Largest Magic Square — LeetCode 1895 Python Solution
MediumArrayMatrixPrefix Sum
- Problem
- #1895
- Pattern
- Prefix Sum
- Reading time
- 8 min
- Source
- leetcode.com
The problem
A k x k magic square is a k x k grid filled with integers such that every row sum, every column sum, and both diagonal sums are all equal. The integers in the magic square do not have to be distinct.
Example
- Input
- grid = [[7,1,4,5,6],[2,5,1,6,4],[1,5,4,3,2],[1,2,7,3,4]]
- Output
- 3
- Explanation
- The largest magic square has a size of 3.
Python solution
Python
class Solution:
def largestMagicSquare(self, grid: List[List[int]]) -> int:
m, n = len(grid), len(grid[0])
rowsum = [[0] * (n + 1) for _ in range(m + 1)]
colsum = [[0] * (n + 1) for _ in range(m + 1)]
for i in range(1, m + 1):
for j in range(1, n + 1):
rowsum[i][j] = rowsum[i][j - 1] + grid[i - 1][j - 1]
colsum[i][j] = colsum[i - 1][j] + grid[i - 1][j - 1]
def check(x1, y1, x2, y2):
val = rowsum[x1 + 1][y2 + 1] - rowsum[x1 + 1][y1]
for i in range(x1 + 1, x2 + 1):
if rowsum[i + 1][y2 + 1] - rowsum[i + 1][y1] != val:
return False
for j in range(y1, y2 + 1):
if colsum[x2 + 1][j + 1] - colsum[x1][j + 1] != val:
return False
s, i, j = 0, x1, y1
while i <= x2:
s += grid[i][j]
i += 1
j += 1
if s != val:
return False
s, i, j = 0, x1, y2
while i <= x2:
s += grid[i][j]
i += 1
j -= 1
if s != val:
return False
return True
for k in range(min(m, n), 1, -1):
i = 0
while i + k - 1 < m:
j = 0
while j + k - 1 < n:
i2, j2 = i + k - 1, j + k - 1
if check(i, j, i2, j2):
return k
j += 1
i += 1
return 1Complexity
| Measure | Complexity |
|---|---|
| Time | O(m \times n \times \min(m, n)^2) |
| Space | O(m \times n) auxiliary |
Pattern: Prefix Sum
Precompute running totals once so any range query becomes a single subtraction. LeetCode 1895. Largest Magic Square is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Prefix Sum.
The prefix sum guide has the Python template for the pattern and the 157 LeetCode problems that use it.
Related problems
Frequently asked questions
- How hard is LeetCode 1895. Largest Magic Square?
- LeetCode 1895. Largest Magic Square is rated Medium on LeetCode.
- What is the time complexity of LeetCode 1895. Largest Magic Square?
- The Python solution on this page runs in O(m \times n \times \min(m, n)^2).
- What is the space complexity of LeetCode 1895. Largest Magic Square?
- The Python solution on this page uses O(m \times n) auxiliary space.
- What topics does LeetCode 1895. Largest Magic Square cover?
- LeetCode 1895. Largest Magic Square is tagged Array, Matrix and Prefix Sum on LeetCode.