Given a number N. Find the count of such numbers that can be formed using digits 3 and 4 only and having length at max N.
Input : N = 2 Output : 6 Explanation : 3, 4, 33, 34, 43, 44 are numbers having length 2 and digits 3 and 4 only. Input : N = 1 Output : 2 Explanation : 3, 4 are the only such numbers.
Approach : There are 2 numbers of length 1. They are 3 and 4. There are 4 numbers of length 2. They are 33, 34, 43 and 44. There are 8 such numbers of length 3. They are 333, 334, 343, 344, 433, 434, 443, 444. For each addition of 1 to the length, the number of numbers is increased times 2.
It is easy to prove: to any number of the previous length one can append 3 or 4, so one number of the previous length creates two numbers of the next length.
So for the length N the amount of such numbers of the length exactly N is 2*N. But in the problem, we need the number of numbers of length not greater than N. Let’s sum up them. 21 = 2, 21 + 22 = 2 + 4 = 6, 21 + 22 + 23 = 2 + 4 + 8 = 14, 21 + 22 + 23 + 24 = 2 + 4 + 8 + 16 = 30.
One can notice that the sum of all previous powers of two is equal to the next power of two minus the first power of two. So the answer to the problem is 2N+1 – 2.
Below is the implementation of the above approach :
- Numbers of Length N having digits A and B and whose sum of digits contain only digits A and B
- Count of numbers between range having only non-zero digits whose sum of digits is N and number is divisible by M
- Count of numbers upto N digits formed using digits 0 to K-1 without any adjacent 0s
- Count numbers formed by given two digit with sum having given digits
- Count of binary strings of length N having equal count of 0's and 1's and count of 1's ≥ count of 0's in each prefix substring
- Find position of given term in a series formed with only digits 4 and 7 allowed
- Find Nth even length palindromic number formed using digits X and Y
- Length of the smallest number which is divisible by K and formed by using 1's only
- Count number of binary strings of length N having only 0's and 1's
- Find maximum number that can be formed using digits of a given number
- Count of N-digit Numbers having Sum of even and odd positioned digits divisible by given numbers
- Count of integers of length N and value less than K such that they contain digits only from the given set
- Length of longest subarray having only K distinct Prime Numbers
- Maximize count of strings of length 3 that can be formed from N 1s and M 0s
- Min and max length subarray having adjacent element difference atmost K
- Sum of all numbers that can be formed with permutations of n digits
- Count of alphabets whose ASCII values can be formed with the digits of N
- Find the largest number that can be formed by changing at most K digits
- Count of substrings formed using a given set of characters only
- Number formed by deleting digits such that sum of the digits becomes even and the number odd
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