Deap
A deap is a double-ended heap that supports the double-ended priority operations of insert, delet-min, and delete-max. Similar to min-max heap but deap is faster on these operations by a constant factor, and the algorithms are simpler.
Definition: A deap is a complete binary tree that is either empty or satisfies the following properties:
(1) The root contains no element
(2) The left subtree is a min heap.
(3) The right subtree is a max heap.
(4) If the right subtree is not empty, then let i be any node in the left subtree. Let j be the corresponding node in the right subtree. If such a j does not exist, then let j be the node in the right subtree that corresponds to the parent of i. The key in node i is less than or equal to that of j.
Example
Insertion into Deap
After the insertion of 4
After the insertion of 30
Deletion of min Element
Implementation
/*
Program Name: Deap.java
* Author: Sarju
* Date: 1-10-12
* Reference: Shiuh-Sheng Yu, Department of Information Management, National Chi Nan University
*
*/
import java.io.*;
public class Deap {
int[] deap;
int n = 1;
public Deap(int maxSize) {
deap = new int[maxSize];
}
private boolean inMaxHeap(int i) {
while (i > 3) {
i /= 2;
}
if (i == 2) return false;
return true;
}
private int maxPartner(int pos) {
int offset = 1;
int i = pos;
while (i > 3) {
i /= 2;
offset *= 2;
}
if ((pos + offset) > n) return (pos+offset)/2;
return pos + offset;
}
private int minPartner(int pos) {
int offset = 1;
int i = pos;
while (i > 3) {
i /= 2;
offset *= 2;
}
return pos - offset;
}
private void minInsert(int at, int key) {
for (int parent; (parent = at / 2) != 1 && key < deap[parent]; deap[at] = deap[parent], at = parent) ;
deap[at] = key;
}
private void maxInsert(int at, int key) {
for (int parent; (parent = at / 2) != 1 && key > deap[parent]; deap[at] = deap[parent], at = parent) ;
deap[at] = key;
}
public int deleteMax() {
int i, j;
int key;
if (n >= 3) { // if more than 2 elements
key = deap[3];
} else {
n--;
return deap[2];
}
int x = deap[n--];
// while i has child, move larger to i
for (i = 3; 2*i <= n; deap[i] = deap[j], i = j) {
j = i * 2;
if (j+1 <= n) {
if (deap[j] < deap[j+1]) {
j++;
}
}
}
// try to put x at leaf i
// find biggest at min partner
j = minPartner(i);
int biggest = j;
if (2*j <= n) {
biggest = 2*j;
if (((2*j + 1) <= n) && (deap[2*j] < deap[2*j+1])) {
biggest++;
}
}
if (x < deap[biggest]) {
// x can't put at i, must change with deap[biggest]
deap[i] = deap[biggest];
minInsert(biggest, x);
} else {
maxInsert(i, x);
}
return key;
}
public int deleteMin() {
int i, j, key = deap[2], x = deap[n--];
// while i has child, move smaller to i
for (i = 2; 2*i <= n; deap[i] = deap[j], i = j) {
j = i * 2;
if (j+1 <= n && deap[j] > deap[j+1]) {
j++;
}
}
// try to put x at leaf i
j = maxPartner(i);
if (x > deap[j]) {
deap[i] = deap[j];
maxInsert(j, x);
} else {
minInsert(i, x);
}
return key;
}
public void insert(int x) {
n++;
if (n == deap.length) {
System.out.println("The heap is full");
System.exit(1);
}
if (n == 2) {
deap[2] = x;
return;
}
if (inMaxHeap(n)) {
int i = minPartner(n);
if (x < deap[i]) {
deap[n] = deap[i];
minInsert(i, x);
} else {
maxInsert(n, x);
}
} else {
int i = maxPartner(n);
if (x > deap[i]) {
deap[n] = deap[i];
maxInsert(i, x);
} else {
minInsert(n, x);
}
}
}
public void print() {
int levelNum = 2;
int thisLevel = 0;
int gap = 8;
for (int i = 2; i <= n; i++) {
for (int j = 0; j < gap-1; j++) {
System.out.print(" ");
}
if (thisLevel != 0) {
for (int j = 0; j < gap-1; j++) {
System.out.print(" ");
}
}
if (Integer.toString(deap[i]).length() == 1) {
System.out.print(" ");
}
System.out.print(deap[i]);
thisLevel++;
if (thisLevel == levelNum) {
System.out.println();
thisLevel = 0;
levelNum *= 2;
gap/=2;
}
}
System.out.println();
if (thisLevel != 0) {
System.out.println();
}
}
public static void main(String[] argv) {
Deap a = new Deap(1024);
int choice,element;
try{
do{
System.out.print("\n1:Insert\n2.DeleteMin\n3.DeleteMax\n4.Exit");
System.out.print("\nEnter Your Choice:");
DataInputStream din = new DataInputStream(System.in);
choice = Integer.parseInt(din.readLine());
switch(choice){
case 1: /*For Adding new Element*/
System.out.println("\nEnter the element to insert:");
din = new DataInputStream(System.in);
element = Integer.parseInt(din.readLine());
a.insert(element);
a.print();
break;
case 2:
a.deleteMin();
a.print();
break;
case 3:
a.deleteMax();
a.print();
}
}while(choice<4 br="br"> }
catch(Exception e){
}
}
}
