Centroid Decomposition - Code

Here's the decomposition:

function decompose(v, treeSize)
    centroid := findCentroid(v, treeSize)
    removed[centroid] := true

    // Process paths through centroid (problem-specific)
    processCentroid(centroid)

    for each neighbor u of centroid (not removed)
        childSize := subtreeSize[u]
        if childSize > treeSize / 2 then
            childSize := treeSize - subtreeSize[centroid]
        centroidParent[decompose(u, childSize)] := centroid

    return centroid

The $processCentroid$ function depends on the specific problem. It typically computes distances or counts for paths passing through the centroid.