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$ curl repovive.com/roadmaps/graph-theory/centroid-decomposition/fixed-length-paths-i-implementation

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$ curl repovive.com/roadmaps/graph-theory/centroid-decomposition/fixed-length-paths-i-implementation

Repovive

Fixed-Length Paths I - Implementation - Centroid Decomposition | Graph Theory | Repovive

Repovive.

Graph Theory37 sections · 1633 units81h total

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Fixed-Length Paths I - Implementation

(Complete solution)

Here is the solution:

function count_paths(node, adj, k)
    c := find_centroid(node, adj)
    result := count_through_centroid(c, adj, k)
    removed[c] := true
    for child in adj[c]
        if not removed[child] then
            result := result + count_paths(child, adj, k)
            return result

you will need to subtract same-subtree paths as well.

This runs in $O(n \log n)$ time and uses $O(n)$ space.