UVA-10003 Cutting Sticks (区间DP)

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

思路：

石子合并问题的逆过程，做法一模一样；

Code：

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 int a[60], dp[60][60], sum[60][60];
 4 
 5 int main() {
 6     int l, n;
 7     while(cin>>l>>n, l) {
 8         memset(dp, 0, sizeof(dp));
 9         memset(sum, 0, sizeof(sum));
10         int now, last = 0;
11         for (int i = 0; i < n; ++i) {
12             cin>>now;
13             a[i] = now - last;
14             last = now;
15         }
16         a[n] = l - last;
17         for (int i = 0; i <= n; ++i)
18             for (int j = i; j <= n; ++j)
19                 sum[i][j] =  sum[i][j-1] + a[j];
20         for (int L = 2; L <= n + 1; ++L)
21             for (int i = 0; i + L - 1 <= n; ++i){
22                 int j = i + L - 1;
23                 dp[i][j] = dp[i][i] + dp[i+1][j] + sum[i][j];
24                 for (int k = i; k < j; ++k)
25                     dp[i][j] = min(dp[i][j], dp[i][k] + dp[k+1][j] + sum[i][j]);
26             }
27         cout<<"The minimum cutting is "<<dp[0][n]<<"."<<endl;
28     }
29 
30     return 0;
31 }