What is the time complexity for while loop inside a while loop?

Question

 int i = 0, j = A.size() - 1;
    while (i < j) {
        while ((i < j) && (A[i] % 2 == 0)) ++ i;
        while ((i < j) && (A[j] % 2 == 1)) -- j;
        swap(A[i], A[j]);
        i ++; 
        j --;

We can scan from both ends of the array, swap them if not in place. Why is the time complexity O(N) and not O(N*N)?

Answer 1

You can rewrite the code to make it clearer:

 int i = 0, j = A.size() - 1;
 while (i < j) {
   if (A[i] % 2 == 0) ++ i;
   else if (A[j] % 2 == 1) -- j;
   else {
     swap(A[i], A[j]);
     i++; 
     j--;
   }
 }

Answer 2

The complexity of the algorithm is O(N) because the number of operation will in any case will be ji times only.

Here the inner loops for any iteration of outer loop will execute for ji times.