LCA in O(logn)

Author: coderick14

LeastCommonAncestor.cpp

@@ -0,0 +1,143 @@
+/*
+ * Deleted code is debugged code :)
+ */
+#include <bits/stdc++.h>
+#define ll long long
+#define ull unsigned long long
+#define vi vector<ll>
+#define pp pair<ll,ll>
+#define mp make_pair
+#define PI acos(-1.0)
+#define all(v) v.begin(),v.end()
+#define pb push_back
+#define FOR(i,a,b) for(i=a;i<b;i++)
+#define FREV(i,a,b) for(i=a;i>=b;i--)
+#define SULL(n) scanf("%llu", &n)
+#define INF 1e18
+#define MOD 1000000007
+
+#ifndef ONLINE_JUDGE
+#define gc getchar
+#define pc putchar
+#else
+#define gc getchar_unlocked
+#define pc putchar_unlocked
+#endif
+
+using namespace std;
+
+int read_int() {
+    char c = gc();
+    while((c < '0' || c > '9') && c != '-') c = gc();
+    int ret = 0, neg = 0;
+    if (c == '-') neg = 1, c = gc();
+    while(c >= '0' && c <= '9') {
+        ret = 10 * ret + c - 48;
+        c = gc();
+    }
+    return neg ? -ret : ret;
+}
+
+ll read_ll() {
+    char c = gc();
+    while((c < '0' || c > '9') && c != '-') c = gc();
+    ll ret = 0;
+    int neg = 0;
+    if (c == '-') neg = 1, c = gc();
+    while(c >= '0' && c <= '9') {
+        ret = 10 * ret + c - 48;
+        c = gc();
+    }
+    return neg ? -ret : ret;
+}
+
+/*******************************************RANDOM STUFF BEGINS HERE**************************************************/
+
+struct node {
+    vi adj;
+};
+
+vector<node> tree;
+vi depth(100005), parent(100005);
+
+// DFS to calculate depths of the nodes
+void dfs(ll u) {
+    ll i, len = tree[u].adj.size();
+    FOR(i,0,len) {
+        ll v = tree[u].adj[i];
+        depth[v] = depth[u] + 1;
+        dfs(v);
+    }
+}
+
+// Preprocessing for LCA in O(nlogn)
+// binary_ancestor[i][j] stores the 2^j ancestor of node i
+
+ll binary_ancestor[1000005][20];
+
+void LCA_preprocessing(ll n) {
+	ll i, j;
+
+	for(i = 1; i <= n; i++) {
+		for(j = 0; 1 << j <= n; j++) {
+			binary_ancestor[i][j] = -1;
+		}
+	}
+
+	for(i = 1; i <= n; i++) {
+		binary_ancestor[i][0] = parent[i];
+	}
+
+	for(j = 1; 1 << j <=n; j++) {
+		for(i = 1; i <= n; i++) {
+			binary_ancestor[i][j] = binary_ancestor[binary_ancestor[i][j-1]][j-1];
+		}
+	}
+}
+
+ll getLCA(ll x, ll y) {
+	ll i, temp, log;
+
+	// make x the node with greater depth
+	if (depth[x] < depth[y]) {
+		temp = x, x = y, y = temp;
+	}
+
+	for(log = 1; 1 << log <= depth[x]; log++);
+	log--;
+
+	// bring x and y to the same level
+	for(i = log; i >= 0; i--) {
+		if (depth[x] - (1 << i) >= depth[y]) {
+			x = binary_ancestor[x][i];
+		}
+	}
+
+	// x and y  are now at the same level
+	for(i = log; i >= 0; i--) {
+		if (binary_ancestor[x][i] != -1 && binary_ancestor[x][i] != binary_ancestor[y][i]) {
+			x = binary_ancestor[x][i];
+			y = binary_ancestor[y][i];
+		}
+	}
+
+	return parent[x];
+}
+
+int main() {
+	ll i,j,t,n,x,y;
+    n = read_ll();
+    tree.resize(n+1);
+    // 1 is the root. Accept parents of the remaining (n-1) nodes
+    FOR(i,2,n+1) {
+        j = read_ll();
+        tree[j].adj.pb(i);
+        parent[i] = j;
+    }
+    dfs(1);
+    LCA_preprocessing(n);
+    x = read_ll();
+    y = read_ll();
+    cout << "LCA of " << x << " and " << y << " = " << getLCA(x,y) << endl;
+	return 0;
+}