192 lines
5.5 KiB
Markdown
192 lines
5.5 KiB
Markdown
|
---
|
||
|
title: Topological sort
|
||
|
id: 594fa2746886f41f7d8bf225
|
||
|
challengeType: 5
|
||
|
forumTopicId: 302340
|
||
|
---
|
||
|
|
||
|
## Description
|
||
|
<section id='description'>
|
||
|
|
||
|
Given a mapping between items, and items they depend on, a <a href="https://en.wikipedia.org/wiki/Topological sorting" title="wp: Topological sorting" target="_blank">topological sort</a> orders items so that no item precedes an item it depends upon.
|
||
|
The compiling of a library in the <a href="https://en.wikipedia.org/wiki/VHDL" title="wp: VHDL" target="_blank">VHDL</a> language has the constraint that a library must be compiled after any library it depends on.
|
||
|
</section>
|
||
|
|
||
|
## Instructions
|
||
|
<section id='instructions'>
|
||
|
|
||
|
Write a function that will return a valid compile order of VHDL libraries from their dependencies.
|
||
|
<ul>
|
||
|
<li>Assume library names are single words.</li>
|
||
|
<li>Items mentioned as only dependents have no dependents of their own, but their order of compiling must be given.</li>
|
||
|
<li>Any self dependencies should be ignored.</li>
|
||
|
<li>Any un-orderable dependencies should be ignored.</li>
|
||
|
</ul>
|
||
|
Use the following data as an example:
|
||
|
<pre>
|
||
|
LIBRARY LIBRARY DEPENDENCIES
|
||
|
======= ====================
|
||
|
des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee
|
||
|
dw01 ieee dw01 dware gtech
|
||
|
dw02 ieee dw02 dware
|
||
|
dw03 std synopsys dware dw03 dw02 dw01 ieee gtech
|
||
|
dw04 dw04 ieee dw01 dware gtech
|
||
|
dw05 dw05 ieee dware
|
||
|
dw06 dw06 ieee dware
|
||
|
dw07 ieee dware
|
||
|
dware ieee dware
|
||
|
gtech ieee gtech
|
||
|
ramlib std ieee
|
||
|
std_cell_lib ieee std_cell_lib
|
||
|
synopsys
|
||
|
</pre>
|
||
|
<small>Note: the above data would be un-orderable if, for example, <code>dw04</code> is added to the list of dependencies of <code>dw01</code>.</small>
|
||
|
<strong>C.f.:</strong>
|
||
|
<ul>
|
||
|
<li><a href="https://rosettacode.org/wiki/Topological sort/Extracted top item" title="Topological sort/Extracted top item" target="_blank">Topological sort/Extracted top item</a>.</li>
|
||
|
</ul>
|
||
|
There are two popular algorithms for topological sorting:
|
||
|
<ul>
|
||
|
<li><a href="https://en.wikipedia.org/wiki/Topological sorting" title="wp: Topological sorting" target="_blank">Kahn's 1962 topological sort</a></li>
|
||
|
<li><a href="https://www.embeddedrelated.com/showarticle/799.php" target="_blank">depth-first search</a></li>
|
||
|
</ul>
|
||
|
</section>
|
||
|
|
||
|
## Tests
|
||
|
<section id='tests'>
|
||
|
|
||
|
```yml
|
||
|
tests:
|
||
|
- text: <code>topologicalSort</code> should be a function.
|
||
|
testString: assert(typeof topologicalSort === 'function');
|
||
|
- text: <code>topologicalSort</code> should return correct library order.
|
||
|
testString: assert.deepEqual(topologicalSort(libsSimple), ['bbb', 'aaa']);
|
||
|
- text: <code>topologicalSort</code> should return correct library order.
|
||
|
testString: assert.deepEqual(topologicalSort(libsVHDL), solutionVHDL);
|
||
|
- text: <code>topologicalSort</code> should return correct library order.
|
||
|
testString: assert.deepEqual(topologicalSort(libsCustom), solutionCustom);
|
||
|
- text: <code>topologicalSort</code> should ignore unorderable dependencies.
|
||
|
testString: assert.deepEqual(topologicalSort(libsUnorderable), solutionUnorderable);
|
||
|
|
||
|
```
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Challenge Seed
|
||
|
<section id='challengeSeed'>
|
||
|
|
||
|
<div id='js-seed'>
|
||
|
|
||
|
```js
|
||
|
function topologicalSort(libs) {
|
||
|
|
||
|
return true;
|
||
|
}
|
||
|
```
|
||
|
|
||
|
</div>
|
||
|
|
||
|
|
||
|
### After Test
|
||
|
<div id='js-teardown'>
|
||
|
|
||
|
```js
|
||
|
const libsSimple =
|
||
|
`aaa bbb
|
||
|
bbb`;
|
||
|
|
||
|
const libsVHDL =
|
||
|
`des_system_lib std synopsys std_cell_lib des_system_lib dw02 dw01 ramlib ieee
|
||
|
dw01 ieee dw01 dware gtech
|
||
|
dw02 ieee dw02 dware
|
||
|
dw03 std synopsys dware dw03 dw02 dw01 ieee gtech
|
||
|
dw04 dw04 ieee dw01 dware gtech
|
||
|
dw05 dw05 ieee dware
|
||
|
dw06 dw06 ieee dware
|
||
|
dw07 ieee dware
|
||
|
dware ieee dware
|
||
|
gtech ieee gtech
|
||
|
ramlib std ieee
|
||
|
std_cell_lib ieee std_cell_lib
|
||
|
synopsys`;
|
||
|
|
||
|
const solutionVHDL = [
|
||
|
'ieee', 'std_cell_lib', 'gtech', 'dware', 'dw07', 'dw06',
|
||
|
'dw05', 'dw02', 'dw01', 'dw04', 'std', 'ramlib', 'synopsys',
|
||
|
'dw03', 'des_system_lib'
|
||
|
];
|
||
|
|
||
|
const libsCustom =
|
||
|
`a b c d
|
||
|
b c d
|
||
|
d c
|
||
|
c base
|
||
|
base`;
|
||
|
const solutionCustom = ['base', 'c', 'd', 'b', 'a'];
|
||
|
|
||
|
const libsUnorderable =
|
||
|
`TestLib Base MainLib
|
||
|
MainLib TestLib
|
||
|
Base`;
|
||
|
|
||
|
const solutionUnorderable = ['Base'];
|
||
|
```
|
||
|
|
||
|
</div>
|
||
|
|
||
|
</section>
|
||
|
|
||
|
## Solution
|
||
|
<section id='solution'>
|
||
|
|
||
|
|
||
|
```js
|
||
|
function topologicalSort(libs) {
|
||
|
// A map of the input data, with the keys as the packages, and the values as
|
||
|
// and array of packages on which it depends.
|
||
|
const D = libs
|
||
|
.split('\n')
|
||
|
.map(e => e.split(' ').filter(ep => ep !== ''))
|
||
|
.reduce((p, c) =>
|
||
|
p.set(c[0], c.filter((e, i) => (i > 0 && e !== c[0] ? e : null))), new Map());
|
||
|
[].concat(...D.values()).forEach(e => {
|
||
|
D.set(e, D.get(e) || []);
|
||
|
});
|
||
|
|
||
|
// The above map rotated so that it represents a DAG of the form
|
||
|
// Map {
|
||
|
// A => [ A, B, C],
|
||
|
// B => [C],
|
||
|
// C => []
|
||
|
// }
|
||
|
// where each key represents a node, and the array contains the edges.
|
||
|
const G = [...D.keys()].reduce((p, c) =>
|
||
|
p.set(
|
||
|
c,
|
||
|
[...D.keys()].filter(e => D.get(e).includes(c))),
|
||
|
new Map()
|
||
|
);
|
||
|
|
||
|
// An array of leaf nodes; nodes with 0 in degrees.
|
||
|
const Q = [...D.keys()].filter(e => D.get(e).length === 0);
|
||
|
|
||
|
// The result array.
|
||
|
const S = [];
|
||
|
while (Q.length) {
|
||
|
const u = Q.pop();
|
||
|
S.push(u);
|
||
|
G.get(u).forEach(v => {
|
||
|
D.set(v, D.get(v).filter(e => e !== u));
|
||
|
if (D.get(v).length === 0) {
|
||
|
Q.push(v);
|
||
|
}
|
||
|
});
|
||
|
}
|
||
|
|
||
|
return S;
|
||
|
}
|
||
|
|
||
|
```
|
||
|
|
||
|
</section>
|