chore(CPlusPlus): add recursion programs (#559)

Co-authored-by: Ming Tsai <37890026+ming-tsai@users.noreply.github.com>

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 @@
 - [Smallest Possible Sum](Arrays/smallest-possible-sum.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)
@@ -31,6 +33,7 @@
 - [Coin Change](Dynamic-Programming/coin-change-problem.cpp)
 
 ## Graphs
+
 - [Bellman Ford Algorithm](Graphs/bellman-ford.cpp)
 - [kruskal Algorithm](Graphs/kruskal-algorithm.cpp)
 - [Breadth First Search](Graphs/breadth-first-search.cpp)
@@ -40,9 +43,11 @@
 - [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)
@@ -57,6 +62,7 @@
 - [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)
@@ -67,12 +73,14 @@
 - [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)
@@ -90,6 +98,7 @@
 - [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)
@@ -102,6 +111,7 @@
 - [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)
@@ -118,6 +128,7 @@
 - [Fenwick Tree](Trees/Fenwick_Tree.cpp)
 
 # Maths
+
 - [Kaprekar Number](Maths/Kaprekar-number.cpp)
 - [Prime Number](Maths/prime-check.cpp)
 - [Prime Sieve](Maths/prime-sieve.cpp)
@@ -131,6 +142,7 @@
 - [Prime-number](Maths/prime-number.cpp)
 
 # Recursion
+
 - [Tower of Hanoi](Recursion/towerofHanoi.cpp)
 - [Factorial](Recursion/factorial.cpp)
 - [Permutation](Recursion/permutation.cpp)
@@ -138,4 +150,10 @@
 - [Sum of all elements of an array](Recursion/Sum-of-all-elements-in-an-array.cpp)
 - [Decimal number to Binary conversion](Recursion/decimal-to-binary-conversion.cpp)
 - [Sum of digits of a decimal integer](Recursion/sum-of-digits-of-an-integer.cpp)
+- [Binary search using recursion](Recursion/binary-search.cpp)
+- [First uppercase letter in a string](Recursion/first-uppercase-letter.cpp)
+- [Reverse a string using recursion](Recursion/reverse-string.cpp)
+- [Find string length using recursion](Recursion/string-length.cpp)
+- [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)

algorithms/CPlusPlus/Recursion/binary-search.cpp

@@ -0,0 +1,62 @@
+/*
+Description: Binary search using recursion
+
+Approach: To use recursion, for updating start and end variables.
+
+Time Complexity: O(log n)
+*/
+
+#include <iostream>
+using namespace std;
+
+//function starts
+int search(int arr[], int n, int start, int end, int target)
+{
+    //base case
+    //if start is greater than end, it means we haven't found our target element
+    //return -1
+    if (start > end)
+    {
+        return -1;
+    }
+    //calculating mind element
+    int mid = start + (end - start) / 2;
+
+    if (arr[mid] == target)
+    {
+        return mid;
+    }
+    if (arr[mid] > target)
+    {
+        //end = mid-1;
+        return search(arr, n, start, mid - 1, target);
+    }
+    else
+    {
+        //start=mid+1;
+        return search(arr, n, mid + 1, end, target);
+    }
+}
+
+//main starts
+int main()
+{
+    // Write C++ code here
+    int arr[] = {1, 2, 3, 4, 5, 6};
+    int n = sizeof(arr) / sizeof(arr[0]);
+    int target = 6;
+    int start = 0;
+    int end = n - 1;
+    int ind = search(arr, n, start, end, target);
+    cout << "Element found at index: " << ind;
+    return 0;
+}
+
+/*
+Sample input:
+arr=[1,2,3,4,5,6]
+target=6;
+
+Output:
+Element found at index: 5
+*/

algorithms/CPlusPlus/Recursion/first-uppercase-letter.cpp

@@ -0,0 +1,52 @@
+/*
+Description: Program to print the first uppercase letter in a string
+
+Approach: Use a varialbe to iterate over the string
+Increment the iterator by 1 at every recursive call
+If the value of iterator reaches till the length of the string, return '\0
+
+Time Complexity: O(n) where n is the length of the string
+*/
+
+#include <iostream>
+using namespace std;
+
+//function starts
+char upper(string s, int i, int len)
+{
+    //base case
+    //if the value of i reaches till length of the string
+    //that means we have not found any uppercase letter
+    //return '\0
+    if (i == len)
+    {
+        return '\0';
+    }
+    //if uppercase letter found
+    //return it
+    if (s[i] >= 'A' and s[i] <= 'Z')
+    {
+        return s[i];
+    }
+    //recursive function call
+    //the iterator i starts from 0 and increments by 1 at each function call
+    return upper(s, i + 1, len);
+}
+
+//main starts
+int main()
+{
+    string s = "helloalL";
+    int len = s.size();
+    char c = upper(s, 0, len);
+    cout << c;
+    return 0;
+}
+
+/*
+Sample Input: helloalL
+Output: L
+
+Sample Input: hELLOaLL
+Output: E
+*/

algorithms/CPlusPlus/Recursion/min-max-element-in-array.cpp

@@ -0,0 +1,57 @@
+/*
+Description: To find minimum and maximum element in array using recursion
+
+Time Complexity: O(n)
+*/
+
+#include <iostream>
+using namespace std;
+
+//function to find minimum element in the array
+int findmin(int arr[], int n)
+{
+    //base case
+    //if there is only 1 element in array, it will be the minimum element
+    if (n == 1)
+    {
+        return arr[0];
+    }
+    //recursive function call
+    int mm = findmin(arr, n - 1);
+    //return minimum element from every recursive call to the function
+    return min(arr[n - 1], mm);
+}
+
+//function to find maximum element in the array
+int findmax(int arr[], int n)
+{
+    //base case
+    //if there is only 1 element in array, it will be the maximum element
+    if (n == 1)
+    {
+        return arr[0];
+    }
+    //recursive function call
+    int mm = findmax(arr, n - 1);
+    //return maximum element from every recursive call to the function
+    return max(arr[n - 1], mm);
+}
+
+//main starts
+int main()
+{
+    int arr[] = {-1, -2, 3, 4, 5, 6};
+    int n = 6;
+    cout << "Minimum element in array: " << findmin(arr, n) << endl;
+    cout << "Maximum element in array: " << findmax(arr, n);
+    return 0;
+}
+
+/*
+Sample Input:
+arr=[-1,-2,3,4,5,6]
+
+Output:
+Minimum element in array: -2
+Maximum element in array: 6
+*/

algorithms/CPlusPlus/Recursion/reverse-string.cpp

@@ -0,0 +1,48 @@
+/*
+Description: Program to reverse string using recursion
+
+Approach: To maintain start and end variables in string.
+Start represents starting index and end represent ending index.
+At each iteration, the character at starting index will be swapped 
+with the character at ending index.
+At every recursive call we will update start and end variables.
+Start will be incremented by 1 and end will be decremented by 1.
+We will return string when the value of start will be greater than end.
+This indicated the string has been reversed.
+
+Time complexity: O(n) where n is the length of string
+*/
+
+#include <iostream>
+using namespace std;
+
+//function starts
+string rev(string s, int start, int end)
+{
+    //base case
+    if (start > end)
+    {
+        return s;
+    }
+    //swapping characters at start and end index
+    swap(s[start], s[end]);
+
+    //recursive call with incrementing start and decrementing end
+    return rev(s, start + 1, end - 1);
+}
+
+//main starts
+int main()
+{
+    // Write C++ code here
+    string s = "hello";
+    int len = s.size();
+    cout << endl;
+    cout << rev(s, 0, len - 1);
+    return 0;
+}
+
+/*
+Input: hello
+Output: olleh
+*/

algorithms/CPlusPlus/Recursion/string-length.cpp

@@ -0,0 +1,41 @@
+/*
+Description: find length of string using recursion.
+
+Approach: To run the recursive call till the end of the string.
+Maintaining a iterator variable which will increment at every recursive call
+If we reach at the end of the string, return the value of the iterator variable
+which will be the length of the string.
+
+Time Complexity: O(n) where n is the length of the string
+*/
+#include <iostream>
+using namespace std;
+
+//function starts
+int cal_length(string s, int i = 0)
+{
+    if (s[i] == '\0')
+    {
+        return i;
+    }
+    return cal_length(s, i + 1);
+}
+
+//main starts
+int main()
+{
+    string s = "hello";
+    cout << cal_length(s);
+    return 0;
+}
+
+/*
+Sample Input: hello
+Output: 5
+
+Sample Input: good
+Output: 4
+
+Sample Input: github
+Output: 6
+*/

algorithms/CPlusPlus/Recursion/sum-of-n.cpp

@@ -0,0 +1,38 @@
+/*
+Description: A program to find sum of n natural numbers using recursion.
+
+Time Complexity: O(n)
+*/
+
+#include <iostream>
+using namespace std;
+
+//function starts
+int sumofN(int n)
+{
+    //base case
+    if (n <= 1)
+    {
+        return n;
+    }
+    //recursive function call
+    int res = sumofN(n - 1);
+    //return sum
+    return n + res;
+}
+
+// Driver code
+int main()
+{
+    int n = 5;
+    cout << sumofN(n);
+    return 0;
+}
+
+/*
+Sample Input: 5
+Output: 15
+
+Sample Input: 3
+Output: 6
+*/