chore(CPlusPlus): add even no of digits (#579)

Co-authored-by: Arsenic <54987647+Arsenic-ATG@users.noreply.github.com>

algorithms/CPlusPlus/Maths/even-no-of-digits.cpp

@@ -0,0 +1,74 @@
+/*
+Description: Given an array nums of integers, return how many of them contain an even number of digits.
+
+Time Complexity: O(n) where n is the size of the array
+*/
+
+#include <iostream>
+#include <vector>
+using namespace std;
+
+//function to count the number of digits of every array element
+int countdigits(int n)
+{
+    int c = 0;
+    while (n > 0)
+    {
+        n = n / 10;
+        c++;
+    }
+    //return the count
+    return c;
+}
+//we can use common logarithms (base 10) to find the number of digits of an integer ( number of digits = log10(n) + 1 )
+//C/C++ provides us with a factory function ( defined in < cmath > header ) to compute common log of a number.
+//same function as above but with this approach
+
+/*
+int countdigits(int n)
+{
+	if(n < 0)
+		n = n * -1;
+	if(n)
+		return (int)log10((double)n) + 1;
+	else
+		return 1;
+}
+*/
+
+int findNumbers(vector<int> &nums)
+{
+    int count = 0;
+    for (auto it : nums)
+    {
+        //countdigits() will return the number of digits present in the element
+        int dc = countdigits(it);
+        //if it is even, increment the count
+        if ( ! (dc & 2) )
+        {
+            count++;
+        }
+    }
+    //at the end, return the count
+    return count;
+}
+
+//main starts
+int main()
+{
+    vector<int> nums = {12, 345, 2, 6, 7896};
+    cout << "Number of even no. digits are: " << findNumbers(nums);
+    return 0;
+}
+
+/*
+Input: nums = [12,345,2,6,7896]
+Output: 2
+Explanation: 
+12 contains 2 digits (even number of digits). 
+345 contains 3 digits (odd number of digits). 
+2 contains 1 digit (odd number of digits). 
+6 contains 1 digit (odd number of digits). 
+7896 contains 4 digits (even number of digits). 
+Therefore only 12 and 7896 contain an even number of digits.
+*/

algorithms/CPlusPlus/Maths/power-of-two.cpp

@@ -0,0 +1,43 @@
+#include <iostream>
+using namespace std;
+
+//function starts
+bool isPowerOfTwo(const n)
+{
+    //declare a variable to know if n is a power of 2 or not
+    long i = 1;
+    //at every iteration it will calcalute power of 2 starting from 1
+    while (i < n)
+    {
+        i = i * 2;
+    }
+    //if n is the power of 2, i and n value will be same
+    //if they are same, it will return true, else it will return false
+    return i == n;
+}
+
+//main starts
+int main()
+{
+    int n;
+    cin >> n;
+    cout << isPowerOfTwo(n);
+    return 0;
+}
+
+/*
+Example 1:
+
+Input: n = 1
+Output:1 (true) 
+Explanation: 20 = 1
+Example 2:
+
+Input: n = 16
+Output:1 (true) 
+Explanation: 24 = 16
+Example 3:
+
+Input: n = 3
+Output: 0 (false)
+*/

algorithms/CPlusPlus/Maths/small-numbers.cpp

@@ -0,0 +1,52 @@
+/*
+Description: Given the array nums, for each nums[i] find out how many numbers in the array are smaller than it. 
+
+Time Complexity: O(n) where n is the number of elements in the array
+*/
+#include <iostream>
+#include <vector>
+using namespace std;
+
+//function starts
+//will check if every jth element is smaller than ith element
+vector<int> smallerNumbersThanCurrent(vector<int> &nums)
+{
+    vector<int> v;
+    for (int i = 0; i < nums.size(); i++)
+    {
+        int count = 0;
+        for (int j = 0; j < nums.size(); j++)
+        {
+            if (nums[j] < nums[i])
+            {
+                count++;
+            }
+        }
+        v.push_back(count);
+    }
+    return v;
+}
+
+//main starts
+int main()
+{
+    vector<int> nums = {8, 1, 2, 2, 3};
+    vector<int> ans = smallerNumbersThanCurrent(nums);
+    cout << "The answer is: \n";
+    for (auto it : ans)
+    {
+        cout << it << " ";
+    }
+    return 0;
+}
+
+/*
+Input: nums = [8,1,2,2,3]
+Output: [4,0,1,1,3]
+Explanation: 
+For nums[0]=8 there exist four smaller numbers than it (1, 2, 2 and 3). 
+For nums[1]=1 does not exist any smaller number than it.
+For nums[2]=2 there exist one smaller number than it (1). 
+For nums[3]=2 there exist one smaller number than it (1). 
+For nums[4]=3 there exist three smaller numbers than it (1, 2 and 2).
+*/

algorithms/CPlusPlus/README.md

@@ -1,6 +1,7 @@
 # C++
 
 ## Arrays
+
 - [Counting Inversions](Arrays/counting-inversions.cpp)
 - [Dutch Flag Algorithm](Arrays/dutch-flag-algo.cpp)
 - [Left Rotation](Arrays/left-rotation.cpp)
@@ -22,6 +23,7 @@
 - [Kadane's Algorithm](Arrays/Kadane's-Algorithm.cpp)
 
 ## Dynamic-Programming
+
 - [Longest Common Subsequence](Dynamic-Programming/longest-common-subsequence.cpp)
 - [Longest Common Substring](Dynamic-Programming/longest-common-substring.cpp)
 - [0/1-knapsack](Dynamic-Programming/01-knapsack.cpp)
@@ -29,6 +31,7 @@
 - [Edit Distance](Dynamic-Programming/edit-distance.cpp)
 
 ## Graphs
+
 - [Bellman Ford Algorithm](Graphs/bellman-ford.cpp)
 - [kruskal Algorithm](Graphs/kruskal-algorithm.cpp)
 - [Breadth First Search](Graphs/breadth-first-search.cpp)
@@ -38,9 +41,11 @@
 - [Connected Components](Graphs/total-connected-components.cpp)
 
 ## Multiplication
+
 - [Karatsuba](Multiplication/karatsuba.cpp)
 
 ## Linked Lists
+
 - [All possible insertions](Linked-Lists/all-possible-insertion.cpp)
 - [Singly linked lists](Linked-Lists/singly.cpp)
 - [doubley linked lists](Linked-Lists/doubly.cpp)
@@ -55,6 +60,7 @@
 - [Remove Duplicate in Sorted linked list](Linked-Lists/remove-duplicates-in-sorted-linked-list.cpp)
 
 ## Searching
+
 - [Linear Search](Searching/linear-search.cpp)
 - [Jump Search](Searching/jump-search.cpp)
 - [Binary Search](Searching/binary-search.cpp)
@@ -65,12 +71,14 @@
 - [Exponential Search](Searching/exponential-search.cpp)
 
 ## Stacks
+
 - [Balancing Parenthesis](Stacks/balanced-parenthesis.cpp)
 - [Reversing Stack](Stacks/reverse-stack.cpp)
 - [Stack using Array](Stacks/stack-using-array.cpp)
 - [Infix to postfix expression conversion](Stacks/infix-to-postfix.cpp)
 
 ## Sorting
+
 - [Bubble Sort](Sorting/bubble-sort.cpp)
 - [Insertion Sort](Sorting/insertion-sort.cpp)
 - [Quicksort](Sorting/quick-sort.cpp)
@@ -88,6 +96,7 @@
 - [Cycle Sort](Sorting/cycle-sort.cpp)
 
 ## Strings
+
 - [Rabin-Karp pattern search algo](Strings/rabin-karp.cpp)
 - [All subsequence of a string (Recursion) ](Strings/sequence.cpp)
 - [String reversal](Strings/string-reverse.cpp)
@@ -100,6 +109,7 @@
 - [Boyer Moore pattern search](Strings/Boyer_Moore.cpp)
 
 ## Trees
+
 - [Creating Binary Tree](Trees/build-binary-tree.cpp)
 - [Counting and finding sum of all the nodes in BST](Trees/count-and-sum-of-nodes-in-binary-tree.cpp)
 - [Level Order Traversal](Trees/level-order-traversal.cpp)
@@ -115,6 +125,7 @@
 - [Iterative Segment Tree](Trees/IterativeSegmentTree.cpp)
 
 # Maths
+
 - [Kaprekar Number](Maths/Kaprekar-number.cpp)
 - [Prime Number](Maths/prime-check.cpp)
 - [Prime Sieve](Maths/prime-sieve.cpp)
@@ -126,9 +137,13 @@
 - [Missing number](Maths/missing-number.cpp)
 - [Factorial of a number](Maths/factorial.cpp)
 - [Prime-number](Maths/prime-number.cpp)
+- [Even number of digits](Maths/even-no-of-digits.cpp)
+- [Power of two](Maths/power-of-two.cpp)
+- [Small numbers](Maths/small-numbers.cpp)
 - [Segmented Sieve](Maths/segmented-sieve-range.cpp)
 
 # Recursion
+
 - [Tower of Hanoi](Recursion/towerofHanoi.cpp)
 - [Factorial](Recursion/factorial.cpp)
 - [Permutation](Recursion/permutation.cpp)
@@ -146,4 +161,3 @@
 - [Array sorted or not](Recursion\array-sorted-or-not.cpp)
 - [Product of two numbers](Recursion\product-of-numbers.cpp)
 - [Product of digits in a number](Recursion\product-of-digits.cpp)
-