LeetCode 48: Rotate Image — Python Solution

Solve LeetCode 48: Rotate Image in Python with a transpose then reverse rows approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Transpose across the main diagonal, then reverse every row to obtain a clockwise quarter-turn in place.

Algorithm

1. Transpose across the main diagonal, then reverse every row to obtain a clockwise quarter-turn in place.
2. Maintain this invariant: After transposition and row reversal, original cell (r,c) reaches (c,n-1-r).
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def rotate(self, matrix):
        n = len(matrix)
        for r in range(n):
            for c in range(r + 1, n):
                matrix[r][c], matrix[c][r] = matrix[c][r], matrix[r][c]
        for row in matrix: row.reverse()

Why this is correct

The proof follows the maintained state: After transposition and row reversal, original cell (r,c) reaches (c,n-1-r). Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n^2) time and O(1) extra space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

The operation mutates the square matrix; a 1×1 matrix remains unchanged.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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