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"questionId": "2233",
"questionFrontendId": "2110",
"categoryTitle": "Algorithms",
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"title": "Number of Smooth Descent Periods of a Stock",
"titleSlug": "number-of-smooth-descent-periods-of-a-stock",
"content": "<p>You are given an integer array <code>prices</code> representing the daily price history of a stock, where <code>prices[i]</code> is the stock price on the <code>i<sup>th</sup></code> day.</p>\n\n<p>A <strong>smooth descent period</strong> of a stock consists of <strong>one or more contiguous</strong> days such that the price on each day is <strong>lower</strong> than the price on the <strong>preceding day</strong> by <strong>exactly</strong> <code>1</code>. The first day of the period is exempted from this rule.</p>\n\n<p>Return <em>the number of <strong>smooth descent periods</strong></em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> prices = [3,2,1,4]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> There are 7 smooth descent periods:\n[3], [2], [1], [4], [3,2], [2,1], and [3,2,1]\nNote that a period with one day is a smooth descent period by the definition.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> prices = [8,6,7,7]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> There are 4 smooth descent periods: [8], [6], [7], and [7]\nNote that [8,6] is not a smooth descent period as 8 - 6 &ne; 1.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> prices = [1]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> There is 1 smooth descent period: [1]\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= prices.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= prices[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
"translatedTitle": "股票平滑下跌阶段的数目",
"translatedContent": "<p>给你一个整数数组&nbsp;<code>prices</code>&nbsp;,表示一支股票的历史每日股价,其中&nbsp;<code>prices[i]</code>&nbsp;是这支股票第&nbsp;<code>i</code>&nbsp;天的价格。</p>\n\n<p>一个 <strong>平滑下降的阶段</strong>&nbsp;定义为:对于&nbsp;<strong>连续一天或者多天</strong>&nbsp;,每日股价都比 <strong>前一日股价恰好少 </strong><code>1</code>&nbsp;,这个阶段第一天的股价没有限制。</p>\n\n<p>请你返回 <strong>平滑下降阶段</strong>&nbsp;的数目。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><b>输入:</b>prices = [3,2,1,4]\n<b>输出:</b>7\n<b>解释:</b>总共有 7 个平滑下降阶段:\n[3], [2], [1], [4], [3,2], [2,1] 和 [3,2,1]\n注意仅一天按照定义也是平滑下降阶段。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><b>输入:</b>prices = [8,6,7,7]\n<b>输出:</b>4\n<b>解释:</b>总共有 4 个连续平滑下降阶段:[8], [6], [7] 和 [7]\n由于 8 - 6 ≠ 1 ,所以 [8,6] 不是平滑下降阶段。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre><b>输入:</b>prices = [1]\n<b>输出:</b>1\n<b>解释:</b>总共有 1 个平滑下降阶段:[1]\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= prices.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= prices[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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"hints": [
"Any array is a series of adjacent longest possible smooth descent periods. For example, [5,3,2,1,7,6] is [5] + [3,2,1] + [7,6].",
"Think of a 2-pointer approach to traverse the array and find each longest possible period.",
"Suppose you found the longest possible period with a length of k. How many periods are within that period? How can you count them quickly? Think of the formula to calculate the sum of 1, 2, 3, ..., k."
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