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.
方法1: 动态规划
方法2: 两个变量(最优解)
方法3: 递归, 最差解
动态规划解法:
public class Solution {
public int climbStairs(int n) {
if(n == 0 ) {
return 0;
}
if(n == 1){
return 1;
}
int[] f = new int[n + 1];
f[0] = 1;
f[1] = 1;
for(int i = 2; i <= n; i++) {
f[i] = f[i - 1] + f[i - 2];
}
return f[n];
}
}
方法二: 两个变量
public class Solution {
public int climbStairs(int n) {
if(n == 0 ) {
return 0;
}
if(n == 1){
return 1;
}
int a = 0;
int b = 1;
int sum = 0;
for(int i = 1; i <= n; i++) {
sum = a + b;
a = b;
b = sum;
}
return sum;
}
}