646. Maximum Length of Pair Chain

Problem Statement

You are given an array of n pairs pairs where pairs[i] = [lefti, righti] and lefti < righti.

A pair p2 = [c, d] follows a pair p1 = [a, b] if b < c. A chain of pairs can be formed in this fashion.

Return the length longest chain which can be formed.

You do not need to use up all the given intervals. You can select pairs in any order.

Example 1:

Input: pairs = [[1,2],[2,3],[3,4]]
Output: 2
Explanation: The longest chain is [1,2] -> [3,4].

Example 2:

Input: pairs = [[1,2],[7,8],[4,5]]
Output: 3
Explanation: The longest chain is [1,2] -> [4,5] -> [7,8].

Constraints:

• n == pairs.length

• 1 <= n <= 1000

• -1000 <= lefti < righti <= 1000

Intuition

Approach:
Sort and at end index, Not take/ Take
If take, using BS find the next just greater index and move along

Links

https://leetcode.com/problems/maximum-length-of-pair-chain/description/

Video Links

Approach 1:

DP + BS

C++

class Solution {
public:
    vector<int>dp;
    int binary_search(vector<vector<int>>& pairs, int index, int val){
        int low=index;
        int high=pairs.size()-1;
        int ans=pairs.size();

        while(low<=high){
            int mid = low + (high-low)/2;
            // Mistake of not writing pairs[index/mid] and <= 
            if(pairs[mid][0] <= val)
                low = mid+1;

            else{
                ans = mid;
                high = mid-1;
            }
        }

        return ans;
    }

    int find_ans(vector<vector<int>>& pairs, int index){
        if(index >= pairs.size())
            return 0;

        if (dp[index] != -1)
            return dp[index];

        int not_take = find_ans(pairs, index+1);

        int next_index = binary_search(pairs, index+1, pairs[index][1]);
        
        int take = 1 + find_ans(pairs, next_index);

        return dp[index] = max(take, not_take);
    }

    int findLongestChain(vector<vector<int>>& pairs) {
        sort(pairs.begin(), pairs.end());
        dp = vector<int> (pairs.size(),-1);
        return find_ans(pairs, 0);
    }
};

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++

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