ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
80 lines
1.2 KiB
Markdown
80 lines
1.2 KiB
Markdown
---
|
||
id: 5900f3881000cf542c50fe9b
|
||
title: 问题28：对角螺旋数
|
||
challengeType: 5
|
||
videoUrl: ''
|
||
dashedName: problem-28-number-spiral-diagonals
|
||
---
|
||
|
||
# --description--
|
||
|
||
从数字1开始，沿顺时针方向向右移动，形成5 x 5螺旋，如下所示：
|
||
|
||
21 22 23 24 25
|
||
|
||
20 7 8 9 10
|
||
|
||
19 6 1 2 11
|
||
|
||
18 5 4 3 12
|
||
|
||
17 16 15 14 13
|
||
|
||
可以验证对角线上的数字之和为101。
|
||
|
||
以相同方式形成的n×n螺旋中的对角线上的数字的总和是多少？
|
||
|
||
# --hints--
|
||
|
||
`spiralDiagonals(101)`应该返回692101。
|
||
|
||
```js
|
||
assert(spiralDiagonals(101) == 692101);
|
||
```
|
||
|
||
`spiralDiagonals(101)`应该返回18591725。
|
||
|
||
```js
|
||
assert(spiralDiagonals(303) == 18591725);
|
||
```
|
||
|
||
`spiralDiagonals(101)`应该返回85986601。
|
||
|
||
```js
|
||
assert(spiralDiagonals(505) == 85986601);
|
||
```
|
||
|
||
`spiralDiagonals(101)`应该返回669171001。
|
||
|
||
```js
|
||
assert(spiralDiagonals(1001) == 669171001);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function spiralDiagonals(n) {
|
||
|
||
return n;
|
||
}
|
||
|
||
spiralDiagonals(1001);
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
const spiralDiagonals = (n) => {
|
||
const Sn2 = (n) => {
|
||
return n*(n+1)*(2*n+1)/6;
|
||
};
|
||
const Sn = (n) => {
|
||
return n*(n+1)/2;
|
||
};
|
||
let sum = (Sn2(n-1) + Sn(n-1) + n-1) + (Math.floor(n/2) + Sn2(n));
|
||
return sum;
|
||
};
|
||
```
|