[luoguP3146] [USACO16OPEN]248（区间DP）

传送门

f[i][j]表示区间 i-j 合并的最大值

转移：

若f[i][k] && f[k+1][j] && f[i][k] == f[k+1][j] --> f[i][j] = max(f[i][k]+1,f[i][j])

但要注意， 若f[i][k]!=f[k+1][j]，那么无法进行转移

代码

#include <cstdio>
#include <iostream>
#define max(x, y) ((x) > (y) ? (x) : (y))

int n, ans;
int f[5001][5001];

inline int read()
{
	int x = 0, f = 1;
	char ch = getchar();
	for(; !isdigit(ch); ch = getchar()) if(ch == '-') f = -1;
	for(; isdigit(ch); ch = getchar()) x = (x << 1) + (x << 3) + ch - '0';
	return x * f;
}

int main()
{
	int i, j, k;
	n = read();
	for(i = 1; i <= n; i++) f[i][i] = read(), ans = max(ans, f[i][i]);
	for(i = n - 1; i >= 1; i--)
		for(j = i + 1; j <= n; j++)
		{
			for(k = i; k < j; k++)
				if(f[i][k] && f[k + 1][j] && f[i][k] == f[k + 1][j])
					f[i][j] = max(f[i][j], f[i][k] + 1);
			ans = max(ans, f[i][j]);
		}
	printf("%d\n", ans);
	return 0;
}