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---
id: 5a23c84252665b21eecc7e06
title: Cut a rectangle
challengeType: 5
forumTopicId: 302242
dashedName: cut-a-rectangle
---
# --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.
<div style="width: 100%; text-align: center;">
<svg xmlns="https://www.w3.org/2000/svg" xmlns:xlink="https://www.w3.org/1999/xlink" width="520" height="170" aria-hidden="true" alt="Diagram showing the possible paths for 2 by 2 and 4 by 3 rectangles">
<style>
.diagram-g { fill: none; stroke: #ccc }
.diagram-s, .diagram-s2 { fill: #bff; stroke: black; fill-opacity: .4 }
.diagram-s2 { fill: #fbf }
.diagram-d { stroke:black; fill:none}
</style>
<defs>
<g id="diagram-m">
<g id="diagram-h4">
<g id="diagram-h2">
<path id="diagram-h" d="m0 10h 640" class="diagram-g"/>
<use xlink:href="#diagram-h" transform="translate(0, 20)"/>
</g>
<use xlink:href="#diagram-h2" transform="translate(0, 40)"/>
</g>
<use xlink:href="#diagram-h4" transform="translate(0, 80)"/>
<g id="diagram-v8">
<g id="diagram-v4">
<g id="diagram-v2">
<path id="diagram-v" d="m10 0v160 m 20 0 v-160" class="diagram-g"/>
<use xlink:href="#diagram-v" transform="translate(40, 0)"/>
</g>
<use xlink:href="#diagram-v2" transform="translate(80, 0)"/>
</g>
<use xlink:href="#diagram-v4" transform="translate(160, 0)"/>
</g>
<use xlink:href="#diagram-v8" transform="translate(320, 0)"/>
</g>
<path id="diagram-b" d="m0 0h80v60h-80z" class="diagram-s"/>
</defs>
<g transform="translate(.5, .5)">
<use xlink:href="#diagram-m"/>
<g transform="translate(10, 10)">
<path d="m0 0v40h40v-40z" class="diagram-s2"/>
<path d="m20 0v40" class="diagram-d"/>
<path d="m60 0v40h40v-40z" class="diagram-s2"/>
<path d="m60 20h40" class="diagram-d"/>
<g transform="translate(120, 0)">
<use xlink:href="#diagram-b"/>
<path d="m0 20h40v20h40" class="diagram-d"/>
</g>
<g transform="translate(220, 0)">
<use xlink:href="#diagram-b"/>
<path d="m0 40h40v-20h40" class="diagram-d"/>
</g>
<g transform="translate(320, 0)">
<use xlink:href="#diagram-b"/>
<path d="m20 0v40h20v-20h20v40" class="diagram-d"/>
</g>
<g transform="translate(420, 0)">
<use xlink:href="#diagram-b"/>
<path d="m60 0v40h-20v-20h-20v40" class="diagram-d"/>
</g>
<g transform="translate(20, 80)">
<use xlink:href="#diagram-b"/>
<path d="m40 0v60" class="diagram-d"/>
</g>
<g transform="translate(120, 80)">
<use xlink:href="#diagram-b"/>
<path d="m60 0v20h-20v20h-20v20" class="diagram-d"/>
</g>
<g transform="translate(220, 80)">
<use xlink:href="#diagram-b"/>
<path d="m20 0v20h20v20h20v20" class="diagram-d"/>
</g>
<g transform="translate(320, 80)">
<use xlink:href="#diagram-b"/>
<path d="m0 20h20v20h20v-20h20v20h20" class="diagram-d"/>
</g>
<g transform="translate(420, 80)">
<use xlink:href="#diagram-b"/>
<path d="m0 40h20v-20h20v20h20v-20h20" class="diagram-d"/>
</g>
</g>
</g>
</svg>
</div>
# --instructions--
Write a function that calculates the number of different ways to cut an *m* × *n* rectangle.
# --hints--
`cutRectangle` should be a function.
```js
assert(typeof cutRectangle == 'function');
```
`cutRectangle(2, 2)` should return a number.
```js
assert(typeof cutRectangle(2, 2) == 'number');
```
`cutRectangle(2, 2)` should return `2`.
```js
assert.equal(cutRectangle(2, 2), 2);
```
`cutRectangle(4, 3)` should return `9`.
```js
assert.equal(cutRectangle(4, 3), 9);
```
`cutRectangle(4, 4)` should return `22`.
```js
assert.equal(cutRectangle(4, 4), 22);
```
`cutRectangle(8, 3)` should return `53`.
```js
assert.equal(cutRectangle(8, 3), 53);
```
`cutRectangle(7, 4)` should return `151`.
```js
assert.equal(cutRectangle(7, 4), 151);
```
# --seed--
## --seed-contents--
```js
function cutRectangle(w, h) {
}
```
# --solutions--
```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;
}
```