Matchsticks To Square Leetcode Problem 473 [Python Solution]
In this blog post, we will delve into solving the Matchsticks To Square problem, which is LeetCode problem 473. This problem falls under the category of backtracking and has been rated as medium difficulty.
The objective is to determine if it's possible to use a given set of matchsticks to construct a perfect square.
Each matchstick can be used only once, and you cannot break or cut them.
We will provide a Python solution that efficiently solves this problem.
Problem Overview
Given an integer array matchsticks, where matchsticks[i] represents the length of the ith matchstick, we need to determine whether it's possible to use all the matchsticks to create a square.
To achieve this, we must ensure that the sum of matchstick lengths can be evenly divided into four equal sides, with each side forming a part of the square.
Example 1:
Input: matchsticks = [1,1,2,2,2]
Output: true
Explanation: You can form a square with a side length of 2, with one side using two sticks of length 1.
Example 2:
Input: matchsticks = [3,3,3,3,4]
Output: false
Explanation: It's impossible to form a square using the given matchsticks without breaking any of them.
Constraints
- 1 <=
matchsticks.length<= 15 - 1 <=
matchsticks[i]<= 10^8
Efficient Python Code Solution
Now, let's take a deep dive into the Python solution for this problem.
The key idea is to use backtracking to explore all possible combinations of matchstick placements.
Here's the Python code solution:
def makesquare(matchsticks):
# Calculate the target side length of the square
length = sum(matchsticks) // 4
sides = [0] * 4 # Initialize four sides with zero length
# If the total sum of matchsticks is not divisible by 4, it's impossible to form a square
if sum(matchsticks) % 4 != 0:
return False
# Sort matchsticks in descending order to prioritize larger matchsticks
matchsticks.sort(reverse=True)
# Backtracking function to find a valid placement of matchsticks
def backtrack(i):
if i == len(matchsticks):
return True
for j in range(4):
if sides[j] + matchsticks[i] <= length:
sides[j] += matchsticks[i]
if backtrack(i + 1):
return True
sides[j] -= matchsticks[i]
return False
return backtrack(0)
The makesquare function starts by calculating the target side length for the square.
If the sum of matchstick lengths is not divisible by 4, it returns False immediately, as it's impossible to form a square.
The matchsticks are sorted in descending order to prioritize using larger matchsticks first.
The heart of the solution lies in the backtrack function, which is a recursive backtracking algorithm.
It explores all possible combinations of placing matchsticks on the four sides of the square.
If it successfully finds a valid placement, it returns True.
The for loop in the backtrack function iterates through the four sides, checking if the current matchstick can be placed on a side without exceeding the target side length.
If it can, the matchstick is placed, and the function makes a recursive call to explore the next matchstick.
If a valid placement is found, the function returns True, indicating that a square can be formed.
If not, the placement is reversed (backtracked), and the algorithm continues to explore other possibilities.
The main function initiates the backtracking process by calling backtrack(0), starting with the first matchstick.
If the backtracking process succeeds in finding a valid placement for all matchsticks, the function returns True, indicating that it's possible to create a square.
Time and Space Complexity
The time complexity of this solution is O(4^N), where N is the number of matchsticks.
This is because, in the worst case, we explore all possible combinations of matchstick placements, and we have four choices for each matchstick.
The space complexity is O(1), as we use a fixed amount of additional space to store the target side length and the sides' lengths.
Reasoning Behind Our Approach
The approach presented in this solution efficiently solves the problem by using backtracking to explore all possible combinations of matchstick placements.
By prioritizing larger matchsticks and backtracking when a valid placement is not found, we optimize the process of finding a solution.
In summary, this solution provides an elegant and efficient way to determine whether it's possible to use a set of matchsticks to create a square, adhering to the constraints provided.
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Conclusion
In this blog post, we explored the LeetCode problem Matchsticks To Square (problem 473) and provided an efficient Python solution that uses backtracking to determine if it's possible to form a square with a given set of matchsticks.
We discussed the problem overview, constraints, and provided a detailed explanation of the solution's code.
If you found this blog post helpful or have any questions or suggestions, please feel free to comment below.
We encourage your participation and sharing of this content to help others looking for solutions to similar problems.
For the full problem description and to practice solving it on LeetCode, you can find the question here.
Happy coding!
