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>
91 lines
1.3 KiB
Markdown
91 lines
1.3 KiB
Markdown
---
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id: 5900f3721000cf542c50fe85
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title: 问题6：求和方差
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challengeType: 5
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videoUrl: ''
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dashedName: problem-6-sum-square-difference
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---
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# --description--
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前十个自然数的平方和是，
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1
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<sup>2</sup>
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- 2
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<sup>2</sup>
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- ... + 10
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<sup>2</sup>
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= 385
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前十个自然数之和的平方是，
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（1 + 2 + ... + 10）
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<sup>2</sup>
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= 55
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<sup>2</sup>
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= 3025
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因此，前十个自然数的平方和与和的平方之间的差值为3025 - 385 = 2640.求出前`n`自然数的平方和与总和的平方之间的差值。
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# --hints--
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`sumSquareDifference(10)`应该返回2640。
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```js
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assert.strictEqual(sumSquareDifference(10), 2640);
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```
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`sumSquareDifference(20)`应该返回41230。
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```js
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assert.strictEqual(sumSquareDifference(20), 41230);
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```
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`sumSquareDifference(100)`应该返回25164150。
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```js
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assert.strictEqual(sumSquareDifference(100), 25164150);
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```
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# --seed--
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## --seed-contents--
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```js
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function sumSquareDifference(n) {
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return true;
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}
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sumSquareDifference(100);
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```
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# --solutions--
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```js
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const sumSquareDifference = (number)=>{
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let squareOfSum = Math.pow(sumOfArithmeticSeries(1,1,number),2);
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let sumOfSquare = sumOfSquareOfNumbers(number);
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return squareOfSum - sumOfSquare;
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}
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function sumOfArithmeticSeries(a,d,n){
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return (n/2)*(2*a+(n-1)*d);
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}
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function sumOfSquareOfNumbers(n){
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return (n*(n+1)*(2*n+1))/6;
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}
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```
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