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feat: Lowest Common Ancestor (LCA) algorithm (TheAlgorithms#512)
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,121 @@ | ||
| // lowestcommonancestor.go | ||
| // description: Implementation of Lowest common ancestor (LCA) algorithm. | ||
| // detail: | ||
| // Let `T` be a tree. The LCA of `u` and `v` in T is the shared ancestor of `u` and `v` | ||
| // that is located farthest from the root. | ||
| // references: [cp-algorithms](https://cp-algorithms.com/graph/lca_binary_lifting.html) | ||
| // author(s) [Dat](https://github.com/datbeohbbh) | ||
| // see lowestcommonancestor_test.go for a test implementation. | ||
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| package graph | ||
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| type TreeEdge struct { | ||
| from int | ||
| to int | ||
| } | ||
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| type ITree interface { | ||
| dfs(int, int) | ||
| addEdge(int, int) | ||
| GetDepth(int) int | ||
| GetDad(int) int | ||
| GetLCA(int, int) int | ||
| } | ||
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| type Tree struct { | ||
| numbersVertex int | ||
| root int | ||
| MAXLOG int | ||
| depth []int | ||
| dad []int | ||
| jump [][]int | ||
| edges [][]int | ||
| } | ||
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| func (tree *Tree) addEdge(u, v int) { | ||
| tree.edges[u] = append(tree.edges[u], v) | ||
| tree.edges[v] = append(tree.edges[v], u) | ||
| } | ||
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| func (tree *Tree) dfs(u, par int) { | ||
| tree.jump[0][u] = par | ||
| tree.dad[u] = par | ||
| for _, v := range tree.edges[u] { | ||
| if v != par { | ||
| tree.depth[v] = tree.depth[u] + 1 | ||
| tree.dfs(v, u) | ||
| } | ||
| } | ||
| } | ||
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| func (tree *Tree) GetDepth(u int) int { | ||
| return tree.depth[u] | ||
| } | ||
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| func (tree *Tree) GetDad(u int) int { | ||
| return tree.dad[u] | ||
| } | ||
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| func (tree *Tree) GetLCA(u, v int) int { | ||
| if tree.GetDepth(u) < tree.GetDepth(v) { | ||
| u, v = v, u | ||
| } | ||
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| for j := tree.MAXLOG - 1; j >= 0; j-- { | ||
| if tree.GetDepth(tree.jump[j][u]) >= tree.GetDepth(v) { | ||
| u = tree.jump[j][u] | ||
| } | ||
| } | ||
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| if u == v { | ||
| return u | ||
| } | ||
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| for j := tree.MAXLOG - 1; j >= 0; j-- { | ||
| if tree.jump[j][u] != tree.jump[j][v] { | ||
| u = tree.jump[j][u] | ||
| v = tree.jump[j][v] | ||
| } | ||
| } | ||
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| return tree.jump[0][u] | ||
| } | ||
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| func NewTree(numbersVertex, root int, edges []TreeEdge) (tree *Tree) { | ||
| tree = new(Tree) | ||
| tree.numbersVertex, tree.root, tree.MAXLOG = numbersVertex, root, 0 | ||
| tree.depth = make([]int, numbersVertex) | ||
| tree.dad = make([]int, numbersVertex) | ||
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| for (1 << tree.MAXLOG) <= numbersVertex { | ||
| (tree.MAXLOG) += 1 | ||
| } | ||
| (tree.MAXLOG) += 1 | ||
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| tree.jump = make([][]int, tree.MAXLOG) | ||
| for j := 0; j < tree.MAXLOG; j++ { | ||
| tree.jump[j] = make([]int, numbersVertex) | ||
| } | ||
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| tree.edges = make([][]int, numbersVertex) | ||
| for _, e := range edges { | ||
| tree.addEdge(e.from, e.to) | ||
| } | ||
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| return tree | ||
| } | ||
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| // For each node, we will precompute its ancestor above him, its ancestor two nodes above, its ancestor four nodes above, etc. | ||
| // Let's call `jump[j][u]` is the `2^j`-th ancestor above the node `u` with `u` in range `[0, numbersVertex)`, `j` in range `[0,MAXLOG)`. | ||
| // These information allow us to jump from any node to any ancestor above it in `O(MAXLOG)` time. | ||
| func LowestCommonAncestor(tree *Tree) { | ||
| // call dfs to compute depth from the root to each node and the parent of each node. | ||
| tree.dfs(tree.root, tree.root) | ||
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| // compute jump[j][u] | ||
| for j := 1; j < tree.MAXLOG; j++ { | ||
| for u := 0; u < tree.numbersVertex; u++ { | ||
| tree.jump[j][u] = tree.jump[j-1][tree.jump[j-1][u]] | ||
| } | ||
| } | ||
| } |
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