[bzoj 1996] [Hnoi2010]chorus 合唱队

[bzoj 1996] [Hnoi2010]chorus 合唱队

Description

Input

Output

Sample Input

4
1701 1702 1703 1704

Sample Output

8

HINT

区间dp,考虑区间[i,j],f[i][j][0/1]表示这次插入的是第i/j个数.
显然有:
f[i][j][0]=f[i+1][j][0] (A[i]<A[i+1]) + f[i+1][j][1] (A[i]<A[j])
f[i][j][1]=f[i][j-1][0] (A[j]>A[i]) + f[i][j-1][1] (A[j]>A[j-1])
初始化时任取一个f[i][i][0/1]为1就可以了,要保证没有重复

#include <cstdio>
#include <algorithm>

typedef long long LL;

static const int maxm = 1e3 + 10;
static const int MOD = 19650827;

int f[maxm][maxm][2],A[maxm];
int n;

int main(){
	scanf("%d",&n);
	for(int i = 1;i <= n;i++) scanf("%d",&A[i]);
	
	for(int i = 1;i <= n;i++) f[i][i][0] = 1;
	
	for(int i = n;i >= 1;i--){
		for(int j = i + 1;j <= n;j++){
			if(A[i] < A[j]) f[i][j][0] += f[i + 1][j][1];
			if(A[i] < A[i + 1]) f[i][j][0] += f[i + 1][j][0];
			if(A[j] > A[j - 1]) f[i][j][1] += f[i][j - 1][1];
			if(A[j] > A[i]) f[i][j][1] += f[i][j-1][0]; 
			f[i][j][1] %= MOD , f[i][j][0] %= MOD;
		}
	}
	
	printf("%d
",(f[1][n][0] + f[1][n][1]) % MOD);
	
	return 0;
}