區間DP-矩陣連乘問題

#include <iostream>
#include <sstream>
#include <stdio.h>
#include <algorithm>
#include <string.h>
#include <stack>
#include <queue>
#include <set>
#include <math.h>


/*=======================================
矩陣連乘問題
dp(i, j) = min( dp(i, k) + dp(k + 1, j) + S);
i < k < j;
dp(i, i) = 0;
========================================*/
#define flush(arr, i) memset(arr, i, sizeof(arr))
typedef long long int64;
using namespace std;
const int MAX_ITEM = 128;
//const int oo = 0x7fffffff;
const int oo = 0x3f3f3f3f;


int dp[MAX_ITEM][MAX_ITEM];
int w[MAX_ITEM], pos[MAX_ITEM][MAX_ITEM];


int DP(int l, int r)
{
    if(l == r)
        return 0;


    if(dp[l][r])
        return dp[l][r];


    int ans = oo, tmp = 0;
    for(int i = l; i < r; i++)
    {
        tmp = DP(l, i) + DP(i + 1, r) + w[l - 1] * w[i] * w[r];
        if(ans > tmp)
        {
            ans = tmp;
            pos[l][r] = i;
        }
    }
    return dp[l][r] = ans;
}


void display(int l, int r)
{
    if(l == r)
    {
        printf("A%d", l);
        return;
    }
    printf("(");
    display(l, pos[l][r]);
    display(pos[l][r] + 1, r);
    printf(")");
}


int main()
{
    freopen("0-data.txt", "r", stdin);
    int n;
    while(scanf("%d", &n) != EOF)
    {
        flush(dp, 0);
        flush(pos, 0);
        for(int i = 0; i <= n; i++)
            scanf("%d", w + i);
        printf("%d\n", DP(1, n));
        display(1, n);
    }
    return 0;
}