---
id: 5a23c84252665b21eecc7e06
title: Cut a rectangle
challengeType: 5
forumTopicId: 302242
---
## Description
A given rectangle is made from m × n squares. If m and n are not both odd, then it is possible to cut a path through the rectangle along the square edges such that the rectangle splits into two connected pieces with the same shape (after rotating one of the pieces by 180°). All such paths for 2 × 2 and 4 × 3 rectangles are shown below.
## Instructions
Write a function that calculates the number of different ways to cut an m × n rectangle.
## Tests
```yml
tests:
- text: cutRectangle should be a function.
testString: assert(typeof cutRectangle == 'function');
- text: cutRectangle(2, 2) should return a number.
testString: assert(typeof cutRectangle(2, 2) == 'number');
- text: cutRectangle(2, 2) should return 2.
testString: assert.equal(cutRectangle(2, 2), 2);
- text: cutRectangle(4, 3) should return 9.
testString: assert.equal(cutRectangle(4, 3), 9);
- text: cutRectangle(4, 4) should return 22.
testString: assert.equal(cutRectangle(4, 4), 22);
- text: cutRectangle(8, 3) should return 53.
testString: assert.equal(cutRectangle(8, 3), 53);
- text: cutRectangle(7, 4) should return 151.
testString: assert.equal(cutRectangle(7, 4), 151);
```
## Challenge Seed
```js
function cutRectangle(w, h) {
}
```
## Solution
```js
function cutRectangle(w, h) {
if (w % 2 == 1 && h % 2 == 1) return;
var dirs = [[0, -1], [-1, 0], [0, 1], [1, 0]];
var grid = new Array(h);
for (var i = 0; i < grid.length; i++) grid[i] = new Array(w);
var stack = [];
var half = Math.floor((w * h) / 2);
var bits = Math.pow(2, half) - 1;
var result = 0;
for (; bits > 0; bits -= 2) {
for (var i = 0; i < half; i++) {
var r = Math.floor(i / w);
var c = i % w;
grid[r][c] = (bits & (1 << i)) != 0 ? 1 : 0;
grid[h - r - 1][w - c - 1] = 1 - grid[r][c];
}
stack.push(0);
grid[0][0] = 2;
var count = 1;
while (stack.length != 0) {
var pos = stack.pop();
var r = Math.floor(pos / w);
var c = pos % w;
for (var dir of dirs) {
var nextR = r + dir[0];
var nextC = c + dir[1];
if (nextR >= 0 && nextR < h && nextC >= 0 && nextC < w) {
if (grid[nextR][nextC] == 1) {
stack.push(nextR * w + nextC);
grid[nextR][nextC] = 2;
count++;
}
}
}
}
if (count == half) {
result++;
}
}
return result;
}
```