70. Climbing Stairs

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Problem

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.

Example 1:

Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:

Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

Solution

/**
 * @param {number} n
 * @return {number}
 */
var climbStairs = function(n) {
  var dp = [0, 1];
  for (var i = 0; i < n; i++) {
    dp = [dp[1], dp[0] + dp[1]];
  }
  return dp[1];
};

Explain:

f(x) = f(x - 1) + f(x - 2)。这里用了滚动数组,只保留前两个值,注意处理 n = 0, 1, 2 时的特殊情况。

Complexity: