# 646 Maximum Length of Pair Chain

## 646. [Maximum Length of Pair Chain](https://leetcode.com/problems/maximum-length-of-pair-chain/description/)

## 1. Question

You are given`n`pairs of numbers. In every pair, the first number is always smaller than the second number.

Now, we define a pair`(c, d)`can follow another pair`(a, b)`if and only if`b < c`. Chain of pairs can be formed in this fashion.

Given a set of pairs, find the length longest chain which can be formed. You needn't use up all the given pairs. You can select pairs in any order.

**Example 1:**

```
Input: [[1,2], [2,3], [3,4]]

Output: 2

Explanation:
The longest chain is [1,2] -> [3,4]
```

**Note:**

1. The number of given pairs will be in the range \[1, 1000].

## 2. Implementation

**(1) Sorting + DP**

```java
class Solution {
    public int findLongestChain(int[][] pairs) {
        Arrays.sort(pairs, (a, b)->(a[0] - b[0]));

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

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

        int res = 1;
        for (int len : LIS) {
            res = Math.max(res, len);
        }
        return res;
    }
}
```

## 3. Time & Space Complexity

**Sorting + DP:**&#x65F6;间复杂度O(nlogn + n^2), n为pairs的个数, 空间复杂度O(n)