Why it matters

Euler tour turns tree problems into array problems. Foundation for tree query.

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The architecture

DFS: in-time + out-time per node.

Subtree = contiguous range.

Path queries via LCA.

Euler tour usesDFS in-out timesfor each nodeSubtree range[in[v], out[v]]Path queriesvia LCA + prefixCombine with segment tree / BIT for subtree sum/update
Euler tour.
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How it works end to end

Subtree sum: range sum on Euler tour array.

Path sum: prefix on root path via LCA.

Update: point on tour.