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| 1 | +/* Author : Ashutosh Maurya |
| 2 | +*/ |
| 3 | +#include <stdio.h> |
| 4 | +#include <stdbool.h> |
| 5 | +#include <limits.h> |
| 6 | +#define MAX 100 // Let this be maximum number of nodes in our Binary Tree |
| 7 | +#define max(a,b) ( (a>b)?a:b ) |
| 8 | +#define min(a,b) ( (a<b)?a:b ) |
| 9 | + |
| 10 | +int euler[2*MAX - 1]; // Euler Tour Array ( DFS Traversal in a Tree ) |
| 11 | +bool visited[MAX+1]; // Level of Nodes in Tour Array |
| 12 | +int first[MAX+1]; // To Store the idx of first occuurence of the node in Euler Tour |
| 13 | +int idx,nodes; |
| 14 | +int segtree[2*MAX - 1]; |
| 15 | + |
| 16 | +void initialize(){ |
| 17 | + int i; |
| 18 | + for(i=0;i<=(2*MAX-2);i++){ |
| 19 | + if(i<=MAX) |
| 20 | + first[i]=-1,visited[i]=false; |
| 21 | + euler[i]=0,segtree[i]=0; |
| 22 | + } |
| 23 | +} |
| 24 | + |
| 25 | +void build(int node,int start,int end){ |
| 26 | + int mid; |
| 27 | + if(start==end) |
| 28 | + segtree[node]=euler[start]; |
| 29 | + else { |
| 30 | + mid=(start+end)/2; |
| 31 | + build(2*node,start,mid); // left sub Segment tree |
| 32 | + build(2*node+1,mid+1,end); // right sub Segment tree |
| 33 | + int x=segtree[2*node]; |
| 34 | + int y=segtree[2*node+1]; |
| 35 | + segtree[node]=(x>y)?y:x; |
| 36 | + } |
| 37 | +} |
| 38 | + |
| 39 | +int query (int node,int start,int end, int l, int r){ |
| 40 | + int mid,x,y; |
| 41 | + if(r<start || end<l) |
| 42 | + return INT_MAX; |
| 43 | + if(l<=start && end<=r) |
| 44 | + return segtree[node]; |
| 45 | + mid=(start+end)/2; |
| 46 | + x=query(2*node,start,mid,l,r); |
| 47 | + y=query(2*node+1,mid+1,end,l,r); |
| 48 | + return ((x>y)?y:x); |
| 49 | +} |
| 50 | + |
| 51 | +void dfs_eulertour(int node,int l){ |
| 52 | + if(node <= nodes){ |
| 53 | + euler[idx]=node; |
| 54 | + idx++; |
| 55 | + |
| 56 | + if(visited[node]==false){ |
| 57 | + visited[node]=true; |
| 58 | + first[node]=idx-1; |
| 59 | + } |
| 60 | + // Left SubTree |
| 61 | + if(2*node <= nodes){ |
| 62 | + dfs_eulertour(2*node,l+1); |
| 63 | + euler[idx]=node; |
| 64 | + idx++; |
| 65 | + } |
| 66 | + // Right Subtree |
| 67 | + if((2*node+1) <= nodes ){ |
| 68 | + dfs_eulertour(2*node+1,l+1); |
| 69 | + euler[idx]=node; |
| 70 | + idx++; |
| 71 | + } |
| 72 | + } |
| 73 | +} |
| 74 | + |
| 75 | +int findLCA(int u,int v){ |
| 76 | + int i; |
| 77 | + idx=0; |
| 78 | + dfs_eulertour(1,0); |
| 79 | + printf("Euler-Tour Array : "); |
| 80 | + for(i=0;i<(2*nodes-1);i++){ |
| 81 | + printf("%d ",euler[i]); |
| 82 | + } |
| 83 | + printf("\n"); |
| 84 | + build(1,0,2*nodes-2); // Building Segment Tree from Euler Tour |
| 85 | + return query(1,0,2*nodes-2,min(first[u],first[v]),max(first[v],first[u])); |
| 86 | +} |
| 87 | + |
| 88 | +int main() { |
| 89 | + int t,u,v; |
| 90 | + printf("Enter the number of nodes in the Binary Tree : "); |
| 91 | + scanf("%d",&nodes); |
| 92 | + printf("Enter the Number of Queries on Binary Tree : "); |
| 93 | + scanf("%d",&t); |
| 94 | + while(t--){ |
| 95 | + initialize(); |
| 96 | + printf("Find LCA of two nodes (U,V) : "); |
| 97 | + scanf("%d%d",&u,&v); |
| 98 | + printf("%d\n",findLCA(u,v)); |
| 99 | + } |
| 100 | + return 0; |
| 101 | +} |
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