【LeetCode】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?
Bad solution↓

class Solution {
public:
int climbStairs(int n)
{
int ways = 0;
int x = 0;
int y = 0;
for(int i = 0; i <= n; i++)
{
x = i;
if( (n-x) % 2 == 0)
{
y = (n-x) / 2;
if(x == 0 || y == 0)
ways++;
else
{
int tmp = x+y;
long long sum = 1;
int cnt = 0;
int minVal = x > y?y:x;
while(cnt < minVal)
{
sum *= tmp;
tmp--;
cnt++;
if(cnt <= minVal)
{
sum /= cnt;
}
}
ways += sum;
}
}
}
return ways;
}
};

此题有排列组合运算，为了防止溢出：

1：sum类型为long long,最大值9223372036854775807

2：除的操作在运算中途就进行

此题是一个斐波那契数列，利用递归，迭代及公式法可以求解。