Distance from Next Greater element

Given an array arr[] of size N, the task is to print the distance of every array element from its next greater element. For array elements having no next greater element, print 0.

Examples: 

Input: arr[] = {73, 74, 75, 71, 69, 72, 76, 73} 
Output: {1, 1, 4, 2, 1, 1, 0, 0} 
Explanation: 
The next greater element for 73 is 74, which is at position 1. Distance = 1 – 0 = 1 
The next greater element for 74 is 75, which is at position 2. Distance = 2 – 1 = 1 
The next greater element for 75 is 76, which is at position 6. Distance = 6 – 2 = 4 
The next greater element for 71 is 72, which is at position 5. Distance = 5 – 3 = 2 
The next greater element for 69 is 72, which is at position 5. Distance = 5 – 4 = 1 
The next greater element for 72 is 76, which is at position 6. Distance = 6 – 5 = 1 
No, next greater element for 76. Distance = 0 
No, next greater element for 73. Distance = 0 

Input: arr[] = {5, 4, 3, 2, 1} 
Output: {0, 0, 0, 0, 0}

Naive Approach: The simplest approach is to traverse the array and for every array element, traverse to its right to obtain its next greater element and calculate the difference between the indices.



Time Complexity: O(N2
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, the idea is to use Stack to find the next greater element. 
Below are the steps: 

  1. Maintain a Stack which will contain the elements in non-increasing order.
  2. Check if the current element arr[i]is greater than the element at the top of the stack.
  3. Keep popping all the elements from the stack one by one from the top, that are found to be smaller than arr[i] and calculate the distance for each of them as the difference of current index and the index of the popped element.
  4. Push the current element into the stack and repeat the above steps.

Below is the implementation of the above approach:

C++

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// C++ implementation of the
// above approach
#include<bits/stdc++.h>
using namespace std;
 
vector<int> mindistance(vector<int> arr)
{
    int N = arr.size();
     
    // Stores the required distances
    vector<int> ans(N);
    int st = 0;
     
    // Maintain a stack of elements
    // in non-increasing order
    for(int i = 0; i < N - 1; i++)
    {
        if (arr[i] < arr[i + 1])
        {
            ans[i] = 1;
        }
        else
        {
            st = i + 1;
            while (st <= N - 1)
            {
                if (arr[i] < arr[st])
                {
                    ans[i] = st - i;
                    break;
                }
                else
                {
                    st++;
                }
            }
        }
    }
    return ans;
}
 
// Driver code
int main()
{
    vector<int> arr = { 73, 74, 75, 71,
                        69, 72, 76, 73 };
     
    vector<int> x = mindistance(arr);
     
    cout << "[";
    for(int i = 0; i < x.size(); i++)
    {
        if (i == x.size() - 1)
            cout << x[i];
        else
          cout << x[i] << ", ";
    }
    cout << "]";
}
 
// This code is contributed by SURENDRA_GANGWAR

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Java

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// Java implementation of the
// above approach
import java.io.*;
 
class GFG{
     
public static int[] mindistance(int[] arr)
{
    int N = arr.length;
     
    // Stores the required distances
    int[] ans = new int[N];
    int st = 0;
     
    // Maintain a stack of elements
    // in non-increasing order
    for(int i = 0; i < N - 1; i++)
    {
        if (arr[i] < arr[i + 1])
        {
            ans[i] = 1;
        }
        else
        {
            st = i + 1;
            while (st <= N - 1)
            {
                if (arr[i] < arr[st])
                {
                    ans[i] = st - i;
                    break;
                }
                else
                {
                    st++;
                }
            }
        }
    }
    return ans;
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = new int[]{ 73, 74, 75, 71,
                           69, 72, 76, 73 };
     
    int x[] = mindistance(arr);
     
    System.out.print("[");
    for(int i = 0; i < x.length; i++)
        System.out.print(x[i]+", ");
         
    System.out.print("]");
}
}
 
// This code is contributed by sai-sampath mahajan
// and ramprasad kondoju

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Python3

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# Python3 implementation of the
# above approach
 
def mindistance(arr, N):
     
    if N <= 1:
        return [0]
       
    # Stores the required distances
    ans = [0 for i in range(N)]
    st = [0]
     
    # Maintain a stack of elements
    # in non-increasing order
    for i in range(1, N): 
         
        # If the current element exceeds
        # the element at the top of the stack
        while(st and arr[i] > arr[st[-1]]): 
            pos = st.pop()
            ans[pos] = i - pos
             
        # Push the current index to the stack
        st.append(i)
 
    return ans
 
# Given array
arr = [73, 74, 75, 71, 69, 72, 76, 73]
N = len(arr)
 
# Function call
print(mindistance(arr, N))

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Output: 

[1, 1, 4, 2, 1, 1, 0, 0]









 

Time Complexity: O(N) 
Auxiliary Space: O(N)

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