【LeetCode】 300. Longest Increasing Subsequence 最长上升子序列（Medium）（JAVA）

题目地址: https://leetcode.com/problems/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:

1. There may be more than one LIS combination, it is only necessary for you to return the length.
2. Your algorithm should run in O(n2) complexity.

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

题目大意

给定一个无序的整数数组，找到其中最长上升子序列的长度。

解题方法

1、维护一个有序队列 list
2、用新的元素替换有序队列中相应的位置，如果比最后一个元素大，就加入有序队列中

class Solution {
    public int lengthOfLIS(int[] nums) {
        List<Integer> list = new ArrayList<>();
        for (int i = 0; i < nums.length; i++) {
            insert(list, nums[i]);
        }
        return list.size();
    }

    public void insert(List<Integer> list, int num) {
        if (list.size() == 0 || list.get(list.size() - 1) < num) {
            list.add(num);
            return;
        }
        int start = 0;
        int end = list.size() - 1;
        while (start <= end) {
            int mid = start + (end - start) / 2;
            if (list.get(mid) == num) {
                start = mid;
                break;
            } else if (list.get(mid) > num) {
                end = mid - 1;
            } else {
                start = mid + 1;
            }
        }
        list.set(start, num);
    }
}

执行用时 : 1 ms, 在所有 Java 提交中击败了 94.83% 的用户
内存消耗 : 37.7 MB, 在所有 Java 提交中击败了 5.05% 的用户