Thursday 22 October 2015

Next Greater Element

Given an array, print the Next Greater Element (NGE) for every element. The Next greater Element for an element x is the first greater element on the right side of x in array. Elements for which no greater element exist, consider next greater element as -1.
Examples:
a) For any array, rightmost element always has next greater element as -1.
b) For an array which is sorted in decreasing order, all elements have next greater element as -1.
c) For the input array [4, 5, 2, 25}, the next greater elements for each element are as follows.
Element       NGE
   4      -->   5
   5      -->   25
   2      -->   25
   25     -->   -1
d) For the input array [13, 7, 6, 12}, the next greater elements for each element are as follows.
  Element        NGE
   13      -->    -1
   7       -->     12
   6       -->     12
   12     -->     -1
Method 1 (Simple)
Use two loops: The outer loop picks all the elements one by one. The inner loop looks for the first greater element for the element picked by outer loop. If a greater element is found then that element is printed as next, otherwise -1 is printed.
Thanks to Sachin for providing following code.
#include<stdio.h>
/* prints element and NGE pair for all elements of
arr[] of size n */
void printNGE(int arr[], int n)
{
    int next = -1;
    int i = 0;
    int j = 0;
    for (i=0; i<n; i++)
    {
        next = -1;
        for (j = i+1; j<n; j++)
        {
            if (arr[i] < arr[j])
            {
                next = arr[j];
                break;
            }
        }
        printf("%d -- %d\n", arr[i], next);
    }
}
 
int main()
{
    int arr[]= {11, 13, 21, 3};
    int n = sizeof(arr)/sizeof(arr[0]);
    printNGE(arr, n);
    getchar();
    return 0;
}
Output:
11 -- 13
13 -- 21
21 -- -1
3 -- -1
Time Complexity: O(n^2). The worst case occurs when all elements are sorted in decreasing order.


Method 2 (Using Stack)
Thanks to pchild for suggesting following approach.
1) Push the first element to stack.
2) Pick rest of the elements one by one and follow following steps in loop.
….a) Mark the current element as next.
….b) If stack is not empty, then pop an element from stack and compare it with next.
….c) If next is greater than the popped element, then next is the next greater element for the popped element.
….d) Keep popping from the stack while the popped element is smaller than next. next becomes the next greater element for all such popped elements
….g) If next is smaller than the popped element, then push the popped element back.
3) After the loop in step 2 is over, pop all the elements from stack and print -1 as next element for them.
#include<stdio.h>
#include<stdlib.h>
#define STACKSIZE 100
 
// stack structure
struct stack
{
    int top;
    int items[STACKSIZE];
};
 
// Stack Functions to be used by printNGE()
void push(struct stack *ps, int x)
{
    if (ps->top == STACKSIZE-1)
    {
        printf("Error: stack overflow\n");
        getchar();
        exit(0);
    }
    else
    {
        ps->top += 1;
        int top = ps->top;
        ps->items [top] = x;
    }
}
 
bool isEmpty(struct stack *ps)
{
    return (ps->top == -1)? true : false;
}
 
int pop(struct stack *ps)
{
    int temp;
    if (ps->top == -1)
    {
        printf("Error: stack underflow \n");
        getchar();
        exit(0);
    }
    else
    {
        int top = ps->top;
        temp = ps->items [top];
        ps->top -= 1;
        return temp;
    }
}
 
/* prints element and NGE pair for all elements of
arr[] of size n */
void printNGE(int arr[], int n)
{
    int i = 0;
    struct stack s;
    s.top = -1;
    int element, next;
 
    /* push the first element to stack */
    push(&s, arr[0]);
 
    // iterate for rest of the elements
    for (i=1; i<n; i++)
    {
        next = arr[i];
 
        if (isEmpty(&s) == false)
        {
            // if stack is not empty, then pop an element from stack
            element = pop(&s);
 
            /* If the popped element is smaller than next, then
                a) print the pair
                b) keep popping while elements are smaller and
                stack is not empty */
            while (element < next)
            {
                printf("\n %d --> %d", element, next);
                if(isEmpty(&s) == true)
                   break;
                element = pop(&s);
            }
 
            /* If element is greater than next, then push
               the element back */
            if (element > next)
                push(&s, element);
        }
 
        /* push next to stack so that we can find
           next greater for it */
        push(&s, next);
    }
 
    /* After iterating over the loop, the remaining
       elements in stack do not have the next greater
       element, so print -1 for them */
    while (isEmpty(&s) == false)
    {
        element = pop(&s);
        next = -1;
        printf("\n %d -- %d", element, next);
    }
}
 
/* Driver program to test above functions */
int main()
{
    int arr[]= {11, 13, 21, 3};
    int n = sizeof(arr)/sizeof(arr[0]);
    printNGE(arr, n);
    getchar();
    return 0;
}
Output:
 11 -- 13
 13 -- 21
 3 -- -1
 21 -- -1
Time Complexity: O(n). The worst case occurs when all elements are sorted in decreasing order. If elements are sorted in decreasing order, then every element is processed at most 4 times.
a) Initialy pushed to the stack.
b) Popped from the stack when next element is being processed.
c) Pushed back to the stack because next element is smaller.
d) Popped from the stack in step 3 of algo.
Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.
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