58 lines
1.6 KiB
Markdown
58 lines
1.6 KiB
Markdown
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---
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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: 5
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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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In the example below, it can be easily verified that the marked triangle satisfies this condition having a sum of −42.
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We wish to make such a triangular array with one thousand rows, so we generate 500500 pseudo-random numbers sk in the range ±219, using a type of random number generator (known as a Linear Congruential Generator) as follows: t := 0
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for k = 1 up to k = 500500:
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t := (615949\*t + 797807) modulo 220 sk := t−219 Thus: s1 = 273519, s2 = −153582, s3 = 450905 etc Our triangular array is then formed using the pseudo-random numbers thus:
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s1 s2 s3 s4 s5 s6
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s7 s8 s9 s10 ...
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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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`euler150()` should return -271248680.
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```js
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assert.strictEqual(euler150(), -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 euler150() {
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return true;
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}
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euler150();
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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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