JavaDataStructures/Heap/TreapModule.java at master · benaich/JavaDataStructures · GitHub

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package Heap;

import java.util.ArrayList;

import java.util.List;

import java.util.Random;

public class TreapModule {

public static final Random r = new Random();

public static interface Treap<T> {

Treap left();

Treap right();

T data();

int rank();

boolean isEmpty();

int size();

@Override

String toString();

public T min();

}

public static class NonEmptyTreap<T> implements Treap<T> {

public Treap left;

public Treap right;

public T data;

public int rank;

public NonEmptyTreap(T x, Treap a, Treap b) {

this(r.nextInt(20), x, a, b);

}

public NonEmptyTreap(int r, T x, Treap a, Treap b) {

rank = r;

data = x;

left = a;

right = b;

}

@Override

public Treap left() {

return left;

}

@Override

public Treap right() {

return right;

}

@Override

public T data() {

return data;

}

@Override

public int rank() {

return rank;

}

@Override

public boolean isEmpty() {

return false;

}

@Override

public int size() {

return 1 + left.size() + right.size();

}

@Override

public T min() {

if (left().isEmpty()) {

return data();

}

return (T) left.min();

}

@Override

public String toString() {

return data + "-" + rank;

}

/**

public static final Treap<? extends Object> EMPTY = new Treap<Object>() {

@Override

public Treap left() {

throw new UnsupportedOperationException();

}

@Override

public Treap right() {

throw new UnsupportedOperationException();

}

@Override

public Object data() {

throw new UnsupportedOperationException();

}

@Override

public int rank() {

return 0;

}

@Override

public String toString() {

return "";

}

@Override

public boolean isEmpty() {

return true;

}

@Override

public int size() {

return 0;

}

@Override

public Object min() {

return null;

}

};

/* retourn EMPTY instnace (singleton pattern) */

public static <T> Treap emptyTreap() {

return (Treap) EMPTY;

}

/* build a Treap v1 */

public static <T> Treap<T> treap(T x, Treap<T> a, Treap<T> b) {

return new NonEmptyTreap<>(x, a, b);

}

/* build a Treap v2 */

public static <T> Treap<T> treap(int rank, T x, Treap<T> a, Treap<T> b) {

return new NonEmptyTreap<>(rank, x, a, b);

}

/* insert an element into a Treap without rotation*/

public static <T extends Comparable<? super T>> Treap<T> insertNoFix(Treap<T> a, T x) {

if (a.isEmpty()) {

return treap(x, emptyTreap(), emptyTreap());

}

if (x.compareTo(a.data()) < 0) {

return treap(a.data(), insertNoFix(a.left(), x), a.right());

}

return treap(a.data(), a.left(), insertNoFix(a.right(), x));

}

public static <T extends Comparable<? super T>> Treap<T> insertNoFix(Treap<T> a, T x, int rank) {

if (a.isEmpty()) {

return treap(rank, x, emptyTreap(), emptyTreap());

}

if (x.compareTo(a.data()) < 0) {

return treap(a.rank(), a.data(), insertNoFix(a.left(), x, rank), a.right());

}

return treap(a.rank(), a.data(), a.left(), insertNoFix(a.right(), x, rank));

}

/* insert (rotate if needed) an element into a Treap */

public static <T extends Comparable<? super T>> Treap<T> insert(Treap<T> a, T x) {

return rotate(insertNoFix(a, x));

}

public static <T extends Comparable<? super T>> Treap<T> insert(Treap<T> a, T x, int rank) {

return rotate(insertNoFix(a, x, rank));

}

/* Rotate to fix the Treap */

public static <T> Treap<T> rotate(Treap<T> root) {

if (root.isEmpty()) {

return root;

}

Treap<T> left = rotate(root.left());

Treap<T> right = rotate(root.right());

root = treap(root.rank(), root.data(), left, right);

if (!root.left().isEmpty()) {

if (root.rank() > root.left().rank()) {

return rotate(rotateRight(root));

}

if (!root.right().isEmpty()) {

if (root.rank() > root.right().rank()) {

return rotate(rotateLeft(root));

}

return treap(root.rank(), root.data(), root.left(), root.right());

}

private static <T> Treap<T> rotateRight(Treap<T> root) {

return treap(root.left().rank(),

root.left().data(),

merge(root.left().left(), root.left().right()),

treap(root.rank(), root.data(), emptyTreap(), root.right()));

}

private static <T> Treap<T> rotateLeft(Treap<T> root) {

return treap(root.right().rank(),

root.right().data(),

treap(root.rank(), root.data(), root.left(), emptyTreap()),

merge(root.right().right(), root.right().left())

);

}

public static <T extends Comparable<? super T>> boolean contains(Treap<T> root, T x) {

if (root.isEmpty()) {

return false;

}

int c = root.data().compareTo(x);

if (c == 0) {

return true;

} else if (c < 0) {

return contains(root.right(), x);

}

return contains(root.left(), x);

}

/* create a balanced Treap from an array */

public static <T extends Comparable<? super T>> Treap<T> insert(T... array) {

Treap<T> root = emptyTreap();

for (T item : array) {

root = insert(root, item);

}

return root;

}

/* merge two balanced Treaps into one balanced Treap*/

public static <T extends Comparable<? super T>> Treap<T> merge(Treap<T> a, Treap<T> b) {

if (a.isEmpty()) {

return b;

}

if (b.isEmpty()) {

return a;

}

if (a.size() > b.size()) {

return merge(insert(a, b.data(), b.rank()), merge(b.left(), b.right()));

}

return merge(insert(b, a.data(), a.rank()), merge(a.left(), a.right()));

}

/* remove the minimum key of a Treap */

public static <T extends Comparable<? super T>> Treap<T> delete(Treap<T> root, T x) {

if (!contains(root, x)) {

return root;

}

int c = root.data().compareTo(x);

if (c == 0) {

return merge(root.left(), root.right());

}

if (c > 0) {

return treap(root.rank(), root.data(), delete(root.left(), x), root.right());

}

return treap(root.rank(), root.data(), root.left(), delete(root.right(), x));

}

/* split a treap */

public static <T extends Comparable<? super T>> List<Treap<T>> split(Treap<T> a, T x, List<Treap<T>> seed) {

if (seed == null || seed.isEmpty()) {

seed = new ArrayList<>();

seed.add(emptyTreap());

}

if(a.isEmpty())

return seed;

if (a.min().compareTo(x) > 0) {

seed.set(0, a);

return seed;

}

int c = a.data().compareTo(x);

if (c < 0) {

seed.set(0,

merge(seed.get(0), treap(a.rank(), a.data(), a.left(), emptyTreap())));

return split(a.right(), x, seed);

}

seed.set(1,

merge(seed.get(1), treap(a.rank(), a.data(), emptyTreap(), a.right())));

return split(a.left(), x, seed);

}

public static <T extends Comparable<? super T>> List<Treap<T>> split2(Treap<T> a, T x, T y) {

List<Treap<T>> seed = new ArrayList<>();

seed.add(emptyTreap());

List<Treap<T>> seed1 = split(a, x, null);

List<Treap<T>> seed2 = split(seed1.get(1), y, null);

seed.set(0, seed1.get(0));

seed.set(1, seed2.get(0));

seed.set(2, seed2.get(1));

return seed;

}

/* print Treap element */

public static <T> void printNice(Treap<T> root, int level) {

if (root.isEmpty()) {

return;

}

printNice(root.right(), level + 1);

if (level != 0) {

for (int i = 0; i < level - 1; i++) {

System.out.print("| ");

}

System.out.println("|---" + root);

} else {

System.out.println(root);

}

printNice(root.left(), level + 1);

}

public static void main(String[] args) {

Treap<Integer> a = emptyTreap();

Treap<Integer> b = emptyTreap();

Treap<Integer> c = emptyTreap();

a = insertNoFix(a, 5, 16);

a = insertNoFix(a, 1, 12);

a = insertNoFix(a, 2, 10);

a = insertNoFix(a, 8, 8);

a = insertNoFix(a, 6, 3);

System.out.println("------------ insert ------------");

printNice(a, 1);

System.out.println("------------ rotate ------------");

b = rotate(a);

printNice(b, 1);

System.out.println("------------ contains 8 ------------");

if (contains(b, 8)) {

System.out.println("yes");

} else {

System.out.println("no");

}

System.out.println("------------ min ------------");

System.out.println(b.min());

System.out.println("------------ delete 2 ------------");

c = delete(b, 2);

printNice(c, 1);

System.out.println("------------ Split 3 ------------");

List<Treap<Integer>> list1 = split(b, 3, null);

System.out.println("list 1");

printNice(list1.get(0), 1);

System.out.println("list 2");

printNice(list1.get(1), 1);

System.out.println("------------ Split 3 & 8 ------------");

List<Treap<Integer>> list2 = split2(b, 3, 8);

System.out.println("list 1");

printNice(list2.get(0), 1);

System.out.println("list 2");

printNice(list2.get(1), 1);

System.out.println("list 3");

printNice(list2.get(2), 1);

}

JavaDataStructures/Heap/TreapModule.java at master · benaich/JavaDataStructures · GitHub

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