【线性dp】AcWing896.最长上升子序列 II

AcWing896.最长上升子序列 II

题解

二分解法

q[i]保存长度为i的最小末尾，这样即可严格单调递增，从而对于每个新的数只要找出小于它的最大值就可算出长度

#include <cstdio>
#include <iostream>

using namespace std;

const int N = 100010;

int q[N], nums[N], cnt = 1;

int find(int x)
{
    int l = 1, r = cnt, mid;
    while(l < r)
    {
        mid = l + r + 1 >> 1;
        if(q[mid] <= x)  l = mid;
        else  r = mid - 1;
    }
    return r;
}

int main()
{
    int n;
    scanf("%d", &n);
    for(int i = 1; i <= n; ++i)
        scanf("%d", &nums[i]);
    q[1] = nums[1];
    for(int i = 2; i <= n; ++i)
    {
        int idx = find(nums[i]);
        if(q[idx] < nums[i])
        {
            cnt = max(cnt, idx + 1);
            q[idx + 1] = nums[i];
        }
        else q[idx] = nums[i];
    }
    printf("%d\n", cnt);
    return 0;
}