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?
思路:
这种题目属于那种“想到解法就很快做出”的类型。n个台阶的楼梯的走法等于:
ways(n) = ways(n-1) + ways(n-2)
恰好是Fibonacci数列。另外提一下,对Fibonacci数列的一个计算方法是,利用矩阵A=
/ \ | 1 1 | | 1 0 | \ /
的N次方来完成。而矩阵的N次方是可以用分而治之O(log N)实现的。这里不用了。
题解:
class Solution { public: int Fibonacci(int k) { if (k==0) return 0; int fib = 1; int prev1 = 0, prev2 = 1; for(int l = 1; l < k; ++l) { prev1 = prev2; prev2 = fib; fib = prev1 + prev2; } return fib; } int climbStairs(int n) { return Fibonacci(n); } };