Climbing Stairs

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?

Solution: DP

ways[n]=ways[n-1]+ways[n-2];

No matter what n is,  it must be reached  from n-1 or n-2 , then use array to  record unique ways from 0 to end 

	/*
	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?
	*/
	//DP Solution
	public class Solution {
	public int climbStairs(int n) {
	if (n<0){
	return 0;
	}
	// record unique ways for each n
	int [] unique_ways=new int[n+1];
	// start point which contains only one situation
	unique_ways[0]=1;
	// can only move 1 step , so ways is only 1
	unique_ways[1]=1;
	for (int i=2; i<n+1; i++){
	unique_ways[i]=unique_ways[i-1]+unique_ways[i-2];
	}
	return unique_ways[n];
	}
	}

view raw climbingStars.java hosted with ❤ by GitHub