A number is called faithful if you can write it as the sum of distinct powers of 7. e.g., 2457 = 7 + 72 + 74 . If we order all the faithful numbers, we get the sequence 1 = 70, 7 = 71, 8 = 70 + 71, 49 = 72, 50 = 70 + 72 . . . and so on. Given some value of N, you have to find the N'th faithful number.
Example 1:
Input:
N = 3Output:8Explanation:8 is the 3rd Faithful number.
Example 2:
Input:
N = 7Output:57Explanation:57 is the 7th Faithful number.
Your Task:
You don't need to read input or print anything. Your task is to complete the function nthFaithfulNum() which takes an Integer N as input and returns the answer.
Expected Time Complexity: O(log(N)) Expected Auxiliary Space: O(log(N))
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Avoid using static/global variables in your code as your code is tested
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Avoid using static/global variables in coding problems as your code is tested
against multiple test cases and these tend to retain their previous values.
Passing the Sample/Custom Test cases in coding problems does not guarantee the
correctness of code. On submission, your code is tested against multiple test cases
consisting of all possible corner cases and stress constraints.
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