48. Rotate Image

At a Glance

• Topic: arrays-hashing
• Pattern: Transpose + reverse rows (90° clockwise)
• Difficulty: Medium
• Companies: Amazon, Google, Meta, Microsoft, Apple
• Frequency: High
• LeetCode: 48

Problem (one-liner)

Given an n × n matrix grid, rotate the image 90 degrees clockwise in-place.

Recognition Cues

• "Rotate image 90° clockwise", "in-place"
• Transpose across main diagonal, then reverse each row — or reverse columns then transpose for CCW

Diagram

At-a-glance flow (replace with problem-specific Mermaid as you refine this note). camelCase node IDs; no spaces in IDs.

Approaches

• Brute force — copy to new matrix with mapping (row,col) -> (col, n-1-row) — O(n²) space.
• Better — rotate four cells at a time layer by layer — O(1) extra.
• Optimal — transpose + reverse each row — O(n²) time / O(1) extra — simple to code.

Optimal Solution

Go

package main

func rotate(grid [][]int) {
	length := len(grid)
	for row := 0; row < length; row++ {
		for col := row + 1; col < length; col++ {
			grid[row][col], grid[col][row] = grid[col][row], grid[row][col]
		}
	}
	for row := 0; row < length; row++ {
		left := 0
		right := length - 1
		for left < right {
			grid[row][left], grid[row][right] = grid[row][right], grid[row][left]
			left++
			right--
		}
	}
}

JavaScript

function rotate(grid) {
	const length = grid.length;
	for (let row = 0; row < length; row++) {
		for (let col = row + 1; col < length; col++) {
			[grid[row][col], grid[col][row]] = [grid[col][row], grid[row][col]];
		}
	}
	for (let row = 0; row < length; row++) {
		let left = 0;
		let right = length - 1;
		while (left < right) {
			[grid[row][left], grid[row][right]] = [grid[row][right], grid[row][left]];
			left++;
			right--;
		}
	}
}

Walkthrough

grid = [[1,2,3],[4,5,6],[7,8,9]]

Final clockwise 90° layout achieved.

Edge Cases

• n = 1 — no-op.
• Even vs odd n — same algorithm.

Pitfalls

• Mixing transpose indices — only swap col > row to avoid double swap.
• Counter-clockwise rotation uses different pair of operations.

Similar Problems

• 054. Spiral Matrix — boundary traversal.
• 189. Rotate Array — 1D rotation analogue.
• 036. Valid Sudoku — grid indexing.

Variants

• Rotate by 180° — double apply or reverse all rows then columns.
• Rectangular matrix — four-way cycle rotation.

Mind-Map Tags

#matrix #transpose #reverse #in-place #geometry