94 lines
3.9 KiB
Markdown
94 lines
3.9 KiB
Markdown
---
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id: 5900f37e1000cf542c50fe91
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challengeType: 5
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title: 'Problem 18: Maximum path sum I'
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forumTopicId: 301815
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localeTitle: 'Задача 18: максимальная длина пути I'
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---
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## Description
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<section id='description'>
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Начав в верхней части треугольника внизу и перемещаясь к соседним номерам в строке ниже, максимальная сумма сверху вниз составляет 23. <span style="display: block; text-align: center;"><b style="color: red;">3</b> <br> <b style="color: red;">7</b> 4 <br> 2 <b style="color: red;">4</b> 6 <br> 8 5 <b style="color: red;">9</b> 3</span> То есть, 3 + 7 + 4 + 9 = 23. Найдите максимальную сумму сверху вниз от треугольника ниже: <span style="display: block; text-align: center;">75 <br> 95 64 <br> 17 47 82 <br> 18 35 87 10 <br> 20 04 82 47 65 <br> 19 01 23 75 03 34 <br> 88 02 77 73 07 63 67 <br> 99 65 04 28 06 16 70 92 <br> 41 41 26 56 83 40 80 70 33 <br> 41 48 72 33 47 32 37 16 94 29 <br> 53 71 44 65 25 43 91 52 97 51 14 <br> 70 11 33 28 77 73 17 78 39 68 17 57 <br> 91 71 52 38 17 14 91 43 58 50 27 29 48 <br> 63 66 04 68 89 53 67 30 73 16 69 87 40 31 <br> 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23</span> <b>ПРИМЕЧАНИЕ.</b> Поскольку существует только 16384 маршрута, можно решить эту проблему, пробовав каждый маршрут. Однако задача 67 - это та же проблема с треугольником, содержащим сто строк; она не может быть решена грубой силой и требует умного метода! ; О)
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</section>
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## Instructions
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<section id='instructions'>
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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>maximumPathSumI(testTriangle)</code> should return 23.
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testString: assert.strictEqual(maximumPathSumI(testTriangle), 23);
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- text: <code>maximumPathSumI(numTriangle)</code> should return 1074.
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testString: assert.strictEqual(maximumPathSumI(numTriangle), 1074);
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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 maximumPathSumI(triangle) {
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// Good luck!
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return true;
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}
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const testTriangle = [[3, 0, 0, 0],
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[7, 4, 0, 0],
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[2, 4, 6, 0],
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[8, 5, 9, 3]];
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maximumPathSumI(testTriangle);
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```
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</div>
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### Before Tests
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<div id='js-setup'>
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```js
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const numTriangle = [[75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [95, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [17, 47, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [18, 35, 87, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [20, 4, 82, 47, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [19, 1, 23, 75, 3, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0], [88, 2, 77, 73, 7, 63, 67, 0, 0, 0, 0, 0, 0, 0, 0], [99, 65, 4, 28, 6, 16, 70, 92, 0, 0, 0, 0, 0, 0, 0], [41, 41, 26, 56, 83, 40, 80, 70, 33, 0, 0, 0, 0, 0, 0], [41, 48, 72, 33, 47, 32, 37, 16, 94, 29, 0, 0, 0, 0, 0], [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14, 0, 0, 0, 0], [70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57, 0, 0, 0], [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48, 0, 0], [63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31, 0], [4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]];
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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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const testTriangle = [[3, 0, 0, 0],
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[7, 4, 0, 0],
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[2, 4, 6, 0],
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[8, 5, 9, 3]];
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function maximumPathSumI(triangle) {
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let maxSum = triangle.slice();
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for (let i = triangle.length - 1; i > 0; i--) {
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let currentRow = maxSum[i];
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let previousRow = maxSum[i - 1];
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const temp = [];
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for (let j = 0; j < i; j++) {
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temp.push(Math.max((currentRow[j] + previousRow[j]), (currentRow[j + 1] + previousRow[j])));
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}
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maxSum[i - 1] = temp;
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maxSum.pop();
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}
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return maxSum[0][0];
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}
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```
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</section>
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