LeetCode: 300. Longest Increasing Subsequence

题目描述

Given an unsorted array of integers, find the length of longest increasing subsequence.

Example:

Input: [10,9,2,5,3,7,101,18]
Output: 4 
Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4.

Note:

• There may be more than one LIS combination, it is only necessary for you to return the length.
• Your algorithm should run in ​​O(n^2)​​ complexity.

解题思路 —— 动态规划

1. 记 ​​dp[i+1]​​​: 以 ​​nums[i]​​ 结尾的最长上升子序列
2. 则 ​​dp[i+1] = max(dp[j]...) + 1​​​ 其中 ​​j​​​是 ​​0​​​ 到 ​​i​​​ 中使得 ​​nums[j] < nums[i]​​ 的数字
3. 最长上升子序列是 ​​dp​​ 数组中的最大值

AC 代码

func lengthOfLIS(nums []int) int {
    // dp[i]: 以 nums[i] 结尾的最长上升子序列 
    dp := []int{0}
    
    for i := 1; i <= len(nums); i++{
        dp = append(dp, 1)
        for j := 0; j < i; j++ {
            if (j == 0 || nums[j-1] < nums[i-1]) && dp[j] + 1 > dp[i]{
                dp[i] = dp[j] + 1
            }
        }
    }
    
    ans := 0
    for _, val := range dp {
        if val > ans {
            ans = val
        }
    }
    
    return ans
}