1
0
mirror of https://gitee.com/coder-xiaomo/leetcode-problemset synced 2025-01-11 02:58:13 +08:00
Code Issues Projects Releases Wiki Activity GitHub Gitee
leetcode-problemset/leetcode/originData/number-of-increasing-paths-in-a-grid.json

224 lines
18 KiB
JSON

{
"data": {
"question": {
"questionId": "2409",
"questionFrontendId": "2328",
"boundTopicId": null,
"title": "Number of Increasing Paths in a Grid",
"titleSlug": "number-of-increasing-paths-in-a-grid",
"content": "<p>You are given an <code>m x n</code> integer matrix <code>grid</code>, where you can move from a cell to any adjacent cell in all <code>4</code> directions.</p>\n\n<p>Return <em>the number of <strong>strictly</strong> <strong>increasing</strong> paths in the grid such that you can start from <strong>any</strong> cell and end at <strong>any</strong> cell. </em>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>Two paths are considered different if they do not have exactly the same sequence of visited cells.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/05/10/griddrawio-4.png\" style=\"width: 181px; height: 121px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,1],[3,4]]\n<strong>Output:</strong> 8\n<strong>Explanation:</strong> The strictly increasing paths are:\n- Paths with length 1: [1], [1], [3], [4].\n- Paths with length 2: [1 -&gt; 3], [1 -&gt; 4], [3 -&gt; 4].\n- Paths with length 3: [1 -&gt; 3 -&gt; 4].\nThe total number of paths is 4 + 3 + 1 = 8.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[1],[2]]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The strictly increasing paths are:\n- Paths with length 1: [1], [2].\n- Paths with length 2: [1 -&gt; 2].\nThe total number of paths is 2 + 1 = 3.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>1 &lt;= m, n &lt;= 1000</code></li>\n\t<li><code>1 &lt;= m * n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
"translatedTitle": null,
"translatedContent": null,
"isPaidOnly": false,
"difficulty": "Hard",
"likes": 1897,
"dislikes": 42,
"isLiked": null,
"similarQuestions": "[{\"title\": \"Longest Increasing Path in a Matrix\", \"titleSlug\": \"longest-increasing-path-in-a-matrix\", \"difficulty\": \"Hard\", \"translatedTitle\": null}, {\"title\": \"All Paths From Source to Target\", \"titleSlug\": \"all-paths-from-source-to-target\", \"difficulty\": \"Medium\", \"translatedTitle\": null}, {\"title\": \"Maximum Strictly Increasing Cells in a Matrix\", \"titleSlug\": \"maximum-strictly-increasing-cells-in-a-matrix\", \"difficulty\": \"Hard\", \"translatedTitle\": null}]",
"exampleTestcases": "[[1,1],[3,4]]\n[[1],[2]]",
"categoryTitle": "Algorithms",
"contributors": [],
"topicTags": [
{
"name": "Array",
"slug": "array",
"translatedName": null,
"__typename": "TopicTagNode"
},
{
"name": "Dynamic Programming",
"slug": "dynamic-programming",
"translatedName": null,
"__typename": "TopicTagNode"
},
{
"name": "Depth-First Search",
"slug": "depth-first-search",
"translatedName": null,
"__typename": "TopicTagNode"
},
{
"name": "Breadth-First Search",
"slug": "breadth-first-search",
"translatedName": null,
"__typename": "TopicTagNode"
},
{
"name": "Graph",
"slug": "graph",
"translatedName": null,
"__typename": "TopicTagNode"
},
{
"name": "Topological Sort",
"slug": "topological-sort",
"translatedName": null,
"__typename": "TopicTagNode"
},
{
"name": "Memoization",
"slug": "memoization",
"translatedName": null,
"__typename": "TopicTagNode"
},
{
"name": "Matrix",
"slug": "matrix",
"translatedName": null,
"__typename": "TopicTagNode"
}
],
"companyTagStats": null,
"codeSnippets": [
{
"lang": "C++",
"langSlug": "cpp",
"code": "class Solution {\npublic:\n int countPaths(vector<vector<int>>& grid) {\n \n }\n};",
"__typename": "CodeSnippetNode"
},
{
"lang": "Java",
"langSlug": "java",
"code": "class Solution {\n public int countPaths(int[][] grid) {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Python",
"langSlug": "python",
"code": "class Solution(object):\n def countPaths(self, grid):\n \"\"\"\n :type grid: List[List[int]]\n :rtype: int\n \"\"\"\n ",
"__typename": "CodeSnippetNode"
},
{
"lang": "Python3",
"langSlug": "python3",
"code": "class Solution:\n def countPaths(self, grid: List[List[int]]) -> int:\n ",
"__typename": "CodeSnippetNode"
},
{
"lang": "C",
"langSlug": "c",
"code": "int countPaths(int** grid, int gridSize, int* gridColSize) {\n \n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "C#",
"langSlug": "csharp",
"code": "public class Solution {\n public int CountPaths(int[][] grid) {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "JavaScript",
"langSlug": "javascript",
"code": "/**\n * @param {number[][]} grid\n * @return {number}\n */\nvar countPaths = function(grid) {\n \n};",
"__typename": "CodeSnippetNode"
},
{
"lang": "TypeScript",
"langSlug": "typescript",
"code": "function countPaths(grid: number[][]): number {\n \n};",
"__typename": "CodeSnippetNode"
},
{
"lang": "PHP",
"langSlug": "php",
"code": "class Solution {\n\n /**\n * @param Integer[][] $grid\n * @return Integer\n */\n function countPaths($grid) {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Swift",
"langSlug": "swift",
"code": "class Solution {\n func countPaths(_ grid: [[Int]]) -> Int {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Kotlin",
"langSlug": "kotlin",
"code": "class Solution {\n fun countPaths(grid: Array<IntArray>): Int {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Dart",
"langSlug": "dart",
"code": "class Solution {\n int countPaths(List<List<int>> grid) {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Go",
"langSlug": "golang",
"code": "func countPaths(grid [][]int) int {\n \n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Ruby",
"langSlug": "ruby",
"code": "# @param {Integer[][]} grid\n# @return {Integer}\ndef count_paths(grid)\n \nend",
"__typename": "CodeSnippetNode"
},
{
"lang": "Scala",
"langSlug": "scala",
"code": "object Solution {\n def countPaths(grid: Array[Array[Int]]): Int = {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Rust",
"langSlug": "rust",
"code": "impl Solution {\n pub fn count_paths(grid: Vec<Vec<i32>>) -> i32 {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Racket",
"langSlug": "racket",
"code": "(define/contract (count-paths grid)\n (-> (listof (listof exact-integer?)) exact-integer?)\n )",
"__typename": "CodeSnippetNode"
},
{
"lang": "Erlang",
"langSlug": "erlang",
"code": "-spec count_paths(Grid :: [[integer()]]) -> integer().\ncount_paths(Grid) ->\n .",
"__typename": "CodeSnippetNode"
},
{
"lang": "Elixir",
"langSlug": "elixir",
"code": "defmodule Solution do\n @spec count_paths(grid :: [[integer]]) :: integer\n def count_paths(grid) do\n \n end\nend",
"__typename": "CodeSnippetNode"
}
],
"stats": "{\"totalAccepted\": \"63.9K\", \"totalSubmission\": \"108.5K\", \"totalAcceptedRaw\": 63940, \"totalSubmissionRaw\": 108484, \"acRate\": \"58.9%\"}",
"hints": [
"How can you calculate the number of increasing paths that start from a cell (i, j)? Think about dynamic programming.",
"Define f(i, j) as the number of increasing paths starting from cell (i, j). Try to find how f(i, j) is related to each of f(i, j+1), f(i, j-1), f(i+1, j) and f(i-1, j)."
],
"solution": {
"id": "1810",
"canSeeDetail": false,
"paidOnly": true,
"hasVideoSolution": false,
"paidOnlyVideo": true,
"__typename": "ArticleNode"
},
"status": null,
"sampleTestCase": "[[1,1],[3,4]]",
"metaData": "{\n \"name\": \"countPaths\",\n \"params\": [\n {\n \"name\": \"grid\",\n \"type\": \"integer[][]\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}",
"judgerAvailable": true,
"judgeType": "large",
"mysqlSchemas": [],
"enableRunCode": true,
"enableTestMode": false,
"enableDebugger": true,
"envInfo": "{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 20 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\"], \"java\": [\"Java\", \"<p><code>OpenJDK 17</code>. Java 8 features such as lambda expressions and stream API can be used. </p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\\r\\n\\r\\n<p>Note that Python 2.7 <a href=\\\"https://www.python.org/dev/peps/pep-0373/\\\" target=\\\"_blank\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu11 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O1</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n\\r\\n<p>For hash table operations, you may use <a href=\\\"https://troydhanson.github.io/uthash/\\\" target=\\\"_blank\\\">uthash</a>. \\\"uthash.h\\\" is included by default. Below are some examples:</p>\\r\\n\\r\\n<p><b>1. Adding an item to a hash.</b>\\r\\n<pre>\\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<p><b>2. Looking up an item in a hash:</b>\\r\\n<pre>\\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<p><b>3. Deleting an item in a hash:</b>\\r\\n<pre>\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n HASH_DEL(users, user); \\r\\n}\\r\\n</pre>\\r\\n</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-10\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use 5.3.0 version of <a href=\\\"https://github.com/datastructures-js/priority-queue/tree/fb4fdb984834421279aeb081df7af624d17c2a03\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and 4.2.1 version of <a href=\\\"https://github.com/datastructures-js/queue/tree/e63563025a5a805aa16928cb53bcd517bfea9230\\\" target=\\\"_blank\\\">datastructures-js/queue</a>.</p>\"], \"ruby\": [\"Ruby\", \"<p><code>Ruby 3.1</code></p>\\r\\n\\r\\n<p>Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms</p>\"], \"swift\": [\"Swift\", \"<p><code>Swift 5.5.2</code>.</p>\"], \"golang\": [\"Go\", \"<p><code>Go 1.21</code></p>\\r\\n<p>Support <a href=\\\"https://github.com/emirpasic/gods/tree/v1.18.1\\\" target=\\\"_blank\\\">https://godoc.org/github.com/emirpasic/gods@v1.18.1</a> library.</p>\"], \"python3\": [\"Python3\", \"<p><code>Python 3.10</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/3/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/3/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/3/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\"], \"scala\": [\"Scala\", \"<p><code>Scala 2.13.7</code>.</p>\"], \"kotlin\": [\"Kotlin\", \"<p><code>Kotlin 1.9.0</code>.</p>\"], \"rust\": [\"Rust\", \"<p><code>Rust 1.58.1</code></p>\\r\\n\\r\\n<p>Supports <a href=\\\"https://crates.io/crates/rand\\\" target=\\\"_blank\\\">rand </a> v0.6\\u00a0from crates.io</p>\"], \"php\": [\"PHP\", \"<p><code>PHP 8.1</code>.</p>\\r\\n<p>With bcmath module</p>\"], \"typescript\": [\"Typescript\", \"<p><code>TypeScript 5.1.6, Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES2022 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\"], \"racket\": [\"Racket\", \"<p>Run with <code>Racket 8.3</code>.</p>\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 25.0\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.4 with Erlang/OTP 25.0\"], \"dart\": [\"Dart\", \"<p>Dart 2.17.3</p>\\r\\n\\r\\n<p>Your code will be run directly without compiling</p>\"]}",
"libraryUrl": null,
"adminUrl": null,
"challengeQuestion": {
"id": "1377",
"date": "2023-06-18",
"incompleteChallengeCount": 0,
"streakCount": 0,
"type": "DAILY",
"__typename": "ChallengeQuestionNode"
},
"__typename": "QuestionNode"
}
}
}