staircase problem or Fibonacci sequence
By | 7 months ago
> **Problem Statement:**
> A climber is climbing a mountain where they can climb one rock at a time. Given the total number of rocks `n` needed to reach the top, write a JavaScript program to calculate the number of ways the climber can reach the top.
Since the climber can only climb one rock at a time, the number of ways to reach the top is straightforward—it's always 1 way, because there's only one sequence of steps the climber can take: one rock at a time until they reach the top.
Here's a simple JavaScript function that returns the number of ways the climber can reach the top:
function countWays(n) { // Since the climber can only climb one rock at a time, there is exactly one way to climb n rocks. return 1; }
Explanation for the Blog:
In your blog, you can explain the problem and the solution like this:
### Climbing a Mountain - JavaScript Solution In this problem, we are tasked with finding out how many ways a climber can reach the top of a mountain by climbing one rock at a time. Since the climber's only option is to move one step at a time to ascend each of the \`n\` rocks, the solution is straightforward. #### Problem Statement Given a mountain that requires climbing \`n\` rocks to reach the top, determine how many different ways the climber can achieve this. The climber can climb one rock per step. #### Solution Explanation Since each step the climber takes is predetermined (one rock at a time), the number of sequences of steps is fixed at one. Regardless of the number of rocks, as long as the climber continues to ascend one rock at a time, there is only one possible way to reach the top. The function \`countWays(n)\` therefore always returns 1, representing this single sequence of steps: ```javascript function countWays(n) { return 1; // One way to climb n rocks, one at a time. }
This solution highlights the simplicity of the problem when the options for movement are limited to a single pattern.
This explanation and code snippet should be appropriate for a blog post discussing this problem. If you intended for the climber to have more options (like climbing more than one rock at a time in some steps), please let me know, and we can adjust the solution and explanation accordingly!