gaspersic/freeCodeCamp
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

fix(curriculum): clean-up Project Euler 462-480 (#43069)

Browse Source 
* fix: clean-up Project Euler 462-480

* fix: missing image extension

* fix: corrections from review

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
This commit is contained in:
gikf
2021-07-30 17:32:21 +02:00
committed by GitHub
parent a2b2ef3f75
commit 397a9f0c3e
19 changed files with 309 additions and 240 deletions
Download Patch File Download Diff File Expand all files Collapse all files

18
curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-465-polar-polygons.md
View File

@ -14,22 +14,24 @@ For this problem, a polygon can have collinear consecutive vertices. However, a
For example, only the first of the following is a polar polygon (the kernels of the second, third, and fourth do not strictly contain the origin, and the fifth does not have a kernel at all):
<img class="img-responsive center-block" alt="five example polygons" src="https://cdn.freecodecamp.org/curriculum/project-euler/polar-polygons.png" style="background-color: white; padding: 10px;">
Notice that the first polygon has three consecutive collinear vertices.
Let P(n) be the number of polar polygons such that the vertices (x, y) have integer coordinates whose absolute values are not greater than n.
Let $P(n)$ be the number of polar polygons such that the vertices $(x, y)$ have integer coordinates whose absolute values are not greater than $n$.
Note that polygons should be counted as different if they have different set of edges, even if they enclose the same area. For example, the polygon with vertices \[(0,0),(0,3),(1,1),(3,0)] is distinct from the polygon with vertices \[(0,0),(0,3),(1,1),(3,0),(1,0)].
Note that polygons should be counted as different if they have different set of edges, even if they enclose the same area. For example, the polygon with vertices [(0,0), (0,3), (1,1), (3,0)] is distinct from the polygon with vertices [(0,0), (0,3), (1,1), (3,0), (1,0)].
For example, P(1) = 131, P(2) = 1648531, P(3) = 1099461296175 and P(343) mod 1 000 000 007 = 937293740.
For example, $P(1) = 131$, $P(2) = 1\\,648\\,531$, $P(3) = 1\\,099\\,461\\,296\\,175$ and $P(343)\bmod 1\\,000\\,000\\,007 = 937\\,293\\,740$.
Find P(713) mod 1 000 000 007.
Find $P(7^{13})\bmod 1\\,000\\,000\\,007$.
# --hints--
`euler465()` should return 585965659.
`polarPolygons()` should return `585965659`.
```js
assert.strictEqual(euler465(), 585965659);
assert.strictEqual(polarPolygons(), 585965659);
```
# --seed--
@ -37,12 +39,12 @@ assert.strictEqual(euler465(), 585965659);
## --seed-contents--
```js
function euler465() {
function polarPolygons() {
return true;
}
euler465();
polarPolygons();
```
# --solutions--