Grokking Dynamic Programming Patterns for Coding Interviews
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Solution: Staircase
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Problem Statement

Given a stair with 'n' steps, implement a method to count how many possible ways are there to reach the top of the staircase, given that, at every step you can either take 1 step, 2 steps, or 3 steps.

Example 1:

Number of stairs (n) : 3
Number of ways = 4
Explanation: Following are the four ways we can climb : {1,1,1}, {1,2}, {2,1}, {3}

Example 2:

Number of stairs (n) : 4
Number of ways = 7
Explanation: Following are the seven ways we can climb : {1,1,1,1}, {1,1,2}, {1,2,1}, {2,1,1}, 
{2,2}, {1,3}, {3,1}

Constraints:

  • 1 <= n <= 45

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