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---
id: 5a23c84252665b21eecc7e06
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title: 長方形を切る
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challengeType: 5
forumTopicId: 302242
dashedName: cut-a-rectangle
---
# --description--
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長方形が *m* × *n* の正方形から作られているとします。 *m* と *n* が両方とも奇数でない場合、(片方を180°回転させて) 長方形が同じ形状のつながった2ピースに分割されるように、正方形の端に沿って長方形を切ることができます。 以下のように、2 × 2 と 4 × 3 の長方形を切ります。
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< 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--
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*m* × *n* の長方形の切り方が何通りあるかを計算する関数を作成します。
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# --hints--
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`cutRectangle` という関数です。
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```js
assert(typeof cutRectangle == 'function');
```
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`cutRectangle(2, 2)` は数字を返します。
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```js
assert(typeof cutRectangle(2, 2) == 'number');
```
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`cutRectangle(2, 2)` は `2` を返します。
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```js
assert.equal(cutRectangle(2, 2), 2);
```
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`cutRectangle(4, 3)` は `9` を返します。
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```js
assert.equal(cutRectangle(4, 3), 9);
```
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`cutRectangle(4, 4)` は `22` を返します。
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```js
assert.equal(cutRectangle(4, 4), 22);
```
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`cutRectangle(8, 3)` は `53` を返します。
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```js
assert.equal(cutRectangle(8, 3), 53);
```
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`cutRectangle(7, 4)` は `151` を返します。
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```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;
}
```