Create recursion_exercises_python.py

Author: silvuple

recursion_exercises_python.py

@@ -0,0 +1,195 @@
+"""
+1. Write a Python program to calculate the sum of a list of numbers.
+"""
+
+def sum_of_list(my_list):
+    if not my_list:
+        return 0
+    elif len(my_list) == 1:
+        return my_list[0]
+    else:
+        return my_list[0] + sum_of_list(my_list[1:])
+
+print(sum_of_list([1,2,3]))
+
+"""
+3. Write a Python program of recursion list sum. 
+Test Data: [1, 2, [3,4], [5,6]]
+Expected Result: 21
+"""
+
+def sum_of_list(my_list):
+    if not my_list:
+        return 0
+    elif isinstance(my_list[0], list):
+        return sum_of_list(my_list[0]) + sum_of_list(my_list[1:])
+    elif len(my_list) == 1:
+        return my_list[0]
+    else:
+        return my_list[0] + sum_of_list(my_list[1:])
+        
+print(sum_of_list([1, 2, [3,4], [5,6]]))
+
+"""
+4. Write a Python program to get the factorial of a non-negative integer.
+"""
+
+def factorial(number):
+    if number == 0 or number == 1:
+        return 1
+    else:
+        return number * factorial(number-1)
+
+print(factorial(2))
+
+"""
+5. Write a Python program to solve the Fibonacci sequence using recursion.
+"""
+
+ solution 1: bad function that will work for a low n but will slow the
+ computation drastically as the n increases
+def fibonacci(n):
+    if n == 1 or n == 2:
+        b = 1
+    if n > 2:
+        b = fibonacci(n-1) + fibonacci(n-2)
+    return b
+
+for i in range(1, 21):
+    print(fibonacci(i), end = ' ')
+print('\n')
+
+# solution 2: with memoization
+# explanation to this solution on Socratica youtube channel at https://youtu.be/Qk0zUZW-U_M
+fibonacci_cache = {}
+def fibonacci(n):
+    if n in fibonacci_cache:
+        return fibonacci_cache[n]
+    if n == 1 or n == 2:
+        b = 1
+    else:
+        b = fibonacci(n-1) + fibonacci(n-2)
+    fibonacci_cache[n] = b
+    return b
+
+for i in range(1, 21):
+    print(fibonacci(i), end = ' ')
+print('\n')
+
+# solution 3: with memoize function
+# more on this at https://www.python-course.eu/python3_memoization.php
+def memoize(func):
+    memo_cache = {}
+    def helper(n):
+        if n not in memo_cache:
+            memo_cache[n] = func(n)
+        return memo_cache[n]
+    return helper
+
+@memoize
+def fibonacci(n):
+    if n == 1 or n == 2:
+        return 1
+    else:
+        return fibonacci(n-1) + fibonacci(n-2)
+
+for i in range(1, 21):
+    print(fibonacci(i), end = ' ')
+
+"""
+6. Write a Python program to get the sum of all digits of a non-negative integer. 
+Test Data: 
+sumDigits(345) -> 12
+sumDigits(45) -> 9
+"""
+
+def sum_digits(n):
+    if n//10 < 1:
+        return n
+    else:
+        return n%10 + sum_digits(n//10)
+
+print(sum_digits(345))
+
+"""
+7. Write a Python program to calculate the sum of the positive integers
+of n+(n-2)+(n-4)... (until n-x =< 0). Go to the editor
+Test Data: 
+sum_series(6) -> 12
+sum_series(10) -> 30
+"""
+
+def sum_series(n):
+    if (n-2) <= 0:
+        return n
+    else:
+        return n + sum_series(n-2)
+
+print(sum_series(6))
+
+"""
+8. Write a Python program to calculate the harmonic sum of n-1. 
+Note: The harmonic sum is the sum of reciprocals of the positive integers. 
+"""
+
+def harmonic_sum(n):
+    if n == 1:
+        return 1
+    else:
+        return 1/n + harmonic_sum(n-1)
+
+print(harmonic_sum(5))
+
+"""
+9. Write a Python program to calculate the geometric sum of n-1.
+Note: In mathematics, a geometric series is a series with a constant
+ratio between successive terms. 
+"""
+
+def geometric_sum(n, a, r):
+    # r is a common ratio, a is a start term
+    if n == 0:
+        return a
+    else:
+        return a*r**n + geometric_sum(n-1, a, r)
+print(geometric_sum(5, 1, 2))
+
+"""
+10. Write a Python program to calculate the value of 'a' to the power 'b'. 
+Test Data : 
+(power(3,4) -> 81
+"""
+
+def power(a,b):
+    if b == 0:
+        return 1
+    else:
+        return a*power(a, b-1)
+
+print(power(3,4))
+
+"""
+11. Write a Python program to find the greatest common divisor (gcd) of two
+integers.
+"""
+
+# solution 1 (without recursion)
+def find_gcd(num1, num2):
+    for i in range(min(num1,num2), 0, -1):
+        if num1%i==0 and num2%i==0:
+            return i
+print(find_gcd(12, 500))
+
+# solution 2
+# from w3resource at https://www.w3resource.com/python-exercises/data-structures-and-algorithms/python-recursion-exercise-11.php
+def gcd(num1, num2):
+    low = min(num1, num2)
+    high = max(num1, num2)
+
+    if low == 0:
+        return high
+    elif low == 1:
+        return 1
+    else:
+        return gcd(low, high%low)
+print(gcd(12,500))