Explanations with examples on recursion (solving sum of integers)

Author: codingEzio

chap03_recursion/recursion_sum_of_integers.py

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+def sum_first_num_normal(n):
+    return n * (n + 1) // 2
+
+
+def sum_first_num_recursive(n):
+    if n == 0:
+        # all of the calculation is actually based on this line!
+        return 0
+
+    # ↓ the order for pushing call frames ↓
+    # 5 + { f(5-1) }
+    #     4 + { f(4-1) }
+    #         3 + { f(3-1) }
+    #             2 + { f(2-1) }
+    #                 1+ { f(1-1) } (0==0, base condition)
+    # ↑ the order for calculating the returned values ↑
+
+    # got the result then return (0->1->2 || 0 or n-1 MEETS 0)
+    #              1+0
+    #           2+(1+0)
+    #         +(2+(1+0)))
+    #     4+(3+(2+(1+0))))
+    #  5+(4+(3+(2+(1+0)))))
+
+    # note that the leftmost 4,3,2,1 above do NOT "exist" (VERIFY-NEEDED)
+    #   they do not influence/being-included in the calculation
+    #   they are merely the returned values
+    #   they are the product of each returning (end-of-function)
+
+    # PUSH the funcs onto the stack
+    # POP  the funcs off  the stack once funcs weren't called anymore (==1)
+
+    # my own explanation
+    # > it follows LIFO operations
+    # > stacked (fig & ds-type) functions won't change
+    # > variable could change, therefore providing a 'base condition' (end/stp)
+
+    # It's all about the RETURNED values, the former n does NOT matter
+    return n + sum_first_num_recursive(n - 1)
+
+
+# references
+#   concept with examples
+#       https://dev.to/kaxmoglan/recursive-functions-explained-5hie
+
+
+def main():
+    _input = int(input("Enter a non-negative and non-zero integer: "))
+
+    print(
+        sum_first_num_normal(_input), sum_first_num_recursive(_input), sep="\n"
+    )
+
+
+if __name__ == "__main__":
+    main()