/*
 * 300. Longest Increasing Subsequence  QuestionEditorial Solution  My Submissions
Total Accepted: 34958
Total Submissions: 99352
Difficulty: Medium
Given an unsorted array of integers, find the length of longest increasing subsequence.

For example,
Given [10, 9, 2, 5, 3, 7, 101, 18],
The longest increasing subsequence is [2, 3, 7, 101], therefore the length is 4. Note that 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?

Credits:
Special thanks to @pbrother for adding this problem and creating all test cases.

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 */
package dp;

import java.util.*;

public class LongestIncreasingSeq {

 public int lengthOfLIS(int[] nums) {
  if (nums == null || nums.length == 0)
   return 0;

  int[] dp = new int[nums.length]; // length of LIS : start from i
  Arrays.fill(dp, 1);

  int max = 0;

  for (int i = 0; i < nums.length; i++) {
   for (int j = 0; j < i; j++) {
    if (nums[j] < nums[i]) {
     dp[i] = Math.max(dp[i], dp[j] + 1);
    }
   }
   max = Math.max(max, dp[i]);
  }
  return max;
 }

 public static void main(String[] args) {
  int[] nums = {};
  LongestIncreasingSeq lis  = new LongestIncreasingSeq();
  System.out.println(lis.lengthOfLIS(nums));

 }

}