Leetcode #473: Matchsticks to Square
In this guide, we solve Leetcode #473 Matchsticks to Square in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given an integer array matchsticks where matchsticks[i] is the length of the ith matchstick. You want to use all the matchsticks to make one square.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Bit Manipulation, Array, Dynamic Programming, Backtracking, Bitmask
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: matchsticks = [1,1,2,2,2]
Output: true
Explanation: You can form a square with length 2, one side of the square came two sticks with length 1.
Python Solution
class Solution:
def makesquare(self, matchsticks: List[int]) -> bool:
def dfs(u):
if u == len(matchsticks):
return True
for i in range(4):
if i > 0 and edges[i - 1] == edges[i]:
continue
edges[i] += matchsticks[u]
if edges[i] <= x and dfs(u + 1):
return True
edges[i] -= matchsticks[u]
return False
x, mod = divmod(sum(matchsticks), 4)
if mod or x < max(matchsticks):
return False
edges = [0] * 4
matchsticks.sort(reverse=True)
return dfs(0)
Complexity
The time complexity is O(n·m) (typical). The space complexity is O(n·m) or optimized.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.