[BUG]: method `pop` in PrimMST.js not working properly

[paulinegarelli]

Description

In Graphs/PrimMST.js, the method _shiftDown of class PriorityQueue does not give the correct output when a node must be shifted to a left-child leaf without a right-child "brother", which results in a wrong behavior of method pop.

Expected Behavior

An example of a tree that produces the bug is given by the following array of nodes denoted by their priority:
queue = [0, 1, 2]

ie

1. root node of priority 0
2. left leaf of priority 1
3. right leaf of priority 0

If we call method pop on this queue, we expect to get the new tree:
queue = [1, 2]

ie

1. root node of priority 1
2. left leaf of priority 2

Actual Behavior

In the case described above, we will get as output a tree represented by:
queue = [2, 1]

ie

1. root node of priority 2
2. left leaf of priority 1

This violates the properties of the heap (we have 2 > 1 but a parent node should never have a bigger value than any of its children).

Steps to reproduce (if applicable)

1. Add an export statement for class PriorityQueue in PrimMST.js

export { PriorityQueue }

2. Add a test file PrimMST.test.js containing the following code

import { PriorityQueue} from '../PrimMST.js'

test('Bug in pop method', () => {
    // create queue
    const queue = new PriorityQueue()
    queue.push(0, 0)
    queue.push(1, 1)
    queue.push(2, 2)
    // create expected queue
    const expectedQueue = new PriorityQueue()
    expectedQueue.push(1, 1)
    expectedQueue.push(2, 2)
    // result from popping element from the queue
    queue.pop()
    expect(queue).toEqual(expectedQueue)
})

3. Run the tests for PrimMST

npm test -- PrimMST.test.js

Additional information

This is due to the fact that in _shiftDown, the children's priorities are computed under a single try {} catch {} statement, thus the priority of the left child is set to Infinity if the right child does not exist.

[paulinegarelli]

I am working on correcting the bug, refactoring the method _shiftDown for a clearer computation of nodes priorities, and adding tests for PrimMST and the pop method.

[Lars Müller]

I am working on correcting the bug, refactoring the method _shiftDown for a clearer computation of nodes priorities, and adding tests for PrimMST and the pop method.

The priority queue should not be a part of PrimMST, it should be its own algo (or rather, data structure) with its own implementation and tests and should only be imported and used by PrimMST.

Please have a look - it should be possible to merge the PQ used & implemented in PrimMST with our existing PQ implementation: https://github.com/TheAlgorithms/JavaScript/blob/master/Data-Structures/Heap/MinPriorityQueue.js

[paulinegarelli]

I couldn't merge the two implementations because the PQ we use has keys in addition to the priority value to be able to track the nodes of the graph, which none of the already existing implementations have.
So I added this implementation as a new algorithm.