Cormen Edition 3 Exercise 10.1 Question 2 (Page No. 235)

Question

Explain how to implement two stacks in one array $A[1...n]$ in such a way that neither stack overflows unless the total number of elements in both stacks together is $n$.The $PUSH$ and $POP$ operations should run in $O(1)$ time.

Answer 1

Method 1 (Divide the space in two halves) (not the answer to above question as it can overflow even when number of elements isn't n)
A simple way to implement two stacks is to divide the array in two halves and assign the half half space to two stacks, i.e., use arr[0] to arr[n/2] for stack1, and arr[(n/2) + 1] to arr[n-1] for stack2 where arr[] is the array to be used to implement two stacks and size of array be n.

The problem with this method is inefficient use of array space. A stack push operation may result in stack overflow even if there is space available in arr[]. For example, say the array size is 6 and we push 3 elements to stack1 and do not push anything to second stack2. When we push 4th element to stack1, there will be overflow even if we have space for 3 more elements in array.

Method 2 (A space efficient implementation)
This method efficiently utilizes the available space. It doesn’t cause an overflow if there is space available in arr[]. The idea is to start two stacks from two extreme corners of arr[]. stack1 starts from the leftmost element, the first element in stack1 is pushed at index 0. The stack2 starts from the rightmost corner, the first element in stack2 is pushed at index (n-1). Both stacks grow (or shrink) in opposite direction. To check for overflow, all we need to check is for space between top elements of both stacks. This check is highlighted in the below code.

#include<iostream> 
#include<stdlib.h> 
  
using namespace std; 
  
class twoStacks 
{ 
    int *arr; 
    int size; 
    int top1, top2; 
public: 
   twoStacks(int n)  // constructor 
   { 
       size = n; 
       arr = new int[n]; 
       top1 = -1; 
       top2 = size; 
   } 
  
   // Method to push an element x to stack1 
   void push1(int x) 
   { 
       // There is at least one empty space for new element 
       if (top1 < top2 - 1) 
       { 
           top1++; 
           arr[top1] = x; 
       } 
       else
       { 
           cout << "Stack Overflow"; 
           exit(1); 
       } 
   } 
  
   // Method to push an element x to stack2 
   void push2(int x) 
   { 
       // There is at least one empty space for new element 
       if (top1 < top2 - 1) 
       { 
           top2--; 
           arr[top2] = x; 
       } 
       else
       { 
           cout << "Stack Overflow"; 
           exit(1); 
       } 
   } 
  
   // Method to pop an element from first stack 
   int pop1() 
   { 
       if (top1 >= 0 ) 
       { 
          int x = arr[top1]; 
          top1--; 
          return x; 
       } 
       else
       { 
           cout << "Stack UnderFlow"; 
           exit(1); 
       } 
   } 
  
   // Method to pop an element from second stack 
   int pop2() 
   { 
       if (top2 < size) 
       { 
          int x = arr[top2]; 
          top2++; 
          return x; 
       } 
       else
       { 
           cout << "Stack UnderFlow"; 
           exit(1); 
       } 
   } 
}; 
  
  
/* Driver program to test twStacks class */
int main() 
{ 
    twoStacks ts(5); 
    ts.push1(5); 
    ts.push2(10); 
    ts.push2(15); 
    ts.push1(11); 
    ts.push2(7); 
    cout << "Popped element from stack1 is " << ts.pop1(); 
    ts.push2(40); 
    cout << "\nPopped element from stack2 is " << ts.pop2(); 
    return 0; 
} 

Ref: https://www.geeksforgeeks.org/implement-two-stacks-in-an-array/