Internal Sorting: Heapsort-1: Sorting by Selection

Heapsort-1:堆排序-1

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Animation

A run of the heapsort algorithm sorting an array of randomly permuted values. In the first stage of the algorithm the array elements are reordered to satisfy the heap property. Before the actual sorting takes place, the heap tree structure is shown briefly for illustration.

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An example on heapsort.

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Complexity

Class Sorting algorithm Data structure Array Worst case performance O(nlogn) Best case performance Ω(n), O(nlogn) Average case performance O(nlogn) Worst case space complexity O(1) auxiliary

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Pseudo code

HEAPSORT(A)    BUILD-MAX-HEAP(A)    for i = A.length downto 2        exchange A[1] with A[i]        A.heap-size = A.heap-size - 1        MAX-HEAPIFY(A, 1)BUILD-MAX-HEAP(A)    A.heap-size = A.length    for i = floor(A.length/2) downto 1        MAX-HEAPIFY(A, i)MAX-HEAPIFY(A, i)    l = LEFT(i)    r = RIGHT(i)    if l <= A.heap-size and A[l] > A[i]        largest = l    else largest = i    if r <= A.heap-size and A[r] > A[largest]        largest = r    if largest != i        exchange A[i] with A[largest]        MAX-HEAPIFY(A, largest)LEFT(i)    return 2iRIGHT(i)    return 2i+1

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Java program

/** * Created with IntelliJ IDEA. * User: 1O1O * Date: 12/2/13 * Time: 10:01 PM * :)~ * Heapsort-1:Sorting by Selection:Internal Sorting */public class Main {    public static int LEFT(int i){        return 2*i;    }    public static int RIGHT(int i){        return 2*i+1;    }    public static void MAX_HEAPIFY(int[] K, int i, int heapSize){        int l = LEFT(i);        int r = RIGHT(i);        int largest;        int temp;        if(l <= heapSize && K[l] > K[i]){            largest = l;        }else {            largest = i;        }        if(r <= heapSize && K[r] > K[largest]){            largest = r;        }        if(largest != i){            temp = K[largest];            K[largest] = K[i];            K[i] = temp;            MAX_HEAPIFY(K, largest, heapSize);        }    }    public static void BUILD_MAX_HEAP(int[] K, int heapSize){        for(int i=(int)Math.floor((K.length-1)/2); i>=1; i--){            MAX_HEAPIFY(K, i, heapSize);        }    }    public static void HEAPSORT(int[] K){        int heapSize = K.length-1;        int temp;        BUILD_MAX_HEAP(K, heapSize);        for(int i=K.length-1; i>=2; i--){            temp = K[i];            K[i] = K[1];            K[1] = temp;            heapSize--;            MAX_HEAPIFY(K, 1, heapSize);        }    }    public static void main(String[] args) {        int N = 16;        int[] K = new int[17];        /*Prepare the data*/        K[1] = 503;        K[2] = 87;        K[3] = 512;        K[4] = 61;        K[5] = 908;        K[6] = 170;        K[7] = 897;        K[8] = 275;        K[9] = 653;        K[10] = 426;        K[11] = 154;        K[12] = 509;        K[13] = 612;        K[14] = 677;        K[15] = 765;        K[16] = 703;        /*Output unsorted Ks*/        System.out.println("Unsorted Ks:");        for(int i=1; i<=N; i++){            System.out.println(i+":"+K[i]);        }        System.out.println();        /*Kernel of the Algorithm!*/        HEAPSORT(K);        /*Output sorted Ks*/        System.out.println("Sorted Ks:");        for(int i=1; i<=N; i++){            System.out.println(i+":"+K[i]);        }    }}

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Outputs

Unsorted Ks:1:5032:873:5124:615:9086:1707:8978:2759:65310:42611:15412:50913:61214:67715:76516:703Sorted Ks:1:612:873:1544:1705:2756:4267:5038:5099:51210:61211:65312:67713:70314:76515:89716:908

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Reference

<< Introduction to Algorithms >> Third Edition, THOMAS H. CORMEN, CHARLES E. LEISERSON, RONALD L. RIVEST, CLIFFORD STEIN
https://en.wikipedia.org/wiki/Heapsort