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leetcode-problemset/leetcode-cn/originData/three-steps-problem-lcci.json
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"question": {
"questionId": "100197",
"questionFrontendId": "面试题 08.01",
"categoryTitle": "LCCI",
"boundTopicId": 49279,
"title": "Three Steps Problem LCCI",
"titleSlug": "three-steps-problem-lcci",
"content": "<p>A child is running up a staircase with n steps and can hop either 1 step, 2 steps, or 3 steps at a time. Implement a method to count how many possible ways the child can run up the stairs.&nbsp;The result may be large, so return it modulo 1000000007.</p>\r\n\r\n<p><strong>Example1:</strong></p>\r\n\r\n<pre>\r\n<strong> Input</strong>: n = 3 \r\n<strong> Output</strong>: 4\r\n</pre>\r\n\r\n<p><strong>Example2:</strong></p>\r\n\r\n<pre>\r\n<strong> Input</strong>: n = 5\r\n<strong> Output</strong>: 13\r\n</pre>\r\n\r\n<p><strong>Note:</strong></p>\r\n\r\n<ol>\r\n\t<li><code>1 &lt;= n &lt;= 1000000</code></li>\r\n</ol>\r\n",
"translatedTitle": "三步问题",
"translatedContent": "<p>三步问题。有个小孩正在上楼梯楼梯有n阶台阶小孩一次可以上1阶、2阶或3阶。实现一种方法计算小孩有多少种上楼梯的方式。结果可能很大你需要对结果模1000000007。</p>\n\n<p> <strong>示例1:</strong></p>\n\n<pre>\n<strong> 输入</strong>n = 3 \n<strong> 输出</strong>4\n<strong> 说明</strong>: 有四种走法\n</pre>\n\n<p> <strong>示例2:</strong></p>\n\n<pre>\n<strong> 输入</strong>n = 5\n<strong> 输出</strong>13\n</pre>\n\n<p> <strong>提示:</strong></p>\n\n<ol>\n<li>n范围在[1, 1000000]之间</li>\n</ol>\n",
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"hints": [
"自上而下地处理这个问题。小孩的最后一跳是什么?",
"如果知道跳到第100级台阶之前的每一级台阶的跳法数量可以计算第100级台阶的跳法数量吗",
"可以通过步数99、98、97的数量来计算100步的数量。这对应孩子最后迈1步、2步或3步。我们把它们加起来还是相乘也就是说它是f(100) = f(99) + f(98)+ f(97) 或者f(100) = f(99)×f(98)×f(97)吗?",
"当“我们这样做然后那样做”时,将这些值相乘。当“我们这样做或者那样做”时,将这些值相加。",
"这个方法的运行时间是多少?仔细想想。你能优化它吗?",
"尝试用制表法的方式优化效率低下的递归过程。"
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