Inserting Sort, Shell Sort, Heap Sort and Quick Sort

Inserting Sort, Shell Sort, Heap Sort and Quick Sort

This passage contains the application of four Sorting Algorithms in the title Inserting Sort, Shell Sort, Heap Sort and Quick Sort . Sorting algorithms are fundamental in Computer Science and these four algorithms are basic for new hand.

Code

Below is the C code

#include<stdio.h>
#include<stdlib.h>

void InsertingSort(int A[], int N);
void ShellSort(int A[], int N);
void Swap(int A[] ,int a, int b);
void PrecDown(int A[], int i, int N);
void HeapSort(int A[], int N);
int Median3(int A[], int left, int right);
void Qsort(int A[], int left, int right);
void QuickSort(int A[], int N);

int main(){
    int size;
    scanf("%d", &size);
    int* A = (int*)malloc(sizeof(int)*size);
    for(int i=0; i<size;i++){
        scanf("%d", &A[i]);
    }
    InsertingSort(A, size);
    ShellSort(A, size);
    HeapSort(A, size);
    QuickSort(A, size);

    for(int i=0; i<size; i++){
        printf("%d ", A[i]);
    }
}

void InsertingSort(int A[], int N){
    int Tmp;
    int P, j;
    for(P=1; P<N; P++){
        Tmp = A[P];
        for(j=P; j>0&&A[j-1]>Tmp; j--){
        //important 1.cmpare with Tmp; start just from P
        //remember j is the place to fit in
            A[j] = A[j-1];  
        }
        A[j] = Tmp;
    }
}

void ShellSort(int A[], int N){
    int Tmp;
    int P, j;
    int Increment = N/2;
    for(; Increment>0; Increment/=2){
    //stop after Increment become 1
        for(P=Increment; P<N; P++){
            Tmp = A[P];
            for(j=P; j>=Increment&&A[j-Increment]>Tmp; j-=Increment){
                A[j] = A[j-Increment];  
            }
            A[j] = Tmp;
        }
    }
}

void Swap(int A[] ,int a, int b){
    int Tmp = A[a];
    A[a] = A[b];
    A[b] = Tmp;
    return;
}

void PrecDown(int A[], int i, int N){
    //be careful that generally when we apply a heap, we start from 1 instead of 0
    int Tmp = A[i];
    int child;
    child = 2*i+1; 
    for(; child<N; child = 2*i+1){
    //notice that left child is not naively i*2
        if(child!=N-1&&A[child+1]>A[child])
            child++;
        if(A[child]>Tmp){
            A[i] = A[child];
            i = child;
        }
        else
            break;
    }
    A[i] = Tmp;
}

void HeapSort(int A[], int N){
    //pay attention that it's a Max heap
    for(int i = N/2-1; i>=0; i--){
        PrecDown(A, i, N);
    }
    int size = N;
    //intitializing the heap
    for(int i=0; i<size; i++){
        Swap(A, 0, N-1);
        PrecDown(A, 0, N-1);
        N--;
        }
    return;
}

int Median3(int A[], int left, int right){
    int mid = (left+right)/2;
    if(A[left]>A[mid])
        Swap(A, left, mid);
    if(A[left]>A[right])
        Swap(A, left, right);
    if(A[mid]>A[right])
        Swap(A, mid, right);
    Swap(A, mid, right-1);
    //the right item > mid, so hide mid just bufore right, instead of at right
    return A[right-1];
    //simple while complex  
}

void Qsort(int A[], int left, int right){
    //Not as easy as first sight
    if(right - left >10){
        int mid = Median3(A, left, right);
        int i=left;
        int j = right-1;

        for(;;){
            while(A[++i]<mid);
            //actually i start from left+1, because after running Median3 the item at left must<mid
            while(A[--j]>mid);
            //j start from right-2
            if(i>j)
                break;
            Swap(A, i, j);
        }
        Swap(A, i, right-1);
        Qsort(A, left, i-1);
        Qsort(A, i+1, right);
    }
    else
        InsertingSort(A+left,  right-left+1);
}


void QuickSort(int A[], int N){
    Qsort(A, 0, N-1);
}