chore(CPlusPlus): add recursion programs - part 2 (#574)

algorithms/CPlusPlus/README.md

@@ -158,3 +158,6 @@
 - [Sum of n natural numbers](Recursion/sum-of-n.cpp)
 - [Minimum and maximum element in array](Recursion/min-max-element-in-array.cpp)
 - [Prime Check](Recursion/recursive-prime.cpp)
+- [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)

algorithms/CPlusPlus/Recursion/array-sorted-or-not.cpp

@@ -0,0 +1,54 @@
+/*
+Description: A program to check if array is sorted or not using recursion
+
+Approach: To compare last (n-1) element with the second last (n-2) element.
+And decrementing the value of n at each recursive call, so that
+we can search the entire array.
+
+Time complexity: O(n)
+*/
+
+#include <iostream>
+using namespace std;
+
+//function starts
+bool sorted(int arr[], int n)
+{
+    //base case
+    if (n == 1 || n == 0)
+    {
+        return true;
+    }
+
+    if (arr[n - 1] > arr[n - 2])
+    {
+        //recursive function call
+        return sorted(arr, n - 1);
+    }
+    //if the element at (n-1) index is not greater than (n-2) element
+    //return false directly, which means array is not sorted
+    return false;
+}
+
+//main starts
+int main()
+{
+    int arr[] = {8, 2, 3, 4, 5, 6};
+    int n = sizeof(arr) / sizeof(arr[0]);
+    cout << sorted(arr, n);
+    return 0;
+}
+
+/*
+Sample Input:
+arr=[8, 2, 3, 4, 5, 6]
+n=6
+
+Output: 0
+
+Sample Input:
+arr=[1,2,3]
+n=3
+
+Output: 1
+*/

algorithms/CPlusPlus/Recursion/product-of-digits.cpp

@@ -0,0 +1,42 @@
+/*
+Description: A program to get product of digits using recursion
+
+TIme Complexity: O(n) where n is the number of digits present in the number 
+*/
+
+#include <iostream>
+using namespace std;
+
+//function starts
+int dp(int n)
+{
+    //base case
+    //where n is a one-digit number
+    if (n % 10 == n)
+    {
+        return n;
+    }
+    //recursive function call
+    //at every recursive call, dividing the number by 10
+    return (n % 10) * dp(n / 10);
+}
+
+//main starts
+int main()
+{
+    int n = 333;
+    cout << dp(n);
+    return 0;
+}
+
+/*
+Sample Input:
+n=333
+
+Output: 27
+
+Sample Input:
+n=412
+
+Output: 8
+*/

algorithms/CPlusPlus/Recursion/product-of-numbers.cpp

@@ -0,0 +1,49 @@
+/*
+Description: C++ program to find product of 2 numbers using Recursion.
+
+Approach: Product of two numbers (x,y) can be defined as y times sum of x.
+Calling the function recursively y times and adding x to it.
+
+Time Complexity: O(n) where n is the value of y
+*/
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// recursive function to calculate multiplication of two numbers
+int product(int x, int y)
+{
+    // if x is less than
+    // y swap the numbers
+    if (x < y)
+        return product(y, x);
+
+    // iteratively calculate
+    // y times sum of x
+    else if (y != 0)
+        return (x + product(x, y - 1));
+
+    // if any of the two numbers is
+    // zero return zero
+    else
+        return 0;
+}
+
+int main()
+{
+    int x = 5, y = 2;
+    cout << product(x, y);
+    return 0;
+}
+
+/*
+Sample Input:
+x=5, y=2
+
+Output: 10
+
+Sample Input:
+x=6, y=7
+
+Output: 42
+*/