112 lines
2.9 KiB
Markdown
112 lines
2.9 KiB
Markdown
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---
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id: 5e4ce2a1ac708cc68c1df25d
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title: Long multiplication
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challengeType: 5
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forumTopicId: 385269
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dashedName: long-multiplication
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---
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# --description--
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Explicitly implement [long multiplication](https://en.wikipedia.org/wiki/long multiplication).
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This is one possible approach to arbitrary-precision integer algebra.
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# --instructions--
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Write a function that takes two strings of large numbers as parameters. Your function should return the product of these two large numbers as a string.
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**Note:** In JavaScript, arithmetic operations are inaccurate with large numbers, so you will have to implement precise multiplication yourself.
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# --hints--
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`mult` should be a function.
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```js
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assert(typeof mult == 'function');
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```
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`mult("18446744073709551616", "18446744073709551616")` should return a string.
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```js
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assert(typeof mult('18446744073709551616', '18446744073709551616') == 'string');
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```
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`mult("18446744073709551616", "18446744073709551616")` should return `"340282366920938463463374607431768211456"`.
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```js
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assert.equal(
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mult('18446744073709551616', '18446744073709551616'),
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'340282366920938463463374607431768211456'
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);
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```
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`mult("31844674073709551616", "1844674407309551616")` should return `"58743055272886011737990786529368211456"`.
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```js
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assert.equal(
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mult('31844674073709551616', '1844674407309551616'),
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'58743055272886011737990786529368211456'
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);
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```
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`mult("1846744073709551616", "44844644073709551616")` should return `"82816580680737279241781007431768211456"`.
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```js
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assert.equal(
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mult('1846744073709551616', '44844644073709551616'),
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'82816580680737279241781007431768211456'
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);
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```
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`mult("1844674407370951616", "1844674407709551616")` should return `"3402823669833978308014392742590611456"`.
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```js
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assert.equal(
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mult('1844674407370951616', '1844674407709551616'),
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'3402823669833978308014392742590611456'
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);
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```
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`mult("2844674407370951616", "1844674407370955616")` should return `"5247498076580334548376218009219475456"`.
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```js
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assert.equal(
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mult('2844674407370951616', '1844674407370955616'),
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'5247498076580334548376218009219475456'
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);
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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 mult(strNum1, strNum2) {
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}
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```
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# --solutions--
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```js
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function mult(strNum1, strNum2) {
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var a1 = strNum1.split("").reverse();
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var a2 = strNum2.toString().split("").reverse();
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var aResult = new Array;
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for ( var iterNum1 = 0; iterNum1 < a1.length; iterNum1++ ) {
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for ( var iterNum2 = 0; iterNum2 < a2.length; iterNum2++ ) {
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var idxIter = iterNum1 + iterNum2; // Get the current array position.
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aResult[idxIter] = a1[iterNum1] * a2[iterNum2] + ( idxIter >= aResult.length ? 0 : aResult[idxIter] );
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if ( aResult[idxIter] > 9 ) { // Carrying
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aResult[idxIter + 1] = Math.floor( aResult[idxIter] / 10 ) + ( idxIter + 1 >= aResult.length ? 0 : aResult[idxIter + 1] );
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aResult[idxIter] %= 10;
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}
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}
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}
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return aResult.reverse().join("");
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}
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```
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