feat: Branch mst #74
feat: Branch mst #74
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| # Prim's Algorithm | |||
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yup fill this up!
Could you also dedicate a section to briefly discuss the slight difference in how a PriorityQueue/heap is used (specifically, the updating of nodes) in dijkstra and prim's? their implementation is actually very very similar, the key difference lies in that dijkstra sums up edge weights cumulatively whereas prim's replaces known shortest weight to an unexplored node
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| # Prim's Algorithm | |||
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| ## Background | |||
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would be helpful to explain what the queue intuitively stores. It should store distance/edge weights from known set S (nodes that are part of MST) to unexplored nodes.
But, do also mention that implementation-wise, this isn't always uphold. Because to strictly enforce this, would mean for any unexplored node in the queue, if a shorter distance from any of the explored nodes is found, we would need to update the distance to the unexplored node tracked in the queue. In practise, we don't do this but simply add (new_shorter_dist, node) to the queue, while leaving the old data in the queue (Hence, the explicit need to check if a node is alrwady explored when we poll from the queue). This doesn't worsen complexity because in the worst case of E = V^2 edges, log(V^2) = 2log(V).
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| # Prim's Algorithm | |||
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Maybe can also squeeze in this little tip that could be helpful in remembering the difference:
prim's - Find MST by growing 1 connected component. Queue tracks distance from this growing component to unexplored nodes, and iteratively explore nodes that are closest of this growing component.
kruskal's - Sorted edges by weight and identify connectivity using some Union Find / Disjoint Set structure
| PriorityQueue<Node> pq = new PriorityQueue<>((a, b) -> a.getCurrMinWeight() - b.getCurrMinWeight()); | ||
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| // Values in the map represent the corresponding node with only the edges in the MST | ||
| Map<Node, Node> nodeToMSTNode = new HashMap<>(); |
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can't quite remember our discussion from before or if there are any concerns you brought up. Because, conventionally, we would use a 2D array for adjacency matrix or a Map<Node, List> for adjacency list
| int[] weights = new int[v]; | ||
| while (!pq.isEmpty()) { | ||
| Node current = pq.poll(); | ||
| current.setVisited(true); |
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notice u did not have an explicit check to see if current has already added as part of the MST. reason u do not need to do is because u use remove() method of PQ. See below for why this is discouraged
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| System.arraycopy(adjM[0], 0, weights, 0, v); | ||
| if (!adjacent.isVisited() && weight < adjacent.getCurrMinWeight()) { | ||
| pq.remove(adjacent); |
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remove() is actually not a typical operation supported by heap / PriorityQueue (see the GitHub notes on Heap).
While java implementation includes a remove operation (for convenience), this remove will ultimately incur O(n) since a heap (if not augmented), can do no better but O(n) to first search for the node before proceeding with removal.
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Changes moved to new PR. |
Do not merge, Prim's README not updated