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$ curl repovive.com/roadmaps/graph-theory/euler-tour-technique/path-queries-implementation

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Path Queries - Implementation - Euler Tour Technique | Graph Theory | Repovive

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Graph Theory37 sections · 1633 units81h total

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Path Queries - Implementation

(BIT for prefix sums)

Use BIT (Fenwick tree) for efficient prefix sum queries and point updates. Pseudocode:

function dfs(v, parent):
    tin[v] := timer
    timer := timer + 1
    for child in adj[v]:
        if child != parent then
            dfs(child, v)
    tout[v] := timer

Complexity: $O(n \log n)$ build, $O(\log n)$ per query.

Space complexity is $O(n)$ for the data structures used.