Check if a pair of integers A and B can coincide by shifting them by distances arr[(A%N +N)%N] and arr[(B%N +N)%N]

Given an array arr[] of size N, the task is to check if any two integers A and B coincide at a single point on the number line after shifting them by a distance arr[(A%N +N)%N] and arr[(B%N +N)%N] respectively. If it is not possible, then print “No”. Otherwise, print “Yes”.

Examples:

Input: arr[] = {5, 4, 3}
Output: Yes 
Explanation:
Let the value of A = -4 and B = -6 coincide at point -1 on the number line.
After shifting,
A = -4 + arr[(-4 % 3 + 3) % 3] = -4 + arr[2] = -4 + 3 = -1.
B = -6 + arr[(-6 % 3 + 3) % 3] = -6 + 5 = -1.

Input: arr[]= {-4, 4, 4, 4}
Output: No

Approach: Follow the steps below to solve the problem:

• Initialize a Hashmap, say mp, to store the final position of integers.
• Initialize a string, say ans, as “No” to store the required answer.
• Iterate over the range [0, N – 1] using the variable i and perform the following steps:
  • Store the final position of i in a variable, say temp = ((i + arr[i]) % N + N) % N.
  • If the value of temp is present in mp, then set ans as “Yes” and break out of the loop.
  • Mark temp as visited by incrementing mp[temp] by 1.
• After completing the above steps, print the value of ans as the required answer.

Below is the implementation of the above approach:

C++14

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to check if two
// integers coincide at a point
void checkSamePosition(int arr[], int n)
{
    // Store the final position
    // of integers A and B
    unordered_map<int, int> mp;

    // Iterate over the range[0, n]
    for (int i = 0; i < n; i++) {

        // Store the final position
        // of the integer i
        int temp = ((i + arr[i]) % n + n) % n;

        // If temp is present in the Map
        if (mp.find(temp) != mp.end()) {

            // Print Yes and return
            cout << "Yes";
            return;
        }

        // Mark its final
        // position as visited
        mp[temp]++;
    }

    // If every integer stored
    // in the Map is unique
    cout << "No";
}

// Driver Code
int main()
{
    int arr[] = { 5, 4, 3 };
    int N = sizeof(arr) / sizeof(arr[0]);

    checkSamePosition(arr, N);

    return 0;
}

Java

// Java program to implement
// the above approach
import java.util.*;

class GFG{

  // Function to check if two
  // integers coincide at a point
  static void checkSamePosition(int[] arr, int n)
  {

    // Store the final position
    // of integers A and B
    Map<Integer,
    Integer> mp = new HashMap<Integer,
    Integer>();

    // Iterate over the range[0, n]
    for (int i = 0; i < n; i++) {

      // Store the final position
      // of the integer i
      int temp = ((i + arr[i]) % n + n) % n;

      // If temp is present in the Map
      if (mp.get(temp) == null) {

        // Print Yes and return
        System.out.println("Yes");
        return;
      }

      // Mark its final
      // position as visited

      mp.get(temp + 1);
    }

    // If every integer stored
    // in the Map is unique
    System.out.println("No");
  }


  // Driver Code
  public static void main(String[] args)
  {
    int[] arr = { 5, 4, 3 };
    int N = arr.length;

    checkSamePosition(arr, N);
  }
}

// This code is contributed by splevel62.

Python3

# Python 3 program for the above approach

# Function to check if two
# integers coincide at a point
def checkSamePosition(arr, n):
    # Store the final position
    # of integers A and B
    mp = {}

    # Iterate over the range[0, n]
    for i in range(n):
        # Store the final position
        # of the integer i
        temp = ((i + arr[i]) % n + n) % n

        # If temp is present in the Map
        if temp in mp:
            # Print Yes and return
            print("Yes")
            return

        # Mark its final
        # position as visited
        if(temp in mp):
            mp[temp] += 1
        else:
            mp[temp] = mp.get(temp,0)+1

    # If every integer stored
    # in the Map is unique
    print("No")

# Driver Code
if __name__ == '__main__':
    arr =  [5, 4, 3]
    N = len(arr)
    checkSamePosition(arr, N)

    # This code is contributed by ipg2016107.

C#

// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG {

    // Function to check if two
    // integers coincide at a point
    static void checkSamePosition(int[] arr, int n)
    {

        // Store the final position
        // of integers A and B
        Dictionary<int, int> mp = new Dictionary<int, int>();

        // Iterate over the range[0, n]
        for (int i = 0; i < n; i++) {

            // Store the final position
            // of the integer i
            int temp = ((i + arr[i]) % n + n) % n;

            // If temp is present in the Map
            if (mp.ContainsKey(temp)) {

                // Print Yes and return
                Console.Write("Yes");
                return;
            }

            // Mark its final
            // position as visited
            mp[temp] = 1;
        }

        // If every integer stored
        // in the Map is unique
        Console.Write("No");
    }

  // Driver code
  static void Main() {
    int[] arr = { 5, 4, 3 };
    int N = arr.Length;

    checkSamePosition(arr, N);
  }
}

// This code is contributed by divyeshrabadiya07.

Javascript

<script>

// JavaScript program for the above approach

// Function to check if two
// integers coincide at a point
function checkSamePosition(arr, n)
{
    // Store the final position
    // of integers A and B
    var mp = new Map();

    // Iterate over the range[0, n]
    for (var i = 0; i < n; i++) {

        // Store the final position
        // of the integer i
        var temp = ((i + arr[i]) % n + n) % n;

        // If temp is present in the Map
        if (mp.has(temp)) {

            // Print Yes and return
            document.write( "Yes");
            return;
        }

        // Mark its final
        // position as visited
        if(mp.has(temp))
        {
            mp.set(temp, mp.get(temp)+1)
        }
        else
            mp.set(temp, 1)
    }

    // If every integer stored
    // in the Map is unique
    document.write( "No");
}

// Driver Code

var arr = [5, 4, 3 ];
var N = arr.length;

checkSamePosition(arr, N);


</script>

Output:

Yes

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