POJ_2353_Ministry

//经典的DP，双向DP，状态转移方程为1。num[i][j]=min{num[i][j-1],num[i+1][j]}+fee[i][j];//2。num[i][j]={num[i][j],num[i][j+1]+fee[i][j]};以上为先比较左侧与下侧，然后再和右侧//比较来确定最终的num[i][j]的值。同时用di[i][j]确定回溯的方向。 #include<stdio.h>#include<climits>#include<string.h>int fee[105][505],num[105][505],di[105][505];int m,n;//回溯，输出结果 int back(int x,int y){int t1=x,t2=y;if(x==m){printf("%d/n",y);return 0;}else{if(di[x][y]==-1)t2=y-1;else if(di[x][y]==0)t1=x+1;elset2=y+1;back(t1,t2);printf("%d/n",y);}}int main(){//freopen("mini13.in","r",stdin);//freopen("out13.txt","w",stdout);//双向DP while(scanf("%d%d",&m,&n)==2){int i,j,k;for(i=m;i>0;i--){for(j=1;j<=n;j++)scanf("%d",&fee[i][j]);}for(i=1;i<=n;i++)num[m][i]=fee[m][i];int t1,t2,t3,min,t;for(i=m-1;i>=1;i--){num[i][1]=num[i+1][1]+fee[i][1];di[i][1]=0;for(j=2;j<=n;j++){t1=num[i][j-1]+fee[i][j];t2=num[i+1][j]+fee[i][j];if(t1<t2){num[i][j]=t1;di[i][j]=-1;}else{num[i][j]=t2;di[i][j]=0;}}for(j=n-1;j>=0;j--){t1=num[i][j+1]+fee[i][j];if(t1<num[i][j]){num[i][j]=t1;di[i][j]=1;}}}//查找顶层的最小值 min=INT_MAX;for(i=1;i<=n;i++){if(num[1][i]<min){min=num[1][i];t=i;}}int x=1,y=t;//输出 back(x,t);}return 0;}

 另外一种查找路径

#include<stdio.h>#include<climits>#include<string.h>int fee[105][505];int num[105][505],f[105][505];int m,n;int main(){freopen("mini2.in","r",stdin);freopen("out2.txt","w",stdout);while(scanf("%d%d",&m,&n)==2){int i,j;for(i=1;i<=m;i++){for(j=1;j<=n;j++)scanf("%d",&fee[i][j]);}for(i=1;i<=n;i++){num[1][i]=fee[1][i];f[1][i]=i;}for(i=2;i<=m;i++){num[i][1]=num[i-1][1]+fee[i][1];f[i][1]=1;for(j=2;j<=n;j++){ num[i][j]=fee[i][j];if(num[i-1][j]>num[i][j-1]){num[i][j]+=num[i][j-1];f[i][j]=j-1;}else{num[i][j]+=num[i-1][j];f[i][j]=j;}}//printf("/n");for(j=n-1;j>0;j--){if(num[i][j+1]+fee[i][j]<num[i][j]){num[i][j]=num[i][j+1]+fee[i][j];f[i][j]=j+1;}}}int min=INT_MAX;for(i=1;i<=n;i++){if(num[m][i]<min){min=num[m][i];j=i;}}int ans[50005],x=m,t=0;ans[0]=j;while(x!=1){t++;ans[t]=f[x][ans[t-1]];if(ans[t]==ans[t-1])x--;}for(i=t;i>=0;i--)printf("%d/n",ans[i]);}return 0;}