动态规划之矩阵链乘法

#include <iostream> 
#include <stdio.h>
#include <assert.h>
#include <stdlib.h>
#include <String.h>

#define MAX 100

typedef struct Matrix{
    int left;
    int right;
}Matrix;

using namespace std;

//自底向上的矩阵链乘法 
void MATRIX_CHAIN_ORDER(Matrix a[], int num){
    //创建存储最优子问题解的数组 
    int m[MAX][MAX], s[MAX][MAX];
    //数组初始化 
    memset(m, MAX*MAX, sizeof(int));
    memset(s, MAX*MAX, sizeof(int));

    for(int i=0; i<num; i++)
        m[i][i] = 0;

    for(int l=2; l<=num; l++){
        for(int i=0; i<num-1; i++){
            //依次计算计算链长为l的最小矩阵乘积 
            int j = i+l-1;
            m[i][j] = 2e31;
            for(int k=i; k<=j-1; k++){
                int i_j_sum = m[i][k]+m[k+1][j]+a[i].left*a[k].right*a[j].right;
                if(i_j_sum<m[i][j]){
                    m[i][j] = i_j_sum;
                    s[i][j] = k;
                }
            } 
        }
        for(int i=0; i<num; i++){
            for(int j=0; j<num; j++){
                cout <<m[i][j]<<" ";
            }
            cout<<endl;
        }
    }
    cout<<m[0][num-1];
    return;
}

int LOOKUP_CHAIN(int m[][MAX], Matrix a[], int i, int j){
    if(i == j){
        m[i][j]=0;
    }
    for(int k=i; k<j; k++){
        int q = LOOKUP_CHAIN(m, a, i, k)+LOOKUP_CHAIN(m, a, k+1, j) + a[i].left*a[k].right*a[j].right;
        if(q<m[i][j]){
            m[i][j] = q;
        }
    }
    return m[i][j];
} 

//自顶向下的矩阵链乘法 
void MEMOIZED_MATRIX_CHAIN(Matrix a[], int num){
    //创建存储最优子问题解的数组 
    int m[MAX][MAX], s[MAX][MAX];
    //数组初始化 
    memset(m, MAX*MAX, sizeof(int));
    memset(s, MAX*MAX, sizeof(int));

    for(int i=0; i<num; i++){
        for(int j=i; j<num; j++){
            m[i][j] = 2e31;
        }
    }
    //递归计算
    LOOKUP_CHAIN(m, a, 0, num-1);

    cout<<m[0][num-1];
    return;
}




int main(){
    Matrix a[MAX];
    int num = -1;
    while(cin>>num){
        //输入矩阵参数 
        for(int i=0; i<num; i++)
            cin>>a[i].left>>a[i].right;
        //  MATRIX_CHAIN_ORDER(a, num);
        MEMOIZED_MATRIX_CHAIN(a, num);
    }
    return 0; 
}