矩阵相乘（uva348）

来源：互联网发布：中国mysql用户组编辑：程序博客网时间：2024/06/06 04:44

题意：求矩阵相乘的最佳花括号的方式并打印出来

#include<iostream>#include<cstdio>#include<string>#include<cstring>#include<vector>#include<cmath>#include<queue>#include<stack>#include<map>#include<set>#include<algorithm>using namespace std;const int INF=0x3f3f3f3f;const int maxn=110;struct node{    int n,m;}a[maxn];int N;int dp[maxn][maxn];int path[maxn][maxn];void dfs(int x,int y){    if(x==y)    {        printf("A%d",x);        return;    }    printf("(");    dfs(x,path[x][y]);    printf(" x ");    dfs(path[x][y]+1,y);    printf(")");}int main(){    int cas=1;    while(scanf("%d",&N)!=EOF,N)    {        for(int i=1;i<=N;i++)scanf("%d%d",&a[i].n,&a[i].m);        memset(dp,INF,sizeof(dp));        memset(path,-1,sizeof(path));        for(int i=1;i<=N;i++)dp[i][i]=0,path[i][i]=i;        for(int len=1;len<=N;len++)        {            for(int i=1;i+len-1<=N;i++)            {                int j=i+len-1;                for(int k=i;k<j;k++)                {                    if(dp[i][k]+dp[k+1][j]+a[i].n*a[k].m*a[j].m<dp[i][j])                    {                        dp[i][j]=dp[i][k]+dp[k+1][j]+a[i].n*a[k].m*a[j].m;                        path[i][j]=k;                    }                }            }        }        printf("Case %d: ",cas++);        dfs(1,N);        printf("\n");    }    return 0;}

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