[AcWing 1014] 登山

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点击查看代码

#include<iostream>

using namespace std;

const int N = 1010;

int n;
int a[N], f[N], ff[N];

int main()
{
	cin >> n;
	for (int i = 1; i <= n; i ++)	cin >> a[i];
	int res = 0;
	for (int i = 1; i <= n; i ++) {
		f[i] = 1;
		for (int j = 1; j < i; j ++)
			if (a[i] > a[j])
				f[i] = max(f[i], f[j] + 1);
	}
	for (int i = n; i >= 1; i--) {
		ff[i] = 1;
		for (int j = n; j > i; j --)
			if (a[i] > a[j])
				ff[i] = max(ff[i], ff[j] + 1);
	}
	for (int i = 1; i <= n; i ++) {
		f[i] += ff[i] - 1;
		res = max(res, f[i]);
	}
	cout << res << endl;
	return 0;
}

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1. 先分别求出以 $a_i$ 结尾，从左往后看最大上升子序列和从右往左看最大上升子序列，要求的是两个上升子序列相加（$a_i$ 被算了两次，要减 $1$）的最大值