300. Longest Increasing Subsequence

300. Longest Increasing Subsequence

• 題目描述：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?

• 題目大意：給定一個數組，找出數組中的最長上升子序列

• 思路：DP，dp[i]表示以第i個位置爲結尾處的最長子序列

• 代碼

  package DP;
  
  import java.util.Arrays;
  
  /**
  * @Author OovEver
  * @Date 2017/12/17 17:13
  */
  public class LeetCode300 {
    public static int lengthOfLIS(int[] nums) {
        if (nums == null || nums.length == 0) {
            return 0;
        }
        int[] dp = new int[nums.length];
        int max = 1;
        Arrays.fill(dp, 1);
        for(int i=0;i<nums.length;i++) {
            for(int j=0;j<i;j++) {
                if (nums[i] > nums[j] && dp[j]+1>dp[i]) {
                    dp[i] = dp[j] + 1;
                }
            }
            max = Math.max(max, dp[i]);
        }
        return max;
    }
  
  }