83 lines
3.3 KiB
Markdown
83 lines
3.3 KiB
Markdown
---
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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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---
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## Description
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<section id='description'>
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Explicitly implement <a href="https://en.wikipedia.org/wiki/long multiplication">long multiplication</a>.
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This is one possible approach to arbitrary-precision integer algebra.
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</section>
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## Instructions
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<section id='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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<strong>Note:</strong> In JavaScript, arithmetic operations are inaccurate with large numbers, so you will have to implement precise multiplication yourself.
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</section>
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## Tests
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<section id='tests'>
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``` yml
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tests:
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- text: <code>mult</code> should be a function.
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testString: assert(typeof mult == 'function');
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- text: <code>mult("18446744073709551616", "18446744073709551616")</code> should return a string.
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testString: assert(typeof mult("18446744073709551616", "18446744073709551616") == 'string');
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- text: <code>mult("18446744073709551616", "18446744073709551616")</code> should return <code>"340282366920938463463374607431768211456"</code>.
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testString: assert.equal(mult("18446744073709551616", "18446744073709551616"), "340282366920938463463374607431768211456");
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- text: <code>mult("31844674073709551616", "1844674407309551616")</code> should return <code>"58743055272886011737990786529368211456"</code>.
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testString: assert.equal(mult("31844674073709551616", "1844674407309551616"), "58743055272886011737990786529368211456");
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- text: <code>mult("1846744073709551616", "44844644073709551616")</code> should return <code>"82816580680737279241781007431768211456"</code>.
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testString: assert.equal(mult("1846744073709551616", "44844644073709551616"), "82816580680737279241781007431768211456");
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- text: <code>mult("1844674407370951616", "1844674407709551616")</code> should return <code>"3402823669833978308014392742590611456"</code>.
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testString: assert.equal(mult("1844674407370951616", "1844674407709551616"), "3402823669833978308014392742590611456");
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- text: <code>mult("2844674407370951616", "1844674407370955616")</code> should return <code>"5247498076580334548376218009219475456"</code>.
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testString: assert.equal(mult("2844674407370951616", "1844674407370955616"), "5247498076580334548376218009219475456");
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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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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</div>
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</section>
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## Solution
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<section id='solution'>
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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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</section>
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