[AcWing 1012] 友好城市

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点击查看代码

#include<iostream>
#include<algorithm>

#define fi first
#define se second

using namespace std;

const int N = 5010;

int n;
int f[N];
pair<int,int> p[N];

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

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1. 保证任意两条航线不相交的条件：
   任意两个航线 \((a_1, b_1)\) 和 \((a_2, b_2)\) ，都必须满足
   ① $if \ \ a_1 < a_2 \ \ then \ \ b_1 < b_2 $
   ② $if \ \ a_1 > a_2 \ \ then \ \ b_1 > b_2 $
2. 同时考虑两个坐标的最长上升子序列