LeetCode 300 Longest Increasing Subsequence

Given an integer array nums, return the length of the longest strictly increasing subsequence.

A subsequence is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements. For example, [3,6,2,7] is a subsequence of the array [0,3,1,6,2,2,7].

Solution

我们用 \(dp[i]\) 表示以 \(i\) 结尾的最长长度。考虑转移：

\[dp[i]=\max(dp[i],dp[j]+1) \]

其中 \(j<i\)，且：

\[nums[i]>nums[j] \]

此时我们需要遍历所有的 \(j<i\), 所以复杂度为 \(O(n^2)\)

点击查看代码

class Solution {
private:
    int dp[2502];
    int ans = 1;
public:
    int lengthOfLIS(vector<int>& nums) {
        int n = nums.size();
        if(n==1)return 1;
        for(int i=0;i<n;i++)dp[i]=1;
        for(int i=1;i<n;i++){
            for(int j=0;j<i;j++){
                if(nums[i]>nums[j])dp[i]=max(dp[i],1+dp[j]);
            }
            ans = max(ans, dp[i]);
        }
        return ans;
    }
};