Two questions about quicksort - c++

Question

I have two questions when learning quicksort currently. The standard code is here(copy from my book):
void Quicksort(int a[], int low, int high){
if(low<high){
int pivotpos=Patrition(a,low,high);
Quicksort(a,low,pivotpos-1);
Quicksort(a,pivotpos+1,high);
}
}
int Patrition(int a[], int low, int high){
int pivot=a[low]; //first elemnent as pivot
while(low<high){
while(low<high&&a[high]>=pivot) --high; //1
a[low]=a[high];
while(low<high&&a[low]<=pivot) ++low; //2
a[high]=a[low];
}
a[low]=pivot;
return low;
}
My questions are in the above code(marked 1 and 2):
a. why the program cannot be performed(core dumped) when I type this in 1:
while(a[high]>=pivot) --high (similarly in 2). It seems that I have to add the condition(low<high) in the second and third while loop or it said core dumped?
b. another question is why there must be a operator= in second and third while loop. I am confused why it won't work when I type while(low<high&& a[high]>pivot (similarly in 2). If I do so, this program will keep looping and never goes to end.
Thanks for your attention. Any suggestion will be highly appreciated.

Answer 1

The reason for having to write low < high in each while-loop is because it first checks the condition for the first while (the big one), starts looping, then it check the condition in while //1 and keeps looping, but during that time, the first while's (the big one) condition is never checked.
Example:
a = 6;
while (a > 5) {
while (a > 3) {
--a;
}
}
In this code, the second loop only stops when a = 3.
As for question b, it's because it never actually reaches the value that needs to be changed, hence never actually sorting it.
Example: If you'd want the loop to stop at a = 3, the following loop would stop one step earlier.
a = 5;
while (a > 4) {
--a;
}
Value a never reaches 3, it stops at a = 4,