70. Climbing Stairs #

Problem #

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Note: Given n will be a positive integer.

Example 1:

Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:

Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

Problem Summary #

Suppose you are climbing stairs. It takes n steps to reach the top. Each time you can climb 1 or 2 steps. In how many distinct ways can you climb to the top? Note: the given n is a positive integer

Solution Approach #

• Simple DP, the classic climbing stairs problem. A staircase can be climbed from the n-1 and n-2 stairs.
• The value to solve for in this problem is the Fibonacci sequence.

Code #

package leetcode

func climbStairs(n int) int {
	dp := make([]int, n+1)
	dp[0], dp[1] = 1, 1
	for i := 2; i <= n; i++ {
		dp[i] = dp[i-1] + dp[i-2]
	}
	return dp[n]
}