Question

I was asked this question in an interview.The problem was i would be given a stack and have to find the element in the middle position of the stack.”top” index is not available (so that you don’t pop() top/2 times and return the answer).Assume that you will reach the bottom of the stack when pop() returns -1.Don’t use any additional data structure.

Eg:

stack   index
----- 
 2    nth element
 3
 99
 .
 1    n/2 th element
 .
 -1   bottom of the stack(0th index)

Answer: 1 (I didn’t mean the median.Find the element in middle position)

Is recursion the only way?

Thanks,

psy

Answer 1

Walk through the stack, calculate the depth and on the way back return the appropriate element.

int middle(stack* s, int n, int* depth) {
  if (stack_empty(s)) {
    *depth = n;
    return 0; //return something, doesn't matter..
  }
  int val = stack_pop(s);
  int res = middle(s, n+1, depth);
  stack_push(s, val);
  if (n == *depth/2)
    return val;
  return res;
}

int depth;
middle(&stack, 0, &depth);

Note: yes, recursion is the only way. Not knowing the depth of the stack means you have to store those values somewhere.