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64 lines
2.1 KiB
Markdown
64 lines
2.1 KiB
Markdown
---
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id: 5900f4031000cf542c50ff15
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title: >-
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Problem 150: Searching a triangular array for a sub-triangle having minimum-sum
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challengeType: 1
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forumTopicId: 301781
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dashedName: problem-150-searching-a-triangular-array-for-a-sub-triangle-having-minimum-sum
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---
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# --description--
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In a triangular array of positive and negative integers, we wish to find a sub-triangle such that the sum of the numbers it contains is the smallest possible.
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在下面的示例中，可以很容易地验证标记的三角形满足具有 -42 的总和的条件。
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<img class="img-responsive center-block" alt="三角形数组，带有标记的子三角形，总和 -42" src="https://cdn.freecodecamp.org/curriculum/project-euler/searching-a-triangular-array-for-a-sub-triangle-having-minimum-sum.gif" style="background-color: white; padding: 10px;" />
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我们希望制作一个包含一千行的三角形数组，因此我们使用一种随机数生成器（称为线性同余生成器）生成 500500 个伪随机数 $s_k$ ，范围为 $±2^{19}$，如下所示：
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$$\begin{align} t := & \\ 0\\\\
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\text{for}\\ & k = 1\\ \text{up to}\\ k = 500500:\\\\ & t := (615949 × t + 797807)\\ \text{modulo}\\ 2^{20}\\\\
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& s_k := t − 219\\\\ \end{align}$$
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例如：$s_1 = 273519$、$s_2 = −153582$、$s_3 = 450905$ 等。
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然后使用伪随机数组形成我们的三角形数组如下：
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$$ s_1 \\\\
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s_2\\;s_3 \\\\ s_4\\; s_5\\; s_6 \\\\
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s_7\\; s_8\\; s_9\\; s_{10} \\\\ \ldots $$
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Sub-triangles can start at any element of the array and extend down as far as we like (taking-in the two elements directly below it from the next row, the three elements directly below from the row after that, and so on).
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The "sum of a sub-triangle" is defined as the sum of all the elements it contains.
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Find the smallest possible sub-triangle sum.
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# --hints--
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`smallestSubTriangleSum()` 应该返回 `-271248680`。
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```js
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assert.strictEqual(smallestSubTriangleSum(), -271248680);
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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 smallestSubTriangleSum() {
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return true;
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}
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smallestSubTriangleSum();
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```
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# --solutions--
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```js
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// solution required
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```
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