最长上升子序列

普通
#include<iostream>
using namespace std;
#include<algorithm>
#include<cstring>
const int N = 5010;
int n, f[N];
int a[N];
int main() {
	cin >> n;
	for (int i = 1; i <= n; i++)cin >> a[i];

	for (int i = 1; i <= n; i++)f[i] = 1;

	for (int i = 1; i <= n; i++)
		for (int j = 1; j < i; j++)
	if(a[i]>a[j])f[i] = max(f[i], f[j] + 1);

	int res = 0;
	for (int i = 1; i <= n; i++)
		res = max(res, f[i]);

	cout << res;
}

二分优化
#include<iostream>

using namespace std;
const int N = 5010;
int a[N], b[N], f[N];
int n;
int len;
int find(int x) {
	int l = 1, r = len, mid;
	while (l <= r) {
		mid = (l + r) / 2;
		if (b[mid] == x)return mid;
		else if (x < b[mid])r = mid - 1;
		else l = mid + 1;
	}
	return l;
}

int main() {
	cin >> n;
	for (int i = 1; i <= n; i++)cin >> a[i];
	int i, j;
	len = 1; b[1] = a[1];
	for (int i = 2; i <= n; i++) {
		if (a[i] > b[len])
			b[++len] = a[i];
		else
		{
			j = find(a[i]);
			b[j] = a[i];
		}
	}
	cout << len << endl;
}