70. Climbing Stairs
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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.
public int climbStairs(int n) { // base cases if(n <= 0) return 0; if(n == 1) return 1; if(n == 2) return 2; int one_step_before = 2; int two_steps_before = 1; int all_ways = 0; for(int i=2; i<n; i++){ all_ways = one_step_before + two_steps_before; two_steps_before = one_step_before; one_step_before = all_ways; } return all_ways;}
Here are the steps to get the solution incrementally.
Base cases:
if n <= 0, then the number of ways should be zero.
if n == 1, then there is only way to climb the stair.
if n == 2, then there are two ways to climb the stairs. One solution is one step by another; the other one is two steps at one time.The key intuition to solve the problem is that given a number of stairs n, if we know the number ways to get to the points
[n-1]
and[n-2]
respectively, denoted asn1
andn2
, then the total ways to get to the point[n]
isn1 + n2
. Because from the[n-1]
point, we can take one single step to reach[n]
. And from the[n-2]
point, we could take two steps to get there. There is NO overlapping between these two solution sets, because we differ in the final step.
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