Modifique una string binaria cambiando los caracteres de modo que cualquier par de índices que consistan en 1 no sean coprimos ni divisibles entre sí.

Dado un número entero N y una string binaria que consta de 4*N número de 0 inicialmente, la tarea es invertir los caracteres de modo que dos pares cualesquiera de índices de la string que consta de 1 no sean coprimos ni el par de índices pueda ser divisibles entre sí. 
Nota: considere la indexación basada en 1 .

Ejemplos:

Entrada: N = 3, S = “ 000000000000”
Salida: 000000010101
Explicación: En la string modificada “000000010101”, los índices de 1 son {8, 10, 12}. En el conjunto de índices anterior, no existe ningún par de índices que sean coprimos y divisibles entre sí.

Entrada: N = 2, S = “00000000”
Salida: 00000101

Enfoque: El problema dado se puede resolver basándose en la observación de que si los caracteres se invierten en las posiciones 4*N, 4*N – 2, 4*N – 4, … hasta N términos , entonces no existe ningún par de índices que son divisibles entre sí y tienen MCD igual a 1 .

A continuación se muestra la implementación del enfoque anterior:

#include <iostream>
using namespace std;
 
// Function to modify a string such
// that there doesn't exist any pair
// of indices consisting of 1s, whose
// GCD is 1 and are divisible by each other
void findString(char S[], int N)
{
  int strLen = 4 * N;
 
  // Flips characters at indices
  // 4N, 4N - 2, 4N - 4 .... upto N terms
  for (int i = 1; i <= N; i++) {
 
    S[strLen - 1] = '1';
    strLen -= 2;
  }
 
  // Print the string
  for (int i = 0; i < 4 * N; i++) {
    cout << S[i];
  }
}
 
// Driver code
int main()
{
 
  int N = 2;
 
  char S[4 * N];
 
  // Initialize the string S
  for (int i = 0; i < 4 * N; i++)
    S[i] = '0';
  // function call
  findString(S, N);
  return 0;
}
 
// This code is contributed by aditya7409.

// Java program for the above approach
import java.io.*;
 
class GFG {
 
    // Function to modify a string such
    // that there doesn't exist any pair
    // of indices consisting of 1s, whose
    // GCD is 1 and are divisible by each other
    public static void findString(char S[], int N)
    {
        int strLen = 4 * N;
 
        // Flips characters at indices
        // 4N, 4N - 2, 4N - 4 .... upto N terms
        for (int i = 1; i <= N; i++) {
 
            S[strLen - 1] = '1';
            strLen -= 2;
        }
 
        // Print the string
        System.out.println(S);
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        int N = 2;
 
        char S[] = new char[4 * N];
 
        // Initialize the string S
        for (int i = 0; i < 4 * N; i++)
            S[i] = '0';
 
        findString(S, N);
    }
}

# Python3 program for the above approach
 
# Function to modify a string such
# that there doesn't exist any pair
# of indices consisting of 1s, whose
# GCD is 1 and are divisible by each other
def findString(S, N) :
  strLen = 4 * N
 
  # Flips characters at indices
  # 4N, 4N - 2, 4N - 4 .... upto N terms
  for i in range(1, N + 1):
    S[strLen - 1] = '1'
    strLen -= 2
   
  # Print the string
  for i in range(4 * N):
    print(S[i], end = "")
 
# Driver code
 
N = 2
S = [0] * (4 * N)
 
# Initialize the string S
for i in range(4 * N):
    S[i] = '0'
     
# function call
findString(S, N)
 
# This code is contributed by sanjoy_62.

// C# program to implement
// the above approach
using System;
 
public class GFG
{
   
    // Function to modify a string such
    // that there doesn't exist any pair
    // of indices consisting of 1s, whose
    // GCD is 1 and are divisible by each other
    public static void findString(char[] S, int N)
    {
        int strLen = 4 * N;
 
        // Flips characters at indices
        // 4N, 4N - 2, 4N - 4 .... upto N terms
        for (int i = 1; i <= N; i++) {
 
            S[strLen - 1] = '1';
            strLen -= 2;
        }
 
        // Print the string
        Console.WriteLine(S);
    }
 
// Driver Code
public static void Main(String[] args)
{
    int N = 2;
    char[] S = new char[4 * N];
 
    // Initialize the string S
    for (int i = 0; i < 4 * N; i++)
        S[i] = '0';
 
    findString(S, N);
}
}
 
// This code is contributed by souravghosh0416.

<script>
      // Function to modify a string such
      // that there doesn't exist any pair
      // of indices consisting of 1s, whose
      // GCD is 1 and are divisible by each other
      function findString(S, N) {
        var strLen = 4 * N;
 
        // Flips characters at indices
        // 4N, 4N - 2, 4N - 4 .... upto N terms
        for (var i = 1; i <= N; i++)
        {
          S[strLen - 1] = "1";
          strLen -= 2;
        }
 
        // Print the string
        for (var i = 0; i < 4 * N; i++)
        {
          document.write(S[i]);
        }
      }
       
      // Driver code
      var N = 2;
      var S = [...Array(4 * N)];
       
      // Initialize the string S
      for (var i = 0; i < 4 * N; i++) S[i] = "0";
       
      // function call
      findString(S, N);
       
      // This code is contributed by rdtank.
    </script>

00000101

Complejidad temporal: O(N)
Espacio auxiliar: O(1)