uva:348 - Optimal Array Multiplication Sequence

来源：互联网发布：百度云管家有mac版吗编辑：程序博客网时间：2024/05/01 18:03

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=114&page=show_problem&problem=284

矩阵乘法问题，区间dp。动规方程为：f[i][j] = min{ f[i][k] + f[k+1][j] + p[i] * q[k] * q[j] } (k>=i && k < j)。其中f[i][j] 表示的是区间[i ,j ]内的最优值。p[i]表示矩阵i的行，q[i]表示矩阵i的列。递推的时候采用区间j-i的长度来一次递推。这样比较容易计算以及状态的转移。代码如下：

/*ID; csuanchenPROG: 348 Optimal Array Multiplication SequenceLANG: C++*/#include<iostream>#include<stdio.h>#include<string.h>#include<algorithm>using namespace std ;#define INF 100000000const int maxn = 15 ;int martix[maxn][2] ;int dp[maxn][maxn] ;int fl[maxn][maxn] ;int n ;void print(int left , int right) ;int main(){int test ;test = 0 ;while(cin>>n && n){int i ;int j ;int len ;int k ;memset(martix , 0 , sizeof(martix)) ;memset(dp , 0 , sizeof(dp)) ;memset(fl , 0 , sizeof(fl)) ;for(i = 0 ; i < n ; i ++)cin>>martix[i][0]>>martix[i][1] ;for(len = 1 ; len <= n ; len ++){for(i = 0 ; i <= n - len ; i ++){j = i + len - 1 ;dp[i][j] = INF  ;if(i == j )dp[i][j] = 0 ;for(k = i ; k < j ; k ++){int temp = dp[i][k] + dp[k + 1][j] + martix[i][0] * martix[k][1] * martix[j][1] ;if(dp[i][j] > temp){dp[i][j] = temp ;fl[i][j] = k ;}}}}cout<<"Case "<<++test<<": ";print(0 , n - 1) ;cout<<endl ;}return 0 ;}void print(int left , int right){if(left!=right){cout<<"(" ;print(left , fl[left][right]) ;cout<<" x " ;print(fl[left][right] + 1 , right) ;cout<<")" ;}else if( left == right && left != n - 1 )cout<<"A"<<left + 1;else if( left == right && left == n - 1 )cout<<"A"<<right + 1 ;}