Merge pull request #1163 from Abhinavcode13/patch-11

Create Uniquedigits.cpp

Author: akgmage

Math/Uniquedigits.cpp

@@ -0,0 +1,39 @@
+/*Name : Abhinav kumar
+Github username : Abhinavcode13
+Repository name : data-structures-and-algorithms
+Problem : Count Numbers with Unique Digits in C++
+Issue Number : #500
+Problem statement : 
+
+Explanation of the below C++ code :
+
+In this implementation, we first handle the base case of n = 0 by returning 1. Then, we initialize the answer ans to 10 since there are 10 unique digits between 0 and 9. We also initialize the variables unique_digits and available_digits to 9 since we can't use 0 as the first digit.
+
+Next, we enter a loop that runs n-1 times (since we have already considered the case of i = 1). In each iteration of the loop, we compute unique_digits as the product of the current value of unique_digits and available_digits. We then add unique_digits to the answer ans and decrement available_digits. This is because we can't use the digits that have already been used for the previous digits.
+
+Finally, we return the value of ans.
+
+The time complexity of this algorithm is O(n), where n is the input parameter representing the number of digits.
+
+The space complexity of this algorithm is O(1), as we are only using a constant amount of extra memory to store the variables ans, unique_digits, and available_digits, regardless of the input size.
+
+*/
+-------------------------------------------------------------------------//C++ code begins here----------------------------------------------------------------------------
+
+class Solution {
+public:
+    int countNumbersWithUniqueDigits(int n) {
+        if (n == 0) {
+            return 1;   // return 1 for n = 0
+        }
+        int ans = 10;   // start with 10 unique digits, as we can have numbers 0-9
+        int unique_digits = 9;  // start with 9 digits, as we cannot use 0 as first digit
+        int available_digits = 9;   // remaining available digits
+        while (n-- > 1 && available_digits > 0) {
+            unique_digits *= available_digits; // calculate number of unique numbers that can be formed
+            ans += unique_digits; // add number of unique numbers to the answer
+            available_digits--; // reduce available digits by 1
+        }
+        return ans; // return final answer
+    }
+};