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---
id: 5a23c84252665b21eecc7e06
title: Cut a rectangle
challengeType: 5
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forumTopicId: 302242
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dashedName: cut-a-rectangle
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---
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# --description--
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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.
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< div style = "width: 100%; text-align: center;" >
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< 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" >
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< style >
.g { fill: none; stroke: #ccc }
.s, .s2 { fill: #bff ; stroke: black; fill-opacity: .4 }
.s2 { fill: #fbf }
.d { stroke:black; fill:none}
< / style >
< defs > < g id = "m" >
< g id = "h4" > < g id = "h2" >
< path id = "h" d = "m0 10h 640" class = "g" / >
< use xlink:href = "#h" transform = "translate(0,20)" / > < / g >
< use xlink:href = "#h2" transform = "translate(0, 40)" / > < / g >
< use xlink:href = "#h4" transform = "translate(0,80)" / >
< g id = "v8" > < g id = "v4" > < g id = "v2" >
< path id = "v" d = "m10 0v160 m 20 0 v-160" class = "g" / >
< use xlink:href = "#v" transform = "translate(40,0)" / > < / g >
< use xlink:href = "#v2" transform = "translate(80,0)" / > < / g >
< use xlink:href = "#v4" transform = "translate(160,0)" / > < / g >
< use xlink:href = "#v8" transform = "translate(320,0)" / > < / g >
< path id = "b" d = "m0 0h80v60h-80z" class = "s" / >
< / defs >
< g transform = "translate(.5,.5)" >
< use xlink:href = "#m" / >
< g transform = "translate(10,10)" >
< path d = "m0 0v40h40v-40z" class = "s2" / > < path d = "m20 0v40" class = "d" / >
< path d = "m60 0v40h40v-40z" class = "s2" / > < path d = "m60 20h40" class = "d" / >
< g transform = "translate(120, 0)" >
< use xlink:href = "#b" / > < path d = "m0 20h40v20h40" class = "d" / > < / g >
< g transform = "translate(220, 0)" >
< use xlink:href = "#b" / > < path d = "m0 40h40v-20h40" class = "d" / > < / g >
< g transform = "translate(320, 0)" >
< use xlink:href = "#b" / > < path d = "m20 0v40h20v-20h20v40" class = "d" / > < / g >
< g transform = "translate(420, 0)" >
< use xlink:href = "#b" / > < path d = "m60 0v40h-20v-20h-20v40" class = "d" / > < / g >
< g transform = "translate(20, 80)" >
< use xlink:href = "#b" / > < path d = "m40 0v60" class = "d" / > < / g >
< g transform = "translate(120, 80)" >
< use xlink:href = "#b" / > < path d = "m60 0v20h-20v20h-20v20" class = "d" / > < / g >
< g transform = "translate(220, 80)" >
< use xlink:href = "#b" / > < path d = "m20 0v20h20v20h20v20" class = "d" / > < / g >
< g transform = "translate(320, 80)" >
< use xlink:href = "#b" / > < path d = "m0 20h20v20h20v-20h20v20h20" class = "d" / > < / g >
< g transform = "translate(420, 80)" >
< use xlink:href = "#b" / > < path d = "m0 40h20v-20h20v20h20v-20h20" class = "d" / > < / g >
< / g > < / g >
< / svg >
< / div >
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# --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');
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```
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`cutRectangle(2, 2)` should return a number.
```js
assert(typeof cutRectangle(2, 2) == 'number');
```
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`cutRectangle(2, 2)` should return `2` .
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```js
assert.equal(cutRectangle(2, 2), 2);
```
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`cutRectangle(4, 3)` should return `9` .
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```js
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assert.equal(cutRectangle(4, 3), 9);
```
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`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);
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```
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# --seed--
## --seed-contents--
```js
function cutRectangle(w, h) {
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}
```
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# --solutions--
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```js
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function cutRectangle(w, h) {
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if (w % 2 == 1 & & h % 2 == 1) return;
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var dirs = [[0, -1], [-1, 0], [0, 1], [1, 0]];
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var grid = new Array(h);
for (var i = 0; i < grid.length ; i + + ) grid [ i ] = new Array ( w ) ;
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var stack = [];
var half = Math.floor((w * h) / 2);
var bits = Math.pow(2, half) - 1;
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var result = 0;
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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;
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while (stack.length != 0) {
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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;
}
```