UVa 10003 Cutting Sticks（区间DP）

题意：

给定一个l长得木棍，要把它从给定的n个点截断，每截断一次需要的费用为木棍的长度。

求截断这个木棍所要花费的最小代价。

思路：

典型的区间DP，要额外添加2个点：0和l，于是区间从1不断扩展到n+1，dp[i][j]代表点i到点j所要花费的最小代价。

#include <cstdio> #include <cstdlib> #include <cstring> #include <algorithm>



#define min(a,b) (((a) < (b)) ? (a) : (b))



const int INF = 1e9; int a[60]; int dp[60][60]; int main() { int l, n; while (scanf("%d", &l) && l) { scanf("%d", &n); for (int i = 1; i <= n; ++i) scanf("%d", &a[i]); a[0] = 0, a[n+1] = l; n += 1; memset(dp, 0, sizeof(dp)); for (int i = 0; i <= n; ++i) { for (int j = 0; j <= n; ++j) dp[i][j] = INF; dp[i][i] = 0; } for (int i = 0; i < n; ++i) dp[i][i+1] = 0; for (int p = 2; p <= n; ++p) for (int i = 0, j = p; j <= n; ++i, ++j) for (int k = i; k < j; ++k) dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + a[j] - a[i]); printf("The minimum cutting is %d.\n", dp[0][n]); } return 0; }