c++,algorithm,sorting,c++11 , Should checking loop conditions be counted towards total number of comparisons?

## Question:

Tag: c++,algorithm,sorting,c++11

I have implemented three different sorting algorithms and now I want to confirm that my approach of counting the total number of comparisons is correct. In my mind, the number of comparisons shouldn't be tied to the conditional branches because if the condition isn't met, the comparison was still made to compare the values. I also use this same thought process to add one to the comparison count for the exit loop conditions.

The implementations for my algorithms are below. Am I setting up the counter correctly in each scenario?

Insertion Sort

``````int insertionSort(double* A, int arrayLength) {
int count = 1; // Initialized 1 to count for exit conditions of for loop
for (int j = 1; j < arrayLength; j++) {
count++;
double key = A[j];
int i = j - 1;

while (i > -1 && A[i] > key) {
count++;
A[i + 1] = A[i];
i = i - 1;
}

count+=2 // Plus 2 for the while loop exit condition

A[i + 1] = key;
}

return count;
}
``````

Heap Sort

``````void heapSort(double* A, int arrayLength, int* c) {
int heapSize = 0;
buildMaxHeap(A, arrayLength, &heapSize, c);

for (int i = arrayLength - 1; i > 0; i--) {
swap(A[0], A[i]);
heapSize = heapSize - 1;
maxHeapify(A, 0, &heapSize, c);
}
}

void buildMaxHeap(double* A, int arrayLength, int* heapSize, int* c) {
*heapSize = arrayLength - 1;
*c = *c + 1; // Counts comparison of loop for exit condition
for (int i = floor((arrayLength)/ 2); i > -1; i--) {
*c = *c + 1;
maxHeapify(A, i, heapSize, c);
}
}
void maxHeapify(double* A, int i, int* heapSize, int* c) {
int l = (2 * i) + 1;
int r = (2 * i) + 2;
int largest;

if (l <= *heapSize && A[l] > A[i])
largest = l;
else largest = i;

if (r <= *heapSize && A[r] > A[largest])
largest = r;

if (largest != i) {
swap(A[i], A[largest]);
maxHeapify(A, largest, heapSize, c);
}

*c = *c + 5;
}
``````

Quick Sort

``````void quickSort(double* A, int p, int r, int* c) {

if (p < r) {
int q = partition(A, p, r, c);
quickSort(A, p, q - 1, c);
quickSort(A, q + 1, r, c);
}
*c = *c + 1;
}

int partition(double* A, int p, int r, int* c) {
double x = A[r];
int i = p - 1;

for (int j = p; j < r; j++) {
if (A[j] <= x) {
i = i + 1;
swap(A[i], A[j]);
}
*c = *c + 2;
}

*c = *c + 1 // Adding 1 for for loop exit condition

swap(A[i + 1], A[r]);
return i + 1;
}
``````

If you look at your inserstion sort

As you already put count =1 because as for exits on exit condition of for loop.

for same reason then it also make sense that when while loop cancels the count++ inside will not get executed but there was a comparison made. but you do a count+=2. why 2? it makes sense because you added 2 as you do 2 comparisons in while loop

``````(i > -1 && A[i] > key)
``````
• i>-1
• A[i] > key

but then you need to increase counter by 2 inside while loop as everytime while is correct 2 comparisons are made.

``````int insertionSort(double* A, int arrayLength) {
int count = 1; // Initialized 1 to count for exit conditions of for loop
for (int j = 1; j < arrayLength; j++) {
count++;
double key = A[j];
int i = j - 1;

while (i > -1 && A[i] > key) {
count++;
A[i + 1] = A[i];
i = i - 1;
}

count+2 // Plus 2 for the while loop exit condition

A[i + 1] = key;
}

return count;
}
``````

same way you can check other algorithms also.

still for a better approach I will suggest you read some starting chapter in any book about analysis of algorithm. They usually explains about how to estimate running time of algorithm which will help you understand how to analyse better.

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