Abstract / Summary

Given a square matrix, rotate its elements ninety degrees clockwise in place.

Note

The full problem description, including helpful examples, can be found on LeetCode.

This problem is ranked as

and has an acceptance rate of about 81% (3+ million submissions).

Typical patterns to solve this problem:

• Array
• Math
• Matrix

Every single line of code was written by me, 100% from scratch, between August 2023 and August 2024.
However, two years later I set up this website and used various AI tools to generate most of the walkthrough / explanations below.

See this dedicated page for more details.

Overview

The provided rotate method implements an in-place 90-degree clockwise rotation of a square matrix represented as a vector<vector<int>>. The algorithm works by moving elements in groups of four, effectively rotating the outer layer first and then proceeding inward. All operations are performed directly on the input matrix, eliminating the need for auxiliary storage.

Key Steps

Determining matrix dimensions

int size = matrix.size();
int m    = size - 1;

The variable size holds the length of one side of the square matrix. The helper m represents the index of the last row or column, simplifying later calculations that reference the opposite side of the matrix.

Iterating over the upper-left quadrant

for (int x = 0; x < (size+1)/2; x++)
    for (int y = 0; y < size/2; y++)
    {
        // rotation logic
    }

Two nested loops traverse only the cells that belong to the upper-left quadrant of the matrix. The outer loop runs up to the middle row (rounded up for odd sizes), while the inner loop runs up to the middle column (rounded down). This selection guarantees that each group of four cells is visited exactly once.

Performing the four-way swap

int tmp = matrix[x][y];
matrix[  x][  y] = matrix[m-y][  x];
matrix[m-y][  x] = matrix[m-x][m-y];
matrix[m-x][m-y] = matrix[  y][m-x];
matrix[  y][m-x] = tmp;

A temporary variable stores the value at the current position (x, y). The subsequent assignments rotate the values from the left side to the top, from the bottom to the left, from the right to the bottom, and finally place the saved top value into the right side. The use of direct index arithmetic (m - y, m - x) maps each position to its counterpart after a 90-degree rotation.

Edge Cases Handled

When the matrix is empty (size == 0), the outer loop condition evaluates to false, and the function exits without performing any work. For a single-element matrix (size == 1), the inner loop range becomes zero, so no swaps occur, leaving the matrix unchanged as expected. The loop bounds also correctly handle both even and odd dimensions, ensuring that the central row or column in odd-sized matrices is not processed redundantly.

Performance Optimizations

The algorithm achieves in-place transformation, requiring only a single integer temporary variable regardless of matrix size. By limiting iteration to half the rows and half the columns, the number of processed elements is reduced to exactly one quarter of the total cells, which is the theoretical minimum for a four-way rotation. The use of simple arithmetic for index calculation avoids function calls or additional data structures, keeping the inner loop tight and cache-friendly. This design results in a fast execution path that scales linearly with the number of elements in the matrix.

Imagine a square puzzle board filled with colorful tiles. The goal is to turn the whole board to the right, just like how you might spin a plate on a table. To do this, the computer looks at the tiles in groups of four. It picks up one tile at a time and moves it to a new spot, then moves the next one into the empty hole, and keeps doing this until every corner and middle piece has traveled to its new home. It uses a temporary storage spot to hold one tile while it swaps the others around in a circle. By repeating this little dance, every single tile ends up in the perfect position to make the whole square look like it has been rotated.

Several LLMs ranked my code quality on a scale from 1 (very poor) to 10 (outstanding):

Time: polynomial
As a rule of thumb, the maximum input size for one second execution time is

• factorial: up to 10 elements
• exponential: up to 20 elements
• polynomial: a few thousand elements
• loglinear: up to 100,000 elements
• linear: a few million elements
• logarithmic: a billion elements
• constant: practically unlimited

I wrote a basic crawler to find other solutions to that problem.
Obviously, I did that after I solved the problem myself.

In general, AlgoMonster and WalkCCC solutions are high-quality and always worth a look.
I haven't checked most of the other solutions, but they might be helpful as well.

And of course, the LeetCode forum is always a good place (or even the best) to look for alternative approaches.

(click on a column header to sort the table)

	author
author	solutions
www	AlgoMonster	C++	Python		Java							TS
	WalkCCC	C++	Python		Java
	leetcode.ca	C++	Python	C#	Java		Rust	JS	Go			TS
	LeetcodeHelp	C++	Python		Java
	MemoryLimitExceeded	C++	Python
	Progiez	C++	Python		Java
github	AdelDaniel										Dart
	aylei						Rust
	begeekmyfriend					C
	BigEggStudy			C#
	black-shadows	C++
	chandansgowda		Python
	charles-wangkai				Java
	chenyanzhe	C++
	everthis							JS
	fartem									Ruby
	FelixFan1122			C#
	fengvyi	C++
	fpdjsns	C++
	gaosq0604		Python
	Garvit244		Python
	halfrost								Go
	haoel	C++
	JoshCrozier							JS
	keineahnung2345	C++
	lennylxx					C
	linouk23	C++
	lkwq007		Python
	luangong	C++
	MacJim	C++
	muhammadfarhankt								Go
	pruthvikp		Python
	qiyuangong		Python
	ruoru						Rust
	shreymehul			C#
	sonugiri1043	C++
	suxrobGM			C#
	trung-hn		Python
	varunu28				Java
	vli02					C
	vthwang				Java
	wisdompeak		Python
	withaarzoo	C++
	XiaotaoGuo	C++
	YuriSpiridonov		Python
	zfang399	C++
AlgoMonster	C++, Python, Java, TypeScript
WalkCCC	C++, Python, Java
leetcode.ca	C++, C#, Go, Java, JavaScript, Python, Rust, TypeScript
LeetcodeHelp	C++, Java, Python
MemoryLimitExceeded	Python, C++
Progiez	C++, Java, Python
AdelDaniel	Dart
aylei	Rust
begeekmyfriend	C
BigEggStudy	C#
black-shadows	C++, C++
chandansgowda	Python
charles-wangkai	Java
chenyanzhe	C++
everthis	JavaScript
fartem	Ruby
FelixFan1122	C#
fengvyi	C++
fpdjsns	C++
gaosq0604	Python
Garvit244	Python
halfrost	Go
haoel	C++
JoshCrozier	JavaScript
keineahnung2345	C++
lennylxx	C
linouk23	C++
lkwq007	Python
luangong	C++
MacJim	C++
muhammadfarhankt	Go
pruthvikp	Python
qiyuangong	Python
ruoru	Rust
shreymehul	C#
sonugiri1043	C++
suxrobGM	C#
trung-hn	Python
varunu28	Java
vli02	C
vthwang	Java
wisdompeak	Python
withaarzoo	C++
XiaotaoGuo	C++
YuriSpiridonov	Python
zfang399	C++

There are a few extra pages giving you some insights into my setup:

• Tech Stack - my development environment and tools
• AI - how AI helped me create this website (NOT solving the problems)
• Progress - progression over time
• Quality - code quality