LeetCode 300. Longest Increasing Subsequence

Posted 2022-08-31 CrazyCoder1992

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].

题解：
此类型题目可以使用动态规划算法求解。
已知数组d[0…i]，函数$f(i)$代表以下标i为结尾的最长递增子序列的长度，则有：$$f(0)=1$$
将数组绘制成坐标图，x轴为数组下标，y轴为f(x)，观察坐标图可知，第i个点的最长递增子序列应为其左下方区域内的最长递增子序列加上第i个点，即以下公式：
$$f(i)=max(f(0),f(1),...,f(j)),其中j<i,d[j]<d[i]$$

根据递推公式实现代码：

func lengthOfLIS(input []int) int 
	maxLenArr := make([]int, len(input))
	for i := range input 
		if i == 0 
			maxLenArr[i] = 1
			continue
		
		maxLenArr[i] = 1
		for j := 0; j < i; j++ 
			if input[j] >= input[i] 
				continue
			
			if maxLenArr[j]+1 > maxLenArr[i] 
				maxLenArr[i] = maxLenArr[j] + 1
			
		
	
	maxLen := 1
	for i := range maxLenArr 
		if maxLenArr[i] > maxLen 
			maxLen = maxLenArr[i]
		
	
	return maxLen