Big O How to trace iteration in QuickSort Algorithm? C

Question

I have the following C code Quick Sort algorithm.

#include <stdio.h>
#include <stdbool.h>

int list[] = {8, 1, 3, 4, 2, 10, 4, 6};
//int list[] = {2, 1, 10, 4, 5, 11, 12, 6};
//int list[] = {35, 33, 42, 10, 14, 19, 27, 44, 26, 31};
int main(int argc, char **argv)
{

    printf("Unsorted list is: ");
    printArray(list);
    quickSort(0, 7);
    printf("Sorted list is: ");
    printArray(list);

    return 0;
}

int partition(int left, int right, int pivot){

    int leftPointer = left -1;
    int rightPointer = right;
    while(true){

        while(list[++leftPointer] < pivot){
         //do nothing
//       printf("proses index kiri %d\n", leftPointer);

        }

        while(rightPointer > 0 && list[--rightPointer] > pivot){
         //do nothing
//       printf("proses index kanan %d\n", rightPointer);
        }

        if(leftPointer >= rightPointer){
            break;
        }else{
            printf("item swapped :%d,%d\n", 
            list[leftPointer],list[rightPointer]);

            swap(leftPointer, rightPointer);
//          return;
//          left++;
//          right--;
        }

    }
    printf("pivot swapped :%d,%d\n", list[leftPointer],list[right]);
    swap(leftPointer, right);
    printf("pivot index %d\n", leftPointer);
    return leftPointer;

}

void quickSort(int left, int right){
    if(right - left <= 0){
        return;
    }else{
        int pivot = list[right];
        int pIndex = partition(left, right, pivot);
        quickSort(left, pIndex-1);
        quickSort(pIndex+1, right);
//      printf("aman lanjut proses");
    }
}

void printArray(int list[]){
    int i;
    for(i = 0; i < 8; i++){
        printf(" %d ", list[i]);
    }   
    printf("\n\n");
}

void swap(int left, int right){
    //variabel sementara untuk menampung i
    int temporary = list[left];

    //tukar posisi, sehingga yg kecil di kiri, yg besar di kanan.
    list[left] = list[right];
    list[right] = temporary;
}

Where should I put "printf" to indicate step of iteration (trace)?

Because the goal is I want to check/count with the current data how the complexity in Big O notation? meet the best, average, or worst case.

Answer 1

Big O says that every "operation" has the same cost. Even it is is as trivial as incrementing a pointer. So you need to set up a global counter, then increment it with every inner loop. So the two while leftpointer and while rightpointer loops, plus the while true loop. One increment for each pass.\\