Climbing Stairs
Explore how to use dynamic programming to solve the climbing stairs problem, where you calculate the number of distinct ways to reach the top by taking one or two steps. This lesson helps you understand problem constraints, develop an optimal O(n) time and space solution, and implement it using C++. Gain practical insights into applying dynamic programming techniques to similar problems.
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Statement
You are climbing a staircase. It takes n steps to reach the top. Each time, you can either climb or steps. In how many distinct ways can you climb to the top?
Constraints:
-
n
Examples
Understand the problem
Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:
What is the correct number of ways to climb to the top if n = 3?
2
3
1
4
Figure it out!
We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.
Note: As an additional challenge, we have intentionally hidden the solution to this puzzle.
Try it yourself
Implement your solution in the following coding playground.
We have left the solution to this challenge as an exercise for you. An optimal solution to this problem runs in O(n) time and takes O(n) space. You may try to translate the logic of the solved puzzle into a coded solution.
int ClimbStairs(int n){// Replace this placeholder return statement with your codereturn -1;}