POJ 2533 Longest Ordered Subsequence

Description

最长上升子序列（模板）

O(n * n)

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;

int a[10005];
int dp[10005];

int main()
{
    int n;
    while(~scanf("%d", &n))
    {
        for(int i = 0; i < n; ++i)
            scanf("%d", &a[i]);
        int ans = 0;
        for(int i = 0; i < n; ++i)
        {
            dp[i] = 1;
            for(int j = 0; j < i; ++j)
            {
                if(a[j] < a[i])
                    dp[i] = max(dp[i], dp[j] + 1);
            }
            ans = max(ans, dp[i]);
        }
        cout << ans << '\n';
    }
    return 0;
}
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O(n * logn) 不能记录路径

#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;
const int INF = 0x3f3f3f3f;

int a[10005];
int low[10005];

int main()
{
    int n;
    while(~scanf("%d", &n))
    {   ///这个算法里数组尽量从1开始存
        for(int i = 1; i <= n; ++i)
            {
                scanf("%d", &a[i]);
                low[i] = INF;
            }
        int ans = 1;
        low[ans] = a[1];
        for(int i = 2; i <= n; ++i)
        {
            if(a[i] > low[ans])
                low[++ans] = a[i];
            else
            {
                int pos = lower_bound(low, low + ans, a[i]) - low;
                low[pos] = a[i];
            }
        }
        cout << ans << '\n';
    }
    return 0;
}
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