58 lines
1.6 KiB
Markdown
58 lines
1.6 KiB
Markdown
---
|
||
id: 5900f4031000cf542c50ff15
|
||
title: >-
|
||
Problem 150: Searching a triangular array for a sub-triangle having minimum-sum
|
||
challengeType: 5
|
||
forumTopicId: 301781
|
||
dashedName: problem-150-searching-a-triangular-array-for-a-sub-triangle-having-minimum-sum
|
||
---
|
||
|
||
# --description--
|
||
|
||
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.
|
||
|
||
In the example below, it can be easily verified that the marked triangle satisfies this condition having a sum of −42.
|
||
|
||
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
|
||
|
||
for k = 1 up to k = 500500:
|
||
|
||
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:
|
||
|
||
s1 s2 s3 s4 s5 s6
|
||
|
||
s7 s8 s9 s10 ...
|
||
|
||
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).
|
||
|
||
The "sum of a sub-triangle" is defined as the sum of all the elements it contains.
|
||
|
||
Find the smallest possible sub-triangle sum.
|
||
|
||
# --hints--
|
||
|
||
`euler150()` should return -271248680.
|
||
|
||
```js
|
||
assert.strictEqual(euler150(), -271248680);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function euler150() {
|
||
|
||
return true;
|
||
}
|
||
|
||
euler150();
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
// solution required
|
||
```
|