实际上已经被优化为x->0->i的更短的路径了，所以dp[state][i]的更新利用dp[state^(1<<(i-1))][x]来更新即可，不必是dp[state^(1<<(i-1))][0]。

若维护dp[state][0]可以这么写，也是没问题的。

#include <iostream>#include <cstring>#include <cstdio>#define INF 0xffffffusing namespace std;int dis[11][11];int dp[1 << 11][11];int n;int min(int x, int y){return x < y ? x : y;}void floyd(){int i, j, k;for (k = 0; k <= n; k++)for (i = 0; i <= n; i++)for (j = 0; j <= n; j++)if (dis[i][k] + dis[k][j] < dis[i][j])dis[i][j] = dis[i][k] + dis[k][j];}int main(){int i, j;while (1){scanf("%d", &n);if (!n)break;for (i = 0; i <= n; i++)for (j = 0; j <= n; j++)scanf("%d", &dis[i][j]);floyd();int state;for (state = 1; state < 1 << n; state++){for (i = 1; i <= n; i++){dp[state][i] = INF;if (state & (1 << (i - 1))){if (state == 1 << (i - 1))dp[state][i] = dis[0][i];else{dp[state][i] = min(dp[state ^ (1 << (i - 1))][0] + dis[0][i], dp[state][i]);for (j = 1; j <= n; j++)if (i != j && (state & (1 << (j - 1))))dp[state][i] = min(dp[state ^ (1 << (i - 1))][j] + dis[j][i], dp[state][i]);}}}dp[state][0] = INF;for (i = 1; i <= n; i++)if (state & (1 << (i - 1)))dp[state][0] = min(dp[state][0], dp[state][i] + dis[i][0]);}printf("%d\n", dp[state - 1][0]);}}

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