{ "data": { "question": { "questionId": "1000029", "questionFrontendId": "面试题 17.21", "categoryTitle": "LCCI", "boundTopicId": 93313, "title": "Volume of Histogram LCCI", "titleSlug": "volume-of-histogram-lcci", "content": "

Imagine a histogram (bar graph). Design an algorithm to compute the volume of water it could hold if someone poured water across the top. You can assume that each histogram bar has width 1.

\r\n\r\n

\r\n\r\n

The above elevation map is represented by array [0,1,0,2,1,0,1,3,2,1,2,1]. In this case, 6 units of water (blue section) are being trapped. Thanks Marcos for contributing this image!

\r\n\r\n

Example:

\r\n\r\n
\r\nInput: [0,1,0,2,1,0,1,3,2,1,2,1]\r\nOutput: 6
\r\n", "translatedTitle": "直方图的水量", "translatedContent": "

给定一个直方图(也称柱状图)，假设有人从上面源源不断地倒水，最后直方图能存多少水量?直方图的宽度为 1。

\n\n

\n\n

上面是由数组 [0,1,0,2,1,0,1,3,2,1,2,1] 表示的直方图，在这种情况下，可以接 6 个单位的水（蓝色部分表示水）。 感谢 Marcos 贡献此图。

\n\n

示例:

\n\n
输入: [0,1,0,2,1,0,1,3,2,1,2,1]\n输出: 6
\n", "isPaidOnly": false, "difficulty": "Hard", "likes": 265, "dislikes": 0, "isLiked": null, "similarQuestions": "[]", "contributors": [], "langToValidPlayground": "{\"cpp\": true, \"java\": true, \"python\": true, \"python3\": true, \"mysql\": false, \"mssql\": false, \"oraclesql\": false, \"c\": false, \"csharp\": false, \"javascript\": false, \"ruby\": false, \"bash\": false, \"swift\": false, \"golang\": false, \"scala\": false, \"html\": false, \"pythonml\": false, \"kotlin\": false, \"rust\": false, \"php\": false, \"typescript\": false, \"racket\": false, \"erlang\": false, \"elixir\": false}", "topicTags": [ { "name": "Stack", "slug": "stack", "translatedName": "栈", "__typename": "TopicTagNode" }, { "name": "Array", "slug": "array", "translatedName": "数组", "__typename": "TopicTagNode" }, { "name": "Two Pointers", "slug": "two-pointers", "translatedName": "双指针", "__typename": "TopicTagNode" }, { "name": "Dynamic Programming", "slug": "dynamic-programming", "translatedName": "动态规划", "__typename": "TopicTagNode" }, { "name": "Monotonic Stack", "slug": "monotonic-stack", "translatedName": "单调栈", "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int trap(vector& height) {\n\n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int trap(int[] height) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def trap(self, height):\n \"\"\"\n :type height: List[int]\n :rtype: int\n \"\"\"", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def trap(self, height: List[int]) -> int:", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "\n\nint trap(int* height, int heightSize){\n\n}\n", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int Trap(int[] height) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[]} height\n * @return {number}\n */\nvar trap = function(height) {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[]} height\n# @return {Integer}\ndef trap(height)\n\nend", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func trap(_ height: [Int]) -> Int {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func trap(height []int) int {\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def trap(height: Array[Int]): Int = {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun trap(height: IntArray): Int {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn trap(height: Vec) -> i32 {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[] $height\n * @return Integer\n */\n function trap($height) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function trap(height: number[]): number {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (trap height)\n (-> (listof exact-integer?) exact-integer?)\n\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec trap(Height :: [integer()]) -> integer().\ntrap(Height) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec trap(height :: [integer]) :: integer\n def trap(height) do\n\n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"46.9K\", \"totalSubmission\": \"73.8K\", \"totalAcceptedRaw\": 46944, \"totalSubmissionRaw\": 73790, \"acRate\": \"63.6%\"}", "hints": [ "直方图中最高的长方形起什么作用?", "想象一下最高的长方形、左边第二高的长方形和右边第二高的长方形。水会填满它们之间的区域。你能计算出其面积吗？其余的面积怎么办？", "为了计算出整体上最高的长方形和左侧最高的长方形之间的面积，你只需遍历直方图并减去这两个长方形之间的任何长方形的面积。你可以在右侧做同样的事情。如何处理剩下的图表?", "你可以通过重复这个过程来处理图的其余部分：找到最高的长方形和第二高的长方形，然后减去它们之间的长方形的面积。", "怎样才能更快地找到两边的下一个最高的长方形?", "你能通过预计算来得出每边下一个最高的长方形是哪个么？", "作为另一种解决方案，请从每个长方形的角度来考虑。每个长方形上面都有水。每个长方形上面会有多少水？", "每个长方形的顶部都有水，水的高度应与左侧最高长方形和右侧最高长方形的较小值相匹配，也就是说，water_on_top[i] = min(tallest_ bar(0->i), tallest_bar(i, n))。", "你应该能在O(N)时间和O(N)空间中解出该题。" ], "solution": null, "status": null, "sampleTestCase": "[0,1,0,2,1,0,1,3,2,1,2,1]", "metaData": "{\r\n \"name\": \"trap\",\r\n \"params\": [\r\n {\r\n \"name\": \"height\",\r\n \"type\": \"integer[]\"\r\n }\r\n ],\r\n \"return\": {\r\n \"type\": \"integer\"\r\n }\r\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

\\u7248\\u672c\\uff1aclang 11<\\/code> \\u91c7\\u7528\\u6700\\u65b0C++ 17\\u6807\\u51c6\\u3002<\\/p>\\r\\n\\r\\n

\\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528-O2<\\/code>\\u7ea7\\u4f18\\u5316\\u3002AddressSanitizer<\\/a> \\u4e5f\\u88ab\\u5f00\\u542f\\u6765\\u68c0\\u6d4bout-of-bounds<\\/code>\\u548cuse-after-free<\\/code>\\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\"],\"java\":[\"Java\",\"

\\u7248\\u672c\\uff1aOpenJDK 17<\\/code>\\u3002\\u53ef\\u4ee5\\u4f7f\\u7528Java 8\\u7684\\u7279\\u6027\\u4f8b\\u5982\\uff0clambda expressions \\u548c stream API\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u88ab\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u5305\\u542b Pair \\u7c7b: https:\\/\\/docs.oracle.com\\/javase\\/8\\/javafx\\/api\\/javafx\\/util\\/Pair.html <\\/p>\"],\"python\":[\"Python\",\"

\\u7248\\u672c\\uff1a Python 2.7.12<\\/code><\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982\\uff1aarray<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u6ce8\\u610f Python 2.7 \\u5c06\\u57282020\\u5e74\\u540e\\u4e0d\\u518d\\u7ef4\\u62a4<\\/a>\\u3002 \\u5982\\u60f3\\u4f7f\\u7528\\u6700\\u65b0\\u7248\\u7684Python\\uff0c\\u8bf7\\u9009\\u62e9Python 3\\u3002<\\/p>\"],\"c\":[\"C\",\"

\\u7248\\u672c\\uff1aGCC 8.2<\\/code>\\uff0c\\u91c7\\u7528GNU99\\u6807\\u51c6\\u3002<\\/p>\\r\\n\\r\\n

\\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528-O1<\\/code>\\u7ea7\\u4f18\\u5316\\u3002 AddressSanitizer<\\/a>\\u4e5f\\u88ab\\u5f00\\u542f\\u6765\\u68c0\\u6d4bout-of-bounds<\\/code>\\u548cuse-after-free<\\/code>\\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n

1. \\u5f80\\u54c8\\u5e0c\\u8868\\u4e2d\\u6dfb\\u52a0\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n

\\r\\nstruct hash_entry {\\r\\n    int id;            \\/* we'll use this field as the key *\\/\\r\\n    char name[10];\\r\\n    UT_hash_handle hh; \\/* makes this structure hashable *\\/\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n    HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\\r\\n\\r\\n
2. \\u5728\\u54c8\\u5e0c\\u8868\\u4e2d\\u67e5\\u627e\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n
\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n    struct hash_entry *s;\\r\\n    HASH_FIND_INT(users, &user_id, s);\\r\\n    return s;\\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\\r\\n\\r\\n
3. \\u4ece\\u54c8\\u5e0c\\u8868\\u4e2d\\u5220\\u9664\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n
\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\"],\"csharp\":[\"C#\",\"
C# 10<\\/a> \\u8fd0\\u884c\\u5728 .NET 6 \\u4e0a<\\/p>\\r\\n\\r\\n
\\u60a8\\u7684\\u4ee3\\u7801\\u5728\\u7f16\\u8bd1\\u65f6\\u9ed8\\u8ba4\\u5f00\\u542f\\u4e86debug\\u6807\\u8bb0(\\/debug:pdbonly<\\/code>)\\u3002<\\/p>\"],\"javascript\":[\"JavaScript\",\"
\\u7248\\u672c\\uff1aNode.js 16.13.2<\\/code><\\/p>\\r\\n\\r\\n
\\u60a8\\u7684\\u4ee3\\u7801\\u5728\\u6267\\u884c\\u65f6\\u5c06\\u5e26\\u4e0a --harmony<\\/code> \\u6807\\u8bb0\\u6765\\u5f00\\u542f \\u65b0\\u7248ES6\\u7279\\u6027<\\/a>\\u3002<\\/p>\\r\\n\\r\\n
lodash.js<\\/a> \\u5e93\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5305\\u542b\\u3002<\\/p>\\r\\n\\r\\n
 \\u5982\\u9700\\u4f7f\\u7528\\u961f\\u5217\\/\\u4f18\\u5148\\u961f\\u5217\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528  datastructures-js\\/priority-queue<\\/a> \\u548c  datastructures-js\\/queue<\\/a>\\u3002<\\/p>\"],\"ruby\":[\"Ruby\",\"
\\u4f7f\\u7528Ruby 3.1<\\/code>\\u6267\\u884c<\\/p>\\r\\n\\r\\n
\\u4e00\\u4e9b\\u5e38\\u7528\\u7684\\u6570\\u636e\\u7ed3\\u6784\\u5df2\\u5728 Algorithms \\u6a21\\u5757\\u4e2d\\u63d0\\u4f9b\\uff1ahttps:\\/\\/www.rubydoc.info\\/github\\/kanwei\\/algorithms\\/Algorithms<\\/p>\"],\"swift\":[\"Swift\",\"
\\u7248\\u672c\\uff1aSwift 5.5.2<\\/code><\\/p>\\r\\n\\r\\n
\\u6211\\u4eec\\u901a\\u5e38\\u4fdd\\u8bc1\\u66f4\\u65b0\\u5230 Apple\\u653e\\u51fa\\u7684\\u6700\\u65b0\\u7248Swift<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u53d1\\u73b0Swift\\u4e0d\\u662f\\u6700\\u65b0\\u7248\\u7684\\uff0c\\u8bf7\\u8054\\u7cfb\\u6211\\u4eec\\uff01\\u6211\\u4eec\\u5c06\\u5c3d\\u5feb\\u66f4\\u65b0\\u3002<\\/p>\"],\"golang\":[\"Go\",\"
\\u7248\\u672c\\uff1aGo 1.17<\\/code><\\/p>\\r\\n\\r\\n
\\u652f\\u6301 https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"
\\u7248\\u672c\\uff1aPython 3.10<\\/code><\\/p>\\r\\n\\r\\n
\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982array<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n
\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap \\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 sortedcontainers<\\/a> \\u5e93\\u3002<\\/p>\"],\"scala\":[\"Scala\",\"
\\u7248\\u672c\\uff1aScala 2.13<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"
\\u7248\\u672c\\uff1aKotlin 1.3.10<\\/code><\\/p>\"],\"rust\":[\"Rust\",\"
\\u7248\\u672c\\uff1arust 1.58.1<\\/code><\\/p>\\r\\n\\r\\n
\\u652f\\u6301 crates.io \\u7684 rand<\\/a><\\/p>\"],\"php\":[\"PHP\",\"
PHP 8.1<\\/code>.<\\/p>\\r\\n\\r\\n
With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"
TypeScript 4.5.4<\\/p>\\r\\n\\r\\n
Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2020<\\/p>\"],\"racket\":[\"Racket\",\"
Racket CS<\\/a> v8.3<\\/p>\\r\\n\\r\\n
\\u4f7f\\u7528 #lang racket<\\/p>\\r\\n\\r\\n
\\u5df2\\u9884\\u5148 (require data\\/gvector data\\/queue data\\/order data\\/heap). \\u82e5\\u9700\\u4f7f\\u7528\\u5176\\u5b83\\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u53ef\\u81ea\\u884c require\\u3002<\\/p>\"],\"erlang\":[\"Erlang\",\"Erlang\\/OTP 24.2\"],\"elixir\":[\"Elixir\",\"Elixir 1.13.0 with Erlang\\/OTP 24.2\"]}",
            "book": {
                "id": "2",
                "bookName": "《程序员面试金典（第 6 版）》",
                "pressName": "图灵公司",
                "source": "《程序员面试金典（第 6 版）》独家授权",
                "shortDescription": "英文版：Cracking the Coding Interview，源自硅谷程序员的面试红宝书",
                "fullDescription": "本书是原谷歌资深面试官的经验之作，帮助了许多想要加入脸书、苹果、谷歌等 IT 名企的求职者拿到 Dream offer。本专题的 100+ 编程面试题是在原书基础上精心挑选出来的，帮助你轻松应战 IT 名企技术面试。",
                "bookImgUrl": "https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2019/09/30/book_2.jpg",
                "pressImgUrl": "https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/02/11/logo20190828-02.png",
                "productUrl": "",
                "__typename": "CategoryInfoNode"
            },
            "isSubscribed": false,
            "isDailyQuestion": false,
            "dailyRecordStatus": null,
            "editorType": "CKEDITOR",
            "ugcQuestionId": null,
            "style": "LEETCODE",
            "exampleTestcases": "",
            "__typename": "QuestionNode"
        }
    }
}