How do you solve Maximum Length of Pair Chain on LeetCode?

Maximum Length of Pair Chain (LeetCode #646) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Sorting the pairs by their end values allows us to efficiently build the longest chain.

What is the time complexity of Maximum Length of Pair Chain?

The optimal solution for Maximum Length of Pair Chain runs in O(n log n) time and uses O(1) space. The time complexity is O(n log n) due to the sorting step, which is much more efficient than the brute-force approach.

What is the brute force solution for Maximum Length of Pair Chain?

The brute force approach for Maximum Length of Pair Chain is Brute Force, with O(n²) time complexity and O(1) space complexity. We can generate all possible chains of pairs and check their lengths. This approach is straightforward but inefficient as it explores all combinations. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Maximum Length of Pair Chain?

Maximum Length of Pair Chain uses the following concepts: Array, Dynamic Programming, Greedy, Sorting. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Maximum Length of Pair Chain?

Always consider sorting as a first step for interval problems. Explain your thought process clearly while coding; it helps the interviewer follow your logic. Practice recognizing patterns in problems, such as greedy vs. dynamic programming approaches.

What are common mistakes when solving Maximum Length of Pair Chain?

Not sorting the pairs before processing, which leads to incorrect results. Failing to check if the current pair can be added to the chain.

#646

Maximum Length of Pair Chain

Medium

ArrayDynamic ProgrammingGreedySortingGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

By sorting the pairs based on their end values and using a greedy approach, we can efficiently find the longest chain without checking all combinations.

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Algorithm

3 steps

1Step 1: Sort the pairs based on the second element (right value).
2Step 2: Initialize a variable to track the end of the last added pair in the chain.
3Step 3: Iterate through the sorted pairs, and for each pair, check if it can be added to the chain (i.e., if its left value is greater than the last end). If yes, update the end and increase the count.

solution.py11 lines

1# Full working Python code
2
3def findLongestChain(pairs):
4    pairs.sort(key=lambda x: x[1])
5    count = 0
6    last_end = float('-inf')
7    for left, right in pairs:
8        if last_end < left:
9            count += 1
10            last_end = right
11    return count

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Complexity note: The time complexity is O(n log n) due to the sorting step, which is much more efficient than the brute-force approach.

1Sorting the pairs by their end values allows us to efficiently build the longest chain.
2Using a greedy approach helps in making optimal choices at each step without backtracking.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.