算法--最长上升子序列

1、最长上升子序列

#include<iostream>
#include<algorithm>
using namespace std;
int a[100];//原始数组
int dp[100];//以x结尾的数组
int main() {
	int n;//数组长度
	cin >> n;
	for (int i = 1; i <= n; i++) {
		cin >> a[i];//数组中的每个元素
	}
	for (int i = 1; i <= n; i++) {
		dp[i] = 1;
		for (int j = 1; j < i; j++) {
			if (a[j] < a[i]) {
				dp[i] = max(dp[i], dp[j] + 1);
			}
		}
	}
	int max_step = 0;
	for (int i = 1; i <= n; i++) {
		if (dp[i] > max_step) {
			max_step = dp[i];
		}
	}
	cout << max_step << endl;
}

 

 2、例题

 

#include<bits/stdc++.h>
using namespace std;
const int N = 1e6;
int g[N],a[N];
int main()
{
    int n;
    cin>>n;
    int len=0;
    for(int i = 1; i <= n; i ++) {
        cin>>a[i];
    }
    for(int i = 1; i <= n; i ++) {
        if(a[i] > g[len]){
          g[++len] = a[i];
        }else {
            int pos = upper_bound(g+1,g+1+len,a[i]) - g;
            g[pos] = a[i];
        }
    }
    cout<<len;
    return 0;
}