UVA-10003 Cutting Sticks (区间DP)

题目链接：https://vjudge.net/problem/UVA-10003

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思路：

• 石子合并问题的逆过程，做法一模一样；

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Code：

#include<bits/stdc++.h>
using namespace std;
int a[60], dp[60][60], sum[60][60];

int main() {
    int l, n;
    while(cin>>l>>n, l) {
        memset(dp, 0, sizeof(dp));
        memset(sum, 0, sizeof(sum));
        int now, last = 0;
        for (int i = 0; i < n; ++i) {
            cin>>now;
            a[i] = now - last;
            last = now;
        }
        a[n] = l - last;
        for (int i = 0; i <= n; ++i)
            for (int j = i; j <= n; ++j)
                sum[i][j] =  sum[i][j-1] + a[j];
        for (int L = 2; L <= n + 1; ++L)
            for (int i = 0; i + L - 1 <= n; ++i){
                int j = i + L - 1;
                dp[i][j] = dp[i][i] + dp[i+1][j] + sum[i][j];
                for (int k = i; k < j; ++k)
                    dp[i][j] = min(dp[i][j], dp[i][k] + dp[k+1][j] + sum[i][j]);
            }
        cout<<"The minimum cutting is "<<dp[0][n]<<"."<<endl;
    }

    return 0;
}