# 300 Longest Increasing Subsequence

## 300. [Longest Increasing Subsequence](https://leetcode.com/problems/longest-increasing-subsequence/description/)

## 1. Question

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(nlogn) time complexity?

## 2. Implementation

**(1) DP**

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

        int n = nums.length;
        int[] LIS = new int[n];
        Arrays.fill(LIS, 1);

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < i; j++) {
                if (nums[j] < nums[i] && (LIS[j] + 1 > LIS[i])) {
                    LIS[i] = LIS[j] + 1;
                }
            }
        }

        int res = 0;
        for (int e : LIS) {
            res = Math.max(e, res);
        }
        return res;
    }
}
```

**(2) Binary Search优化**

```
```

## 3. Time & Space Complexity

**DP**: 时间复杂度O(n^2), 空间复杂度O(n)


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