add recursion programs

Author: Code-Recursion

Recurison/Programs/exponent.cpp

@@ -0,0 +1,18 @@
+#include <iostream>
+using namespace std;
+
+int power(int m, int n)
+{
+    if (n == 0)
+        return 1;
+    return power(m, n - 1) * m;
+}
+
+int main()
+{
+    cout << power(5, 2);
+    return 0;
+}
+
+// output 
+// 25

Recurison/Programs/factorial.cpp

@@ -0,0 +1,26 @@
+#include <iostream>
+using namespace std;
+
+int F[10];
+
+int fib(int n)
+{
+    if (n <= 1)
+    {
+        F[n] = n;
+        return n;
+    }
+    else
+    {
+        if (F[n] == -1)
+            F[n - 2] = fib(n - 2);
+        if (F[n - 1] == -1)
+            F[n - 1] = fib(n - 1);
+        return fib(n - 2) + F[n - 1];
+    }
+}
+int main()
+{
+    cout << fib(5);
+    return 0;
+}

Recurison/Programs/fib_memoization.cpp

@@ -0,0 +1,17 @@
+#include <iostream>
+using namespace std;
+int fib(int n)
+{
+    if (n <= 1)
+        return n;
+    return fib(n - 2) + fib(n - 1);
+}
+int main()
+{
+    cout << fib(5);
+    return 0;
+}
+
+// analysis
+// for n = 5, 15 calls
+// O(2^n)

Recurison/Programs/fibb.cpp

@@ -0,0 +1,13 @@
+#include <iostream>
+using namespace std;
+int sum_n(int n)
+{
+    if (n == 1)
+        return 1;
+    return sum_n(n - 1) + n;
+}
+int main()
+{
+    int n = 5;
+    cout << sum_n(n);
+}

Recurison/Programs/first_n_sum.cpp

@@ -0,0 +1,23 @@
+#include <iostream>
+using namespace std;
+int fact(int n)
+{
+    if (n == 0)
+        return 1;
+    return n * fact(n - 1);
+}
+int ncr(int n, int r)
+{
+    int term_1, term_2, term_3;
+    term_1 = fact(n);
+    term_2 = fact(r);
+    term_3 = fact(n - r);
+    return term_1 / (term_2 * term_3);
+}
+int main()
+{
+    cout << ncr(5, 3);
+    return 0;
+}
+
+// Time O(n)

Recurison/Programs/ncr.cpp

@@ -0,0 +1,42 @@
+/* combination using Pascal's Triangle
+              1
+             / \
+            1   1
+           / \ / \
+          1   2   1
+         / \ / \ / \
+        1   3   3   1
+
+    Can be represented as:
+
+             0c0
+            /   \
+         1c0     1c0
+        /   \   /   \
+      2c0    2c1     2c2
+     /   \  /   \   /   \
+  3c0     3c1    3c2     3c3
+
+*/
+
+#include <iostream>
+using namespace std;
+int fact(int n)
+{
+    if (n == 0)
+        return 1;
+    return n * fact(n - 1);
+}
+
+int ncr(int n, int r)
+{
+    if (n == r || r == 0)
+        return 1;
+    return ncr(n - 1, r - 1) + ncr(n - 1, r);
+}
+
+int main()
+{
+    cout << ncr(10, 2);
+    return 0;
+}

Recurison/Programs/ncr_pascal_triangle.cpp

@@ -0,0 +1,31 @@
+#include <stdio.h>
+
+int fun1(int n)
+{
+    if (n > 0)
+    {
+        return fun1(n - 1) + n;
+    }
+    return 0;
+}
+static int x = 0;
+int fun2(int n)
+{
+    if (n > 0)
+    {
+        x++;
+        return fun2(n - 1) + x;
+    }
+    return 0;
+}
+int main()
+{
+    int result1, result2;
+    result1 = fun1(5);
+    result2 = fun2(5);
+    printf("%d\n", result1);
+    printf("%d", result2);
+}
+
+// fun 2 = output 15 sum of first n natural no.s;
+// fun 1 = output 25;

Recurison/Programs/staticVariable.c

@@ -0,0 +1,24 @@
+#include <iostream>
+using namespace std;
+
+// TOH(no. of disks, tower 1, tower 2, tower3)
+
+void TOH(int n, int A, int B, int C)
+{
+    if (n > 0)
+    {
+        TOH(n - 1, A, C, B);
+        static int i = 0;
+        cout << "Step " << ++i << " (" << A << "," << C << ")" << endl;
+        TOH(n - 1, B, A, C);
+    }
+}
+
+int main()
+{
+    TOH(64, 1, 2, 3);
+    return 0;
+}
+
+// Analysis
+// Time O(2^n)