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z?g^zkk64TzvABHD7IwWH+Gr8%8yXrL8kQRxUK<+G8yYz`G-_>V^xn{zv!StfL*w3t KrgL*JSOWm))1J5h literal 0 HcmV?d00001 diff --git a/0070-Climbing-Stairs/Article/0070-Climbing-Stairs.md b/0070-Climbing-Stairs/Article/0070-Climbing-Stairs.md new file mode 100644 index 00000000..c4282c73 --- /dev/null +++ b/0070-Climbing-Stairs/Article/0070-Climbing-Stairs.md @@ -0,0 +1,102 @@ +## **LeetCode 第 70 号问题:爬楼梯** + +> 本文首发于公众号「图解面试算法」,是 [图解 LeetCode ]() 系列文章之一. +> +> 同步博客:https://www.algomooc.com + +题目来源于 LeetCode 上第 70 号问题:爬楼梯。题目难度为 Easy。 + +### 题目描述 + +假设你正在爬楼梯。需要 `n` 阶你才能到达楼顶。 + +每次你可以爬 `1` 或 `2` 个台阶。你有多少种不同的方法可以爬到楼顶呢? + +**注意:给定 n 是一个正整数。** + +### 示例1 + +> 输入: 2 +> +> 解释: 有两种方法可以爬到楼顶。 +> +> 1. 1 阶 + 1 阶 +> +> 2. 2 阶 + +### 题目解析 + +试着倒推想一下,就能发现这个问题可以被分解为一些包含最优子结构的子问题,它的最优解可以从其子问题 +的最优解来有效地构建,因此我们可以使用`动态规划`解决这个问题. + +第 `i` 阶可以由以下两种方法得到: + +在第 `(i - 1)` 阶后向上爬 1 阶。 + +在第 `(i - 2)` 阶后向上爬 2 阶 + +所以到达第 `i` 阶的方法总数就是到第 `(i - 1)` 阶和第 `(i - 2)` 阶的方法数之和。 + +`dp[i]dp[i]` 表示能到达第 `i` 阶的方法总数,那么DP推导公式就是: + +> $$ +> dp[i] = dp[i − 1] + dp[i − 2] +> $$ + + + +### 动画理解 + +Animation + +### 参考代码 + +```javascript +/** + * JavaScript 描述 + */ +var climbStairs = function(n) { + let temp = new Array(n+1); + temp[1] = 1; + temp[2] = 2; + for (let i = 3; i < temp.length; i++) { + temp[i] = temp[i-1] + temp[i-2]; + } + return temp[n]; +} +``` + +#### 复杂度分析 + +- 时间复杂度:`O(n)`,单循环到 n。 +- 空间复杂度:`O(n)`,dpdp 数组用了 n 的空间。 + +### 进一步优化 + +根据推导公式不难发现,我们要求的结果就是数组的最后一项,而最后一项又是前面数值叠加起来的,那么我们只需要两个变量保存 `i - 1` 和 `i - 2` 的值就可以了. + +```javascript +/** + * JavaScript 描述 + */ +var climbStairs = function(n) { + if (n == 1) { + return 1; + } + let first = 1, + second = 2; + for (let i = 3; i <= n; i++) { + let third = first + second; + first = second; + second = third; + } + return second; +} +``` + +#### 复杂度分析 + +- 时间复杂度:O(n),单循环到 n。 +- 空间复杂度:O(1),用到了常量的空间。 + +![qrcode](../../Pictures/qrcode.jpg) \ No newline at end of file

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