Find position of given term in a series formed with only digits 4 and 7 allowed

There is a series of numbers that have only digits, 4 and 7, and numbers are arranged in increasing order. The first few numbers of the series are 4, 7, 44, 47, 74, 77, 444, …etc. Given a number N, the task is to find the position of that number in the given series.

Examples:

Input: N = 4
Output: 1
Explanation:
The first number in the series is 4

Input: N = 777
Output: 14
Explanation:
The 14th number in the series is 777

Approach: This problem can be solved using the below observations:



Below is the implementation of the above approach:

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// C++ program for the above approach
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the position
// of the number N
void findPosition(int n)
{
    int i = 0;
  
    // To store the position of N
    int pos = 0;
  
    // Iterate through all digit of N
    while (n > 0) {
  
        // If current digit is 7
        if (n % 10 == 7) {
            pos = pos + pow(2, i + 1);
        }
  
        // If current digit is 4
        else {
            pos = pos + pow(2, i);
        }
  
        i++;
        n = n / 10;
    }
  
    // Print the final position
    cout << pos;
}
  
// Driver Code
int main()
{
    // Given number of the series
    int N = 777;
  
    // Function Call
    findPosition(N);
    return 0;
}
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// Java program for the above approach
import java.util.*;
class GFG{
  
// Function to find the position
// of the number N
static void findPosition(int n)
{
    int i = 0;
  
    // To store the position of N
    int pos = 0;
  
    // Iterate through all digit of N
    while (n > 0
    {
  
        // If current digit is 7
        if (n % 10 == 7)
        {
            pos = pos + (int)Math.pow(2, i + 1);
        }
  
        // If current digit is 4
        else
        {
            pos = pos + (int)Math.pow(2, i);
        }
  
        i++;
        n = n / 10;
    }
  
    // Print the final position
    System.out.print(pos);
}
  
// Driver Code
public static void main(String[] args)
{
    // Given number of the series
    int N = 777;
  
    // Function Call
    findPosition(N);
}
}
  
// This code is contributed by shivanisinghss2110
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# Python3 program for the above approach
  
# Function to find the position
# of the number N
def findPosition(n):
      
    i = 0
  
    # To store the position of N
    pos = 0
  
    # Iterate through all digit of N
    while (n > 0):
  
        # If current digit is 7
        if (n % 10 == 7):
            pos = pos + pow(2, i + 1)
  
        # If current digit is 4
        else:
            pos = pos + pow(2, i)
              
        i += 1
        n = n // 10
  
    # Print the final position
    print(pos)
  
# Driver Code
if __name__ == '__main__':
      
    # Given number of the series
    N = 777
  
    # Function Call
    findPosition(N)
  
# This code is contributed by mohit kumar 29
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// C# program for the above approach
using System;
class GFG{
  
// Function to find the position
// of the number N
static void findPosition(int n)
{
    int i = 0;
  
    // To store the position of N
    int pos = 0;
  
    // Iterate through all digit of N
    while (n > 0) 
    {
  
        // If current digit is 7
        if (n % 10 == 7)
        {
            pos = pos + (int)Math.Pow(2, i + 1);
        }
  
        // If current digit is 4
        else
        {
            pos = pos + (int)Math.Pow(2, i);
        }
  
        i++;
        n = n / 10;
    }
  
    // Print the final position
    Console.Write(pos);
}
  
// Driver Code
public static void Main()
{
    // Given number of the series
    int N = 777;
  
    // Function Call
    findPosition(N);
}
}
  
// This code is contributed by Code_Mech
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Output:
14

Time Complexity: O(log10N)

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