Find the farthest smaller number in the right side

Difficulty Level : Medium
Last Updated : 13 Nov, 2020

Given an array arr[] of size N. For every element in the array, the task is to find the index of the farthest element in the array to the right which is smaller than the current element. If no such number exists then print -1.

Examples:

Input: arr[] = {3, 1, 5, 2, 4}
Output: 3 -1 4 -1 -1
arr[3] is the farthest smallest element to the right of arr[0].
arr[4] is the farthest smallest element to the right of arr[2].
And for the rest of the elements, there is no smaller element to their right.
Input: arr[] = {1, 2, 3, 4, 0}
Output: 4 4 4 4 -1

Approach: An efficient approach is to create a suffix_min[] array where suffix_min[i] stores the minimum element from the subarray arr[i … N – 1]. Now for any element arr[i], binary search can be used on the subarray suffix_min[i + 1 … N – 1] to find the farthest smallest element to the right of arr[i].

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the farthest
// smaller number in the right side
void farthest_min(int a[], int n)
{
    // To store minimum element
    // in the range i to n
    int suffix_min[n];
    suffix_min[n - 1] = a[n - 1];
    for (int i = n - 2; i >= 0; i--) {
        suffix_min[i] = min(suffix_min[i + 1], a[i]);
    }
 
    for (int i = 0; i < n; i++) {
        int low = i + 1, high = n - 1, ans = -1;
 
        while (low <= high) {
            int mid = (low + high) / 2;
 
            // If currnet element in the suffix_min
            // is less than a[i] then move right
            if (suffix_min[mid] < a[i]) {
                ans = mid;
                low = mid + 1;
            }
            else
                high = mid - 1;
        }
 
        // Print the required answer
        cout << ans << " ";
    }
}
 
// Driver code
int main()
{
    int a[] = { 3, 1, 5, 2, 4 };
    int n = sizeof(a) / sizeof(a[0]);
 
    farthest_min(a, n);
 
    return 0;
}

Java

// Java implementation of the approach
class GFG {
 
    // Function to find the farthest
    // smaller number in the right side
    static void farthest_min(int[] a, int n)
    {
        // To store minimum element
        // in the range i to n
        int[] suffix_min = new int[n];
 
        suffix_min[n - 1] = a[n - 1];
        for (int i = n - 2; i >= 0; i--) {
            suffix_min[i]
                = Math.min(suffix_min[i + 1], a[i]);
        }
 
        for (int i = 0; i < n; i++) {
            int low = i + 1, high = n - 1, ans = -1;
 
            while (low <= high) {
                int mid = (low + high) / 2;
 
                // If currnet element in the suffix_min
                // is less than a[i] then move right
                if (suffix_min[mid] < a[i]) {
                    ans = mid;
                    low = mid + 1;
                }
                else
                    high = mid - 1;
            }
 
            // Print the required answer
            System.out.print(ans + " ");
        }
    }
 
    // Driver code
    public static void main(String[] args)
    {
        int[] a = { 3, 1, 5, 2, 4 };
        int n = a.length;
 
        farthest_min(a, n);
    }
}
 
// This code is contributed by ihritik

Python3

# Python3 implementation of the approach
 
# Function to find the farthest
# smaller number in the right side
 
 
def farthest_min(a, n):
 
    # To store minimum element
    # in the range i to n
    suffix_min = [0 for i in range(n)]
    suffix_min[n - 1] = a[n - 1]
    for i in range(n - 2, -1, -1):
        suffix_min[i] = min(suffix_min[i + 1], a[i])
 
    for i in range(n):
        low = i + 1
        high = n - 1
        ans = -1
 
        while (low <= high):
            mid = (low + high) // 2
 
            # If currnet element in the suffix_min
            # is less than a[i] then move right
            if (suffix_min[mid] < a[i]):
                ans = mid
                low = mid + 1
            else:
                high = mid - 1
 
        # Print the required answer
        print(ans, end=" ")
 
 
# Driver code
a = [3, 1, 5, 2, 4]
n = len(a)
 
farthest_min(a, n)
 
# This code is contributed by Mohit Kumar

C#

// C# implementation of the approach
using System;
class GFG {
 
    // Function to find the farthest
    // smaller number in the right side
    static void farthest_min(int[] a, int n)
    {
        // To store minimum element
        // in the range i to n
        int[] suffix_min = new int[n];
 
        suffix_min[n - 1] = a[n - 1];
        for (int i = n - 2; i >= 0; i--) {
            suffix_min[i]
                = Math.Min(suffix_min[i + 1], a[i]);
        }
 
        for (int i = 0; i < n; i++) {
            int low = i + 1, high = n - 1, ans = -1;
 
            while (low <= high) {
                int mid = (low + high) / 2;
 
                // If currnet element in the suffix_min
                // is less than a[i] then move right
                if (suffix_min[mid] < a[i]) {
                    ans = mid;
                    low = mid + 1;
                }
                else
                    high = mid - 1;
            }
 
            // Print the required answer
            Console.Write(ans + " ");
        }
    }
 
    // Driver code
    public static void Main()
    {
        int[] a = { 3, 1, 5, 2, 4 };
        int n = a.Length;
 
        farthest_min(a, n);
    }
}
 
// This code is contributed by ihritik

Output

3 -1 4 -1 -1

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

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