Find Subarray ranges having difference between max and min exactly K

Given an array arr[] of length N and integer K, the task is to print subarray ranges (starting index, ending index) of the array where difference between max and min elements of the subarray is exactly K.( 1-based index )

Examples: 

Input: arr[] = {2, 1, 3, 4, 2, 6}, K = 2
Output: (1, 3), (2, 3), (3, 5), (4, 5)
Explanation: In the above array following sub array ranges have max min difference exactly K
(1, 3) => max = 3 and min = 1. Difference = 3 – 1 = 2
(2, 3) => max = 3 and min = 1. Difference = 3 – 1 = 2
(3, 5) => max = 4 and min = 2. Difference = 4 – 2 = 2
(4, 5) => max = 4 and min = 2. Difference = 4 – 2 = 2

Input: arr[] = {5, 3, 4, 6, 1, 2}, K = 6
Output: -1
Explanation: There is no such sub array ranges.

Approach: The basic idea to solve the problem is to form all the subarrays and find the minimum and maximum and their difference for each subarray. Follow the steps mentioned below to solve the problem.

• Iterate over the array from i = 0 to N-1:
  • Iterate from j = i to N-1:
    • Insert arr[j] current element in a set storing the current subarray starting from i.
    • Find the minimum and maximum of the set.
    • Get their difference and check if their difference is equal to K or not.
    • If it is, then push this range in the answer.
• Return the ranges.
• If no such range then return -1.

Below is the implementation of the above approach.

C++

// C++ implementation of above approach

#include <bits/stdc++.h>
using namespace std;

// Function to print index ranges
void printRanges(vector<int> arr, int n,
                 int K)
{
    int i, j, f = 0;
    for (i = 0; i < n; i++) {

        // Set to store the elements
        // of a subarray
        set<int> s;
        for (j = i; j < n; j++) {

            // Insert current element in set
            s.insert(arr[j]);

            // Calculate max and min for
            // any particular index range
            int max = *s.rbegin();
            int min = *s.begin();

            // If we get max-min = K
            // print 1 based index
            if (max - min == K) {
                cout << i + 1 << " " << j + 1
                     << "\n";
                f = 1;
            }
        }
    }

    // If we didn't find any index ranges
    if (f == 0)
        cout << -1 << endl;
}

// Driver Code
int main()
{
    vector<int> arr = { 2, 1, 3, 4, 2, 6 };
    int N = arr.size();
    int K = 2;

    // Function call
    printRanges(arr, N, K);
    return 0;
}

Java

// Java implementation of above approach
import java.util.*;

class GFG {

  // Function to print index ranges
  static void printRanges(int arr[], int n,
                          int K)
  {
    int i, j, f = 0;
    for (i = 0; i < n; i++) {

      // Set to store the elements
      // of a subarray
      Set<Integer> s = new HashSet<>();
      for (j = i; j < n; j++) {

        // Insert current element in set
        s.add(arr[j]);

        // Calculate max and min for
        // any particular index range
        int max = Collections.max(s);
        int min = Collections.min(s);

        // If we get max-min = K
        // print 1 based index
        if (max - min == K) {
          System.out.println( (i + 1) + " " + (j + 1));
          f = 1;
        }
      }
    }

    // If we didn't find any index ranges
    if (f == 0)
      System.out.println(-1);
  }

  // Driver Code
  public static void main (String[] args) {
    int arr[] = { 2, 1, 3, 4, 2, 6 };
    int N = arr.length;
    int K = 2;

    // Function call
    printRanges(arr, N, K);
  }
}

// This code is contributed by hrithikgarg03188.

Python3

# python3 implementation of above approach

# Function to print index ranges
def printRanges(arr, n, K):

    i, j, f = 0, 0, 0
    for i in range(0, n):

        # Set to store the elements
        # of a subarray
        s = set()
        for j in range(i, n):

            # Insert current element in set
            s.add(arr[j])

            # Calculate max and min for
            # any particular index range
            ma = max(list(s))
            mi = min(list(s))

            # If we get max-min = K
            # print 1 based index
            if (ma - mi == K):
                print(f"{i + 1} {j + 1}")

                f = 1

    # If we didn't find any index ranges
    if (f == 0):
        print(-1)

# Driver Code
if __name__ == "__main__":

    arr = [2, 1, 3, 4, 2, 6]
    N = len(arr)
    K = 2

    # Function call
    printRanges(arr, N, K)

# This code is contributed by rakeshsahni

C#

// C# implementation of above approach
using System;
using System.Collections.Generic;

class GFG {

  // Function to print index ranges
  static void printRanges(int[] arr, int n, int K)
  {
    int i, j, f = 0;
    for (i = 0; i < n; i++) {

      // Set to store the elements
      // of a subarray
      HashSet<int> s = new HashSet<int>();
      for (j = i; j < n; j++) {

        // Insert current element in set
        s.Add(arr[j]);

        // Calculate max and min for
        // any particular index range
        int max = int.MinValue,min = int.MaxValue;
        foreach(var value in s)
        {
          max = Math.Max(max,value);
          min = Math.Min(min,value);
        }

        // If we get max-min = K
        // print 1 based index
        if (max - min == K) {
          Console.Write( (i + 1) + " " + (j + 1) + "\n");
          f = 1;
        }
      }
    }

    // If we didn't find any index ranges
    if (f == 0)
      Console.Write(-1);
  }

  // Driver Code
  public static void Main()
  {
    int[] arr = { 2, 1, 3, 4, 2, 6 };
    int N = arr.Length;
    int K = 2;

    // Function call
    printRanges(arr, N, K);
  }
}

// This code is contributed by aditya942003patil.

Javascript

<script>
// Javascript implementation of above approach

// Function to print index ranges
function printRanges(arr, n, K)
{
  let i = 0, j = 0, f = 0;
  for (i = 0; i < n; i++) {

    // Set to store the elements
        // of a subarray
        const s = new Set();
        for (j = i; j < n; j++) {

            // Insert current element in set
            s.add(arr[j]);

            // Calculate max and min for
            // any particular index range
            let max = Math.max(...s);
            let min = Math.min(...s);

            // If we get max-min = K
            // print 1 based index
            if (max - min == K) {
                document.write((i+1) + " " + (j+1) + "<br>");
                f = 1;
            }
        }
    }

    // If we didn't find any index ranges
    if (f == 0)
    document.write(-1);

}

// Driver Code
let arr = [ 2, 1, 3, 4, 2, 6 ];
let N = arr.length;
let K = 2;

// Function call
printRanges(arr, N, K);

// This code is contributed by aditya942003patil.
</script>

Output

1 3
2 3
3 5
4 5

Time Complexity: O(N² * logN)
Auxiliary Space: O(N)

Efficient Approach: Instead of using the HashSet, keep a track of current maximum and minimum element while traversing the array.

C++

// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;

// Function to print index ranges
void printRanges(vector<int> arr, int n, int K)
{
  int i = 0, j = 0, f = 0;
  for (i = 0; i < n; i++) {

    int mx = INT_MIN, mn = INT_MAX;

    for (j = i; j < n; j++) {

      // Calculate max and min for
      // any particular index range
      mx = max(mx, arr[j]);
      mn = min(mn, arr[j]);

      // If we get max-min = K
      // print 1 based index
      if (mx - mn == K) {
        cout << (i + 1) << " " << (j + 1) << endl;
        f = 1;
      }
    }
  }

  // If we didn't find any index ranges
  if (f == 0)
    cout << -1;
}

// Driver Code
int main()
{
  vector<int> arr = { 2, 1, 3, 4, 2, 6 };
  int N = arr.size();
  int K = 2;

  // Function call
  printRanges(arr, N, K);
}

// This code is contributed by Samim Hossain Mondal.

Java

// Java implementation of above approach
import java.util.*;

public class GFG {

  // Function to print index ranges
  static void printRanges(int[] arr, int n, int K)
  {
    int i = 0, j = 0, f = 0;
    for (i = 0; i < n; i++) {

      int mx = Integer.MIN_VALUE, mn
        = Integer.MAX_VALUE;

      for (j = i; j < n; j++) {

        // Calculate max and min for
        // any particular index range
        mx = Math.max(mx, arr[j]);
        mn = Math.min(mn, arr[j]);

        // If we get max-min = K
        // print 1 based index
        if (mx - mn == K) {
          System.out.println((i + 1) + " "
                             + (j + 1));
          f = 1;
        }
      }
    }

    // If we didn't find any index ranges
    if (f == 0)
      System.out.print(-1);
  }

  // Driver Code
  public static void main(String args[])
  {
    int[] arr = { 2, 1, 3, 4, 2, 6 };
    int N = arr.length;
    int K = 2;

    // Function call
    printRanges(arr, N, K);
  }
}

// This code is contributed by Samim Hossain Mondal.

Python3

# Python3 implementation of above approach

# import the module
import sys

# Function to print index ranges
def printRanges(arr, n, K):

    i, j, f = 0, 0, 0

    for i in range(0, n):

        mn = sys.maxsize
        mx = -1*sys.maxsize

        for j in range(i, n):

            # Calculate max and min for
            # any particular index range

            mx = max(mx, arr[j])
            mn = min(mn, arr[j])
            # If we get max-min=K
            # print 1 based index

            if(mx - mn == K):
                print(f"{i + 1} {j + 1}")
                f=1


    # If we didn't find any index ranges
    if (f == 0):
        print(-1)

# Driver Code
if __name__ == "__main__":

    arr = [2, 1, 3, 4, 2, 6]
    N = len(arr)
    K = 2

    # Function call
    printRanges(arr, N, K)

# This code is contributed by Pushpesh Raj

C#

// C# implementation of above approach
using System;

class GFG {

    // Function to print index ranges
    static void printRanges(int[] arr, int n, int K)
    {
        int i = 0, j = 0, f = 0;
        for (i = 0; i < n; i++) {

            int mx = Int32.MinValue, mn = Int32.MaxValue;

            for (j = i; j < n; j++) {

                // Calculate max and min for
                // any particular index range
                mx = Math.Max(mx, arr[j]);
                mn = Math.Min(mn, arr[j]);

                // If we get max-min = K
                // print 1 based index
                if (mx - mn == K) {
                    Console.WriteLine((i + 1) + " "
                                      + (j + 1));
                    f = 1;
                }
            }
        }

        // If we didn't find any index ranges
        if (f == 0)
            Console.Write(-1);
    }

    // Driver Code
    public static void Main()
    {
        int[] arr = { 2, 1, 3, 4, 2, 6 };
        int N = arr.Length;
        int K = 2;

        // Function call
        printRanges(arr, N, K);
    }
}

// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
// Javascript implementation of above approach

// Function to print index ranges
function printRanges(arr, n, K)
{
  let i = 0, j = 0, f = 0;
  for (i = 0; i < n; i++) {

    let mx = Number.MIN_SAFE_INTEGER, mn = Number.MAX_SAFE_INTEGER;

    for (j = i; j < n; j++) {

      // Calculate max and min for
      // any particular index range
      mx = Math.max(mx, arr[j]);
      mn = Math.min(mn, arr[j]);

      // If we get max-min = K
      // print 1 based index
      if (mx - mn == K) {
        document.write((i + 1) + " " + (j + 1));
        f = 1;
      }
    }
  }

  // If we didn't find any index ranges
  if (f == 0)
    document.write(-1);
}

// Driver Code
let arr = [ 2, 1, 3, 4, 2, 6 ];
let N = arr.length;
let K = 2;

// Function call
printRanges(arr, N, K);

// This code is contributed by Samim Hossain Mondal.
</script>

Output

1 3
2 3
3 5
4 5

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