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 = 4Output:1Explanation:

The first number in the series is 4

Input:N = 777Output:14Explanation:

The 14th number in the series is 777

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

- Below is the pattern observe in the given series. The numbers can be seen as:
"" / \ 4 7 / \ / \ 44 47 74 77 / \ / \ / \ / \

- As we can observe the pattern is increasing in power of
**2**. Therefore the idea is to iterate over the digits of the number starting from the least significant digit and update the position of the number as:- If current digit = 7, then add
to the position. - If current digit = 4, then add
to the position.

- If current digit = 7, then add
- Print the final position after the above operations.

Below is the implementation of the above approach:

`// 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(log _{10}N)*

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