Algorithm-and-Data-Structure/AlgorithmCode/LowestCommonAncestor.java at master · lemidia/Algorithm-and-Data-Structure · GitHub

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/**
 * @Author Gyeong Lemidia, https://github.com/lemidia
 *
 * LCA Algorithm code written in java
 * Euler Tour + Sparse Table for RMQ(Range Minimum Query)
 */

publicclassLowestCommonAncestor {

// Below is code for Sparse Table

staticintmin (inta, intb) {
returna < b ? a : b;
 }

staticbooleanisValid(intj, inti, intn) {
returnj + (int)Math.pow(2, i) <= n;
 }

staticdoublebaseLog(doublex, doublebase){
returnMath.log(x) / Math.log(base);
 }

staticvoidconstruct(intsparseTable[][], intindexTable[][], introw, intn, intarr[]) {
for (inti = 0; i < n; i++){
sparseTable[0][i] = arr[i];
indexTable[0][i] = i;
 }
for (inti = 1; i <= row; i++) {
for (intj = 0; j < n; j++) {
if (isValid(j, i, n)) {
if (sparseTable[i-1][j] < sparseTable[i-1][j+(int)Math.pow(2, i-1)]) {
sparseTable[i][j] = sparseTable[i-1][j];
indexTable[i][j] = indexTable[i-1][j];
 }else {
sparseTable[i][j] = sparseTable[i-1][j+(int)Math.pow(2, i-1)];
indexTable[i][j] = indexTable[i-1][j+(int)Math.pow(2, i-1)];
 }
 }
 }
 }
 }

staticintminQuery(intsparseTable[][], intl, intr) {
intp = (int)baseLog(r-l+1, 2);
intk = (int)Math.pow(2, p);

returnmin(sparseTable[p][l], sparseTable[p][r-k+1]);
 }

staticintminQueryIndex(intsparseTable[][], intindexTable[][], intl , intr) {
intp = (int)baseLog(r-l+1, 2);
intk = (int)Math.pow(2, p);

if (sparseTable[p][l] < sparseTable[p][r-k+1]) {
returnindexTable[p][l];
 }else {
returnindexTable[p][r-k+1];
 }
 }

// Code for Sparse Table End

// Below is code for LCA

staticinttourIndex = 0;

staticintmax (inta, intb) {
returna > b ? a : b;
 }

staticclassTreeNode {
intindex;
TreeNodechildren[];

publicTreeNode(intindex) {
this.index = index;
children = newTreeNode[2];
 }
 }

/*

 Sample Tree used in this code.

 0
 / \
 / \
 1 2
 / \ / \
 / \ / \
 3 4 5 6

 LCA of 1,2 = 0
 LCA of 1,0 = 0
 LCA of 3,4 = 1
 LCA of 4,5 = 0
 LCA of 3,3 = 3
 */

// Do Euler Tour and marking index num for each node
staticvoiddfs (intdepth[], intnodes[], intlast[], TreeNodenode, intcurrentDepth) {
depth[tourIndex] = currentDepth;
nodes[tourIndex] = node.index;
last[node.index] = tourIndex;
tourIndex++;
for (TreeNodechild : node.children) {
if (child != null){
dfs(depth, nodes, last, child, currentDepth+1);
depth[tourIndex] = currentDepth;
nodes[tourIndex] = node.index;
last[node.index] = tourIndex;
tourIndex++;
 }
 }
 }

staticintLCA (inta, intb, intnodes[], intlast[], intsparseTable[][], intindexTable[][]) {
a = last[a];
b = last[b];
intminIndex = minQueryIndex(sparseTable, indexTable, min(a, b), max(a, b));
returnnodes[minIndex];
 }

// Code for LCA End

// Main method
publicstaticvoidmain(String[] args) {
// Construct Sample Tree
TreeNoderoot = newTreeNode(0);
root.children[0] = newTreeNode(1);
root.children[1] = newTreeNode(2);
root.children[0].children[0] = newTreeNode(3);
root.children[0].children[1] = newTreeNode(4);
root.children[1].children[0] = newTreeNode(5);
root.children[1].children[1] = newTreeNode(6);

// Setup Array information for LCA
intnodeCnt = 7;
intdepth [] = newint[2*nodeCnt-1];
intnodes [] = newint[2*nodeCnt-1];
intlast [] = newint[nodeCnt];
if (root != null)
dfs(depth, nodes, last, root, 0);

// Setup Sparse Table for Range Min Query
// depth 배열로 Sparse Table 을 구축한다.
intcolCnt = 2*nodeCnt-1;
introw = (int)baseLog(colCnt, 2);
intsparseTable[][] = newint[row+1][colCnt];
intindexTable[][] = newint[row+1][colCnt];
construct(sparseTable, indexTable, row, colCnt, depth);

intresult = LCA(4, 5, nodes, last, sparseTable, indexTable);
// Output : 0
System.out.print(result);
 }
}