Add Lowest commen ancestor algorithm

Author: Mohamed Ayman

src/lca_demo.cpp

@@ -0,0 +1,99 @@
+#include <bits/stdc++.h>
+
+int numberOfNodes, MAXLOG;
+std::vector< std::vector<int> > adjList;
+int parent[50005], nodeHeight[50005];
+bool visited[50005];
+int binaryLiftDp[50005][27];
+
+void dfs(int currentNode, int currentParent)
+{
+    visited[currentNode] = true;
+    parent[currentNode] = currentParent;
+    nodeHeight[currentNode] = nodeHeight[currentParent] + 1;
+    int adjacencySize = adjList[currentNode].size();
+    for(int idx = 0; idx < adjacencySize; idx++){
+        int nextNode = adjList[currentNode][idx];
+        if(!visited[nextNode])
+        {
+            dfs(nextNode, currentNode);
+        }
+    }
+}
+
+int getMaxLog(){
+    int curValue = 1;
+    int curLog = 1;
+    while(curValue < numberOfNodes) curValue *= 2, curLog++;
+    return curLog;
+}
+
+void initializeDP()
+{
+    nodeHeight[-1] = -1;
+    MAXLOG = getMaxLog();
+    dfs(0, -1);
+    for(int i = 0; i < numberOfNodes; i++) binaryLiftDp[i][0] = parent[i];
+    for(int i = 1; i <= MAXLOG; i++)
+    {
+        for(int j = 0; j < numberOfNodes; j++)
+        {
+            if(binaryLiftDp[j][i - 1] + 1)
+                binaryLiftDp[j][i] = binaryLiftDp[binaryLiftDp[j][i - 1]][i - 1];
+            else binaryLiftDp[j][i] = -1;
+        }
+    }
+}
+
+int LCA(int a, int b)
+{
+    if(nodeHeight[a] < nodeHeight[b]) std::swap(a,b);
+    for(int i = MAXLOG; i >= 0; i--)
+    {
+        if(binaryLiftDp[a][i] + 1 && nodeHeight[binaryLiftDp[a][i]] >= nodeHeight[b])
+            a = binaryLiftDp[a][i];
+    }
+    if(!(a - b)) return a;
+    for(int i = MAXLOG; i >= 0; i--)
+    {
+        if(binaryLiftDp[a][i] + 1 && binaryLiftDp[a][i] - binaryLiftDp[b][i])
+            a = binaryLiftDp[a][i], b = binaryLiftDp[b][i];
+    }
+    return parent[a];
+}
+
+void buildTree()
+{
+    printf("Enter number of nodes of the tree: ");
+    scanf("%d", &numberOfNodes);
+    adjList.resize(numberOfNodes, std::vector<int> ());
+    for(int i = 0; i < numberOfNodes - 1; i++)
+    {
+        int firstNode, secondNode;
+        printf("Enter the two nodes to be connected: ");
+        scanf("%d %d", &firstNode, &secondNode);
+        adjList[firstNode].push_back(secondNode);
+        adjList[secondNode].push_back(firstNode);
+    }
+}
+
+void answerQueries()
+{
+    int queryCount;
+    printf("Enter the number of queries: ");
+    scanf("%d", &queryCount);
+    for(int i = 0; i < queryCount; i++)
+    {
+        int firstNode, secondNode;
+        printf("Enter the two nodes : ");
+        scanf("%d %d", &firstNode, &secondNode);
+        printf("%d\n", LCA(firstNode, secondNode));
+    }
+}
+
+int main()
+{
+    buildTree();
+    initializeDP();
+    answerQueries();
+}