{ "data": { "question": { "questionId": "1224", "questionFrontendId": "1289", "boundTopicId": null, "title": "Minimum Falling Path Sum II", "titleSlug": "minimum-falling-path-sum-ii", "content": "

Given an n x n integer matrix grid, return the minimum sum of a falling path with non-zero shifts.

\n\n

A falling path with non-zero shifts is a choice of exactly one element from each row of grid such that no two elements chosen in adjacent rows are in the same column.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: arr = [[1,2,3],[4,5,6],[7,8,9]]\nOutput: 13\nExplanation: \nThe possible falling paths are:\n[1,5,9], [1,5,7], [1,6,7], [1,6,8],\n[2,4,8], [2,4,9], [2,6,7], [2,6,8],\n[3,4,8], [3,4,9], [3,5,7], [3,5,9]\nThe falling path with the smallest sum is [1,5,7], so the answer is 13.\n
\n\n

Example 2:

\n\n
\nInput: grid = [[7]]\nOutput: 7\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Hard", "likes": 766, "dislikes": 65, "isLiked": null, "similarQuestions": "[{\"title\": \"Minimum Falling Path Sum\", \"titleSlug\": \"minimum-falling-path-sum\", \"difficulty\": \"Medium\", \"translatedTitle\": null}]", "exampleTestcases": "[[1,2,3],[4,5,6],[7,8,9]]\n[[7]]", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Array", "slug": "array", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Dynamic Programming", "slug": "dynamic-programming", "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 minFallingPathSum(vector>& grid) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int minFallingPathSum(int[][] grid) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def minFallingPathSum(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 minFallingPathSum(self, grid: List[List[int]]) -> int:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "\n\nint minFallingPathSum(int** grid, int gridSize, int* gridColSize){\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int MinFallingPathSum(int[][] grid) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[][]} grid\n * @return {number}\n */\nvar minFallingPathSum = function(grid) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[][]} grid\n# @return {Integer}\ndef min_falling_path_sum(grid)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func minFallingPathSum(_ grid: [[Int]]) -> Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func minFallingPathSum(grid [][]int) int {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def minFallingPathSum(grid: Array[Array[Int]]): Int = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun minFallingPathSum(grid: Array): Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn min_falling_path_sum(grid: Vec>) -> i32 {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[][] $grid\n * @return Integer\n */\n function minFallingPathSum($grid) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function minFallingPathSum(grid: number[][]): number {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (min-falling-path-sum grid)\n (-> (listof (listof exact-integer?)) exact-integer?)\n\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec min_falling_path_sum(Grid :: [[integer()]]) -> integer().\nmin_falling_path_sum(Grid) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec min_falling_path_sum(grid :: [[integer]]) :: integer\n def min_falling_path_sum(grid) do\n\n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"27.6K\", \"totalSubmission\": \"45.2K\", \"totalAcceptedRaw\": 27631, \"totalSubmissionRaw\": 45207, \"acRate\": \"61.1%\"}", "hints": [ "Use dynamic programming.", "Let dp[i][j] be the answer for the first i rows such that column j is chosen from row i.", "Use the concept of cumulative array to optimize the complexity of the solution." ], "solution": null, "status": null, "sampleTestCase": "[[1,2,3],[4,5,6],[7,8,9]]", "metaData": "{\n \"name\": \"minFallingPathSum\",\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++\", \"

Compiled with clang 11 using the latest C++ 17 standard.

\\r\\n\\r\\n

Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\"], \"java\": [\"Java\", \"

OpenJDK 17 . Java 8 features such as lambda expressions and stream API can be used.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n

Includes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.

\"], \"python\": [\"Python\", \"

Python 2.7.12.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\\r\\n\\r\\n

Note that Python 2.7 will not be maintained past 2020. For the latest Python, please choose Python3 instead.

\"], \"c\": [\"C\", \"

Compiled with gcc 8.2 using the gnu99 standard.

\\r\\n\\r\\n

Your code is compiled with level one optimization (-O1). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n\\r\\n

For hash table operations, you may use uthash. \\\"uthash.h\\\" is included by default. Below are some examples:

\\r\\n\\r\\n

1. Adding an item to a hash.\\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
\\r\\n

\\r\\n\\r\\n

2. Looking up an item in a hash:\\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
\\r\\n

\\r\\n\\r\\n

3. Deleting an item in a hash:\\r\\n

\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n
\\r\\n

\"], \"csharp\": [\"C#\", \"

C# 10 with .NET 6 runtime

\\r\\n\\r\\n

Your code is compiled with debug flag enabled (/debug).

\"], \"javascript\": [\"JavaScript\", \"

Node.js 16.13.2.

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES6 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\\r\\n\\r\\n

For Priority Queue / Queue data structures, you may use datastructures-js/priority-queue and datastructures-js/queue.

\"], \"ruby\": [\"Ruby\", \"

Ruby 3.1

\\r\\n\\r\\n

Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms

\"], \"swift\": [\"Swift\", \"

Swift 5.5.2.

\"], \"golang\": [\"Go\", \"

Go 1.17.6.

\\r\\n\\r\\n

Support https://godoc.org/github.com/emirpasic/gods library.

\"], \"python3\": [\"Python3\", \"

Python 3.10.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\"], \"scala\": [\"Scala\", \"

Scala 2.13.7.

\"], \"kotlin\": [\"Kotlin\", \"

Kotlin 1.3.10.

\"], \"rust\": [\"Rust\", \"

Rust 1.58.1

\\r\\n\\r\\n

Supports rand v0.6\\u00a0from crates.io

\"], \"php\": [\"PHP\", \"

PHP 8.1.

\\r\\n

With bcmath module

\"], \"typescript\": [\"Typescript\", \"

TypeScript 4.5.4, Node.js 16.13.2.

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES2020 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\"], \"racket\": [\"Racket\", \"

Run with Racket 8.3.

\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 24.2\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.0 with Erlang/OTP 24.2\"]}", "libraryUrl": null, "adminUrl": null, "challengeQuestion": null, "__typename": "QuestionNode" } } }