How do you solve Matchsticks to Square on LeetCode?

Matchsticks to Square (LeetCode #473) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(4^n) time complexity and O(n) space complexity. Key insight: The total length must be divisible by 4 to form a square.

What is the brute force solution for Matchsticks to Square?

The brute force approach for Matchsticks to Square is Brute Force, with O(4^n) time complexity and O(n) space complexity. The brute force approach involves checking every possible combination of matchsticks to see if they can form a square. This is done by recursively trying to place each matchstick on one of the four sides of the square. The optimal Optimal Solution approach improves this to O(4^n).

What are the interview tips for Matchsticks to Square?

Explain your thought process clearly while coding. Consider edge cases and constraints before diving into the solution. Practice backtracking problems to get comfortable with recursive solutions.

What are common mistakes when solving Matchsticks to Square?

Not checking if the total length is divisible by 4. Failing to handle cases where a matchstick is larger than the target side length.

#473

Matchsticks to Square

Medium

ArrayDynamic ProgrammingBacktrackingBit ManipulationBitmaskBacktrackingRecursion

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(4^n)	O(4^n)
Space	O(n)	O(n)

💡

Intuition

Time O(4^n)Space O(n)

The optimal solution uses backtracking with pruning to efficiently explore valid combinations of matchsticks. By sorting the matchsticks in descending order, we can quickly eliminate impossible configurations.

⚙️

Algorithm

3 steps

1Step 1: Calculate the total length of matchsticks and check if it's divisible by 4.
2Step 2: Sort the matchsticks in descending order to try larger sticks first.
3Step 3: Use a recursive function to attempt to build each side of the square, backtracking when necessary.

solution.py23 lines

1def makesquare(matchsticks):
2    total_length = sum(matchsticks)
3    if total_length % 4 != 0:
4        return False
5    target = total_length // 4
6    matchsticks.sort(reverse=True)
7
8    sides = [0] * 4
9
10    def backtrack(index):
11        if index == len(matchsticks):
12            return sides[0] == sides[1] == sides[2] == target
13        for i in range(4):
14            if sides[i] + matchsticks[index] <= target:
15                sides[i] += matchsticks[index]
16                if backtrack(index + 1):
17                    return True
18                sides[i] -= matchsticks[index]
19            if sides[i] == 0:
20                break
21        return False
22
23    return backtrack(0)

ℹ

Complexity note: The complexity remains exponential due to the recursive nature, but sorting the matchsticks helps reduce the number of combinations explored.

1The total length must be divisible by 4 to form a square.
2Sorting the matchsticks helps in reducing the search space.

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