1. Staircase Problem

A staircase of N steps, and a person has the ability to climb one, two, or three steps at a time.

Input: Number of steps in staircase
Output: Unique possible paths.

def n_paths(n):
    if n<0:
        return 0
    if n==0 or n==1:
        return 1
    return n_paths(n-1) + n_paths(n-2) + n_paths(n-3)
n_paths(3)

2. Count Characters

Input: ["ab", "c", "def", "ghij"]
Output: 10

def count_chars(string):
    if not string:
        return 0
    return len(string[0]) + count_chars(string[1:])

count_chars(["ab", "c", "def", "ghij"])

3. Even-Only Array

Input: Any array of integers
Output: A new array of even values of original array

def even_only(arr):
    if not arr:
        return []
    if arr[0]%2==0:
        return [arr[0]] + even_only(arr[1:])
    return even_only(arr[1:])
even_only(arr=[1,2,3,4,5,6])

[2, 4, 6]

4. Get ‘x’ Index

Input: “abcdefghijklmnopqrstuvwxyz”
Output: 23

def get_x_idx(string):
    if string[0]=="x":
        return 0
    else:
        return get_x_idx(string[1:]) + 1
get_x_idx("abcdefghijklmnopqrstuvwxyz")

5. Unique Paths Problem

Input: number of rows & number of columns
Output: calculates the number of possible “shortest” paths from the upper-leftmost square to the lower-rightmost square.

def unique_paths(rows,cols):
    if rows==1 or cols==1:
        return 1
    return unique_paths(rows-1,cols)+unique_paths(rows,cols-1)
unique_paths(3,3)