300.Longest Increasing Subsequence

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Question

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

Example:

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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(n2) complexity.

Follow up: Could you improve it to O(n log n) time complexity?

Answer

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class Solution {
    public int lengthOfLIS(int[] nums) {
        int len = nums.length;
        int[] dp = new int[len];
        int max = 0;
        for(int i = 0; i < len; i++){
            dp[i] = 1;
            for(int j = 0; j < i; j++)
                if(nums[j] < nums[i])
                    dp[i] = Math.max(dp[i], dp[j]+1);
            if(dp[i] > max)
                max = dp[i];
        }
        System.out.println(max);
        return max;
    }
}

Time complexity: $O(n^2)$

corner case: nums:[] or nums:[1]

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Time complexity: $O(n\log n)$