A child is running up a staircase with n steps and can hop either 1 step, 2 steps, or 3 steps at a time. Implement a method to count how many possible ways the child can run up the stairs.

Imagine a robot sitting on the upper left corner of grid with r rows and c columns. The robot can only move in two directions, right and down, but certain cells are "off limits" such that the robot cannot step on them. Design an algorithm to find a path for the robot from the top left to the bottom right.

A magic index in an array A[e... n-1] is defined to be an index such that A[ i] = i. Given a sorted array of distinct integers, write a method to find a magic index, if one exists, in array A.

FOLLOW UP: What if the values are not distinct?

Write a method to return all subsets of a set.

Write a recursive function to multiply two positive integers without using the * operator. You can use addition, subtraction, and bit shifting, but you should minimize the number of those operations

In the classic problem of the Towers of Hanoi, you have 3 towers and N disks of different sizes which can slide onto any tower. The puzzle starts with disks sorted in ascending order of size from top to bottom (Le., each disk sits on top of an even larger one). You have the following constraints:

1. Only one disk can be moved at a time.
2. A disk is slid off the top of one tower onto another tower.
3. A disk cannot be placed on top of a smaller disk.

Write a program to move the disks from the first tower to the last using stacks. https://en.wikipedia.org/wiki/Tower_of_Hanoi

Write a mehtod to compute all permutations of a string of unique characters

Write a method to compute all permutations of a string whose characters are not necessarily unique. The list of permutations should not have duplicates.