add template and example of binary fitting

binary-lifting/lowest-common-ancestor.cpp

@@ -0,0 +1,73 @@
+#include <vector>
+#include <bit>
+#include <bitset>
+#include <cstdint>
+
+class TreeAncestor {
+private:
+    std::vector<std::vector<int>> predecessor;
+    std::vector<int> depth;
+public:
+    TreeAncestor(std::vector<std::pair<int, int>>& edges) {
+        int n = edges.size() + 1;
+        int m = bit_width((unsigned)n);
+        predecessor.resize(n, std::vector<int>(m, -1));
+        depth.resize(n, 0);
+
+        std::vector<std::vector<int>> graph(n);
+        for (const auto& [u, v] : edges) {
+            graph[u].emplace_back(v);
+            graph[v].emplace_back(u);
+        }
+
+        auto dfs = [&](auto&& dfs, int x, int fa) -> void {
+            predecessor[x][0] = fa;
+            for (auto y : graph[x]) {
+                if (y != fa) {
+                    depth[y] = depth[x] + 1;
+                    dfs(dfs, y, x);
+                }
+            }
+        };
+        dfs(dfs, 0, -1);
+
+        for (int i = 1; i < m; i++) {
+            for (int x = 0; x < n; x++) {
+                if (int p = predecessor[x][i - 1]; p != -1) {
+                    predecessor[x][i] = predecessor[p][i - 1];
+                }
+            }
+        }
+    }
+
+    int getKthAncestor(int node, int k) {
+        //for (int i = 0; i < bit_width((unsigned)k) && node != -1; i++) {
+        //    if (k >> i & 1) {
+        //        node = predecessor[node][i];
+        //    }
+        //}
+        for (; k && node != -1; k &= k - 1) {
+            node = predecessor[node][countr_zero(unsigned(k))];
+        }
+        return node;
+    }
+    int getLowestCommonAncestor(int u, int v) {
+        if (depth[u] > depth[v]) {
+            std::swap(u, v);
+        }
+
+        for (int k = depth[v] - depth[u]; k; k &= k - 1) {
+            v = predecessor[v][countr_zero(unsigned(k))];
+        }
+
+        if (u != v) {
+            for (int i = predecessor[u].size() -1; i >= 0; i--) {
+                int pu = predecessor[u][i], pv = predecessor[v][i];
+                if (pu != pv) {
+                    u = pu, v = pv;
+                }
+            }
+        }
+        return predecessor[u][0];
+    }
+};