Range Sum Query 2D - Immutable
<p>Given a 2D matrix <code>matrix</code>, handle multiple queries of the following type:</p>

<ul>
	<li>Calculate the <strong>sum</strong> of the elements of <code>matrix</code> inside the rectangle defined by its <strong>upper left corner</strong> <code>(row1, col1)</code> and <strong>lower right corner</strong> <code>(row2, col2)</code>.</li>
</ul>

<p>Implement the <code>NumMatrix</code> class:</p>

<ul>
	<li><code>NumMatrix(int[][] matrix)</code> Initializes the object with the integer matrix <code>matrix</code>.</li>
	<li><code>int sumRegion(int row1, int col1, int row2, int col2)</code> Returns the <strong>sum</strong> of the elements of <code>matrix</code> inside the rectangle defined by its <strong>upper left corner</strong> <code>(row1, col1)</code> and <strong>lower right corner</strong> <code>(row2, col2)</code>.</li>
</ul>

<p>You must design an algorithm where <code>sumRegion</code> works on <code>O(1)</code> time complexity.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/14/sum-grid.jpg" style="width: 415px; height: 415px;" />
<pre>
<strong>Input</strong>
[&quot;NumMatrix&quot;, &quot;sumRegion&quot;, &quot;sumRegion&quot;, &quot;sumRegion&quot;]
[[[[3, 0, 1, 4, 2], [5, 6, 3, 2, 1], [1, 2, 0, 1, 5], [4, 1, 0, 1, 7], [1, 0, 3, 0, 5]]], [2, 1, 4, 3], [1, 1, 2, 2], [1, 2, 2, 4]]
<strong>Output</strong>
[null, 8, 11, 12]

<strong>Explanation</strong>
NumMatrix numMatrix = new NumMatrix([[3, 0, 1, 4, 2], [5, 6, 3, 2, 1], [1, 2, 0, 1, 5], [4, 1, 0, 1, 7], [1, 0, 3, 0, 5]]);
numMatrix.sumRegion(2, 1, 4, 3); // return 8 (i.e sum of the red rectangle)
numMatrix.sumRegion(1, 1, 2, 2); // return 11 (i.e sum of the green rectangle)
numMatrix.sumRegion(1, 2, 2, 4); // return 12 (i.e sum of the blue rectangle)
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>-10<sup>4</sup> &lt;= matrix[i][j] &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= row1 &lt;= row2 &lt; m</code></li>
	<li><code>0 &lt;= col1 &lt;= col2 &lt; n</code></li>
	<li>At most <code>10<sup>4</sup></code> calls will be made to <code>sumRegion</code>.</li>
</ul>

['range-sum-query-immutable', 'range-sum-query-2d-mutable', 'find-the-grid-of-region-average']
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class NumMatrix {\npublic:\n    NumMatrix(vector<vector<int>>& matrix) {\n        \n    }\n    \n    int sumRegion(int row1, int col1, int row2, int col2) {\n        \n    }\n};\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * NumMatrix* obj = new NumMatrix(matrix);\n * int param_1 = obj->sumRegion(row1,col1,row2,col2);\n */"}, {"value": "java", "text": "Java", "defaultCode": "class NumMatrix {\n\n    public NumMatrix(int[][] matrix) {\n        \n    }\n    \n    public int sumRegion(int row1, int col1, int row2, int col2) {\n        \n    }\n}\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * NumMatrix obj = new NumMatrix(matrix);\n * int param_1 = obj.sumRegion(row1,col1,row2,col2);\n */"}, {"value": "python", "text": "Python", "defaultCode": "class NumMatrix(object):\n\n    def __init__(self, matrix):\n        \"\"\"\n        :type matrix: List[List[int]]\n        \"\"\"\n        \n\n    def sumRegion(self, row1, col1, row2, col2):\n        \"\"\"\n        :type row1: int\n        :type col1: int\n        :type row2: int\n        :type col2: int\n        :rtype: int\n        \"\"\"\n        \n\n\n# Your NumMatrix object will be instantiated and called as such:\n# obj = NumMatrix(matrix)\n# param_1 = obj.sumRegion(row1,col1,row2,col2)"}, {"value": "python3", "text": "Python3", "defaultCode": "class NumMatrix:\n\n    def __init__(self, matrix: List[List[int]]):\n        \n\n    def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:\n        \n\n\n# Your NumMatrix object will be instantiated and called as such:\n# obj = NumMatrix(matrix)\n# param_1 = obj.sumRegion(row1,col1,row2,col2)"}, {"value": "c", "text": "C", "defaultCode": "\n\n\ntypedef struct {\n    \n} NumMatrix;\n\n\nNumMatrix* numMatrixCreate(int** matrix, int matrixSize, int* matrixColSize) {\n    \n}\n\nint numMatrixSumRegion(NumMatrix* obj, int row1, int col1, int row2, int col2) {\n    \n}\n\nvoid numMatrixFree(NumMatrix* obj) {\n    \n}\n\n/**\n * Your NumMatrix struct will be instantiated and called as such:\n * NumMatrix* obj = numMatrixCreate(matrix, matrixSize, matrixColSize);\n * int param_1 = numMatrixSumRegion(obj, row1, col1, row2, col2);\n \n * numMatrixFree(obj);\n*/"}, {"value": "csharp", "text": "C#", "defaultCode": "public class NumMatrix {\n\n    public NumMatrix(int[][] matrix) {\n        \n    }\n    \n    public int SumRegion(int row1, int col1, int row2, int col2) {\n        \n    }\n}\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * NumMatrix obj = new NumMatrix(matrix);\n * int param_1 = obj.SumRegion(row1,col1,row2,col2);\n */"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {number[][]} matrix\n */\nvar NumMatrix = function(matrix) {\n    \n};\n\n/** \n * @param {number} row1 \n * @param {number} col1 \n * @param {number} row2 \n * @param {number} col2\n * @return {number}\n */\nNumMatrix.prototype.sumRegion = function(row1, col1, row2, col2) {\n    \n};\n\n/** \n * Your NumMatrix object will be instantiated and called as such:\n * var obj = new NumMatrix(matrix)\n * var param_1 = obj.sumRegion(row1,col1,row2,col2)\n */"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "class NumMatrix {\n    constructor(matrix: number[][]) {\n        \n    }\n\n    sumRegion(row1: number, col1: number, row2: number, col2: number): number {\n        \n    }\n}\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * var obj = new NumMatrix(matrix)\n * var param_1 = obj.sumRegion(row1,col1,row2,col2)\n */"}, {"value": "php", "text": "PHP", "defaultCode": "class NumMatrix {\n    /**\n     * @param Integer[][] $matrix\n     */\n    function __construct($matrix) {\n        \n    }\n  \n    /**\n     * @param Integer $row1\n     * @param Integer $col1\n     * @param Integer $row2\n     * @param Integer $col2\n     * @return Integer\n     */\n    function sumRegion($row1, $col1, $row2, $col2) {\n        \n    }\n}\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * $obj = NumMatrix($matrix);\n * $ret_1 = $obj->sumRegion($row1, $col1, $row2, $col2);\n */"}, {"value": "swift", "text": "Swift", "defaultCode": "\nclass NumMatrix {\n\n    init(_ matrix: [[Int]]) {\n        \n    }\n    \n    func sumRegion(_ row1: Int, _ col1: Int, _ row2: Int, _ col2: Int) -> Int {\n        \n    }\n}\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * let obj = NumMatrix(matrix)\n * let ret_1: Int = obj.sumRegion(row1, col1, row2, col2)\n */"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class NumMatrix(matrix: Array<IntArray>) {\n\n    fun sumRegion(row1: Int, col1: Int, row2: Int, col2: Int): Int {\n        \n    }\n\n}\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * var obj = NumMatrix(matrix)\n * var param_1 = obj.sumRegion(row1,col1,row2,col2)\n */"}, {"value": "dart", "text": "Dart", "defaultCode": "class NumMatrix {\n\n  NumMatrix(List<List<int>> matrix) {\n    \n  }\n  \n  int sumRegion(int row1, int col1, int row2, int col2) {\n    \n  }\n}\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * NumMatrix obj = NumMatrix(matrix);\n * int param1 = obj.sumRegion(row1,col1,row2,col2);\n */"}, {"value": "golang", "text": "Go", "defaultCode": "type NumMatrix struct {\n    \n}\n\n\nfunc Constructor(matrix [][]int) NumMatrix {\n    \n}\n\n\nfunc (this *NumMatrix) SumRegion(row1 int, col1 int, row2 int, col2 int) int {\n    \n}\n\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * obj := Constructor(matrix);\n * param_1 := obj.SumRegion(row1,col1,row2,col2);\n */"}, {"value": "ruby", "text": "Ruby", "defaultCode": "class NumMatrix\n\n=begin\n    :type matrix: Integer[][]\n=end\n    def initialize(matrix)\n        \n    end\n\n\n=begin\n    :type row1: Integer\n    :type col1: Integer\n    :type row2: Integer\n    :type col2: Integer\n    :rtype: Integer\n=end\n    def sum_region(row1, col1, row2, col2)\n        \n    end\n\n\nend\n\n# Your NumMatrix object will be instantiated and called as such:\n# obj = NumMatrix.new(matrix)\n# param_1 = obj.sum_region(row1, col1, row2, col2)"}, {"value": "scala", "text": "Scala", "defaultCode": "class NumMatrix(_matrix: Array[Array[Int]]) {\n\n    def sumRegion(row1: Int, col1: Int, row2: Int, col2: Int): Int = {\n        \n    }\n\n}\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * val obj = new NumMatrix(matrix)\n * val param_1 = obj.sumRegion(row1,col1,row2,col2)\n */"}, {"value": "rust", "text": "Rust", "defaultCode": "struct NumMatrix {\n\n}\n\n\n/** \n * `&self` means the method takes an immutable reference.\n * If you need a mutable reference, change it to `&mut self` instead.\n */\nimpl NumMatrix {\n\n    fn new(matrix: Vec<Vec<i32>>) -> Self {\n        \n    }\n    \n    fn sum_region(&self, row1: i32, col1: i32, row2: i32, col2: i32) -> i32 {\n        \n    }\n}\n\n/**\n * Your NumMatrix object will be instantiated and called as such:\n * let obj = NumMatrix::new(matrix);\n * let ret_1: i32 = obj.sum_region(row1, col1, row2, col2);\n */"}, {"value": "racket", "text": "Racket", "defaultCode": "(define num-matrix%\n  (class object%\n    (super-new)\n    \n    ; matrix : (listof (listof exact-integer?))\n    (init-field\n      matrix)\n    \n    ; sum-region : exact-integer? exact-integer? exact-integer? exact-integer? -> exact-integer?\n    (define/public (sum-region row1 col1 row2 col2)\n      )))\n\n;; Your num-matrix% object will be instantiated and called as such:\n;; (define obj (new num-matrix% [matrix matrix]))\n;; (define param_1 (send obj sum-region row1 col1 row2 col2))"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec num_matrix_init_(Matrix :: [[integer()]]) -> any().\nnum_matrix_init_(Matrix) ->\n  .\n\n-spec num_matrix_sum_region(Row1 :: integer(), Col1 :: integer(), Row2 :: integer(), Col2 :: integer()) -> integer().\nnum_matrix_sum_region(Row1, Col1, Row2, Col2) ->\n  .\n\n\n%% Your functions will be called as such:\n%% num_matrix_init_(Matrix),\n%% Param_1 = num_matrix_sum_region(Row1, Col1, Row2, Col2),\n\n%% num_matrix_init_ will be called before every test case, in which you can do some necessary initializations."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule NumMatrix do\n  @spec init_(matrix :: [[integer]]) :: any\n  def init_(matrix) do\n    \n  end\n\n  @spec sum_region(row1 :: integer, col1 :: integer, row2 :: integer, col2 :: integer) :: integer\n  def sum_region(row1, col1, row2, col2) do\n    \n  end\nend\n\n# Your functions will be called as such:\n# NumMatrix.init_(matrix)\n# param_1 = NumMatrix.sum_region(row1, col1, row2, col2)\n\n# NumMatrix.init_ will be called before every test case, in which you can do some necessary initializations."}]
{
  "classname": "NumMatrix",
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  "constructor": {
    "params": [
      {
        "type": "integer[][]",
        "name": "matrix"
      },
      {
        "type": "integer",
        "name": "matrixRowSize",
        "lang": "c",
        "value": "size_1"
      },
      {
        "type": "integer",
        "name": "matrixColSize",
        "lang": "c",
        "value": "col_size_1"
      }
    ]
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  "methods": [
    {
      "name": "sumRegion",
      "params": [
        {
          "type": "integer",
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  "systemdesign": true,
  "params": [
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      "type": "integer[]"
    },
    {
      "name": "inputs",
      "type": "integer[]"
    }
  ],
  "return": {
    "type": "list<String>",
    "dealloc": true
  }
}
{"cpp": ["C++", "<p>Compiled with <code> clang 19 </code> using the latest C++ 23 standard, and <code>libstdc++</code> provided by GCC 14.</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 21</code>. Using compile arguments: <code>--enable-preview --release 21</code></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 2.7.18</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\">is not maintained anymore</a>. For the latest Python, please choose Python3 instead.</p>"], "c": ["C", "<p>Compiled with <code>gcc 14</code> using the gnu11 standard.</p>\r\n\r\n<p>Your code is compiled with level one 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>\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-13\" target=\"_blank\">C# 13</a> with .NET 9 runtime</p>"], "javascript": ["JavaScript", "<p><code>Node.js 22.14.0</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 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "ruby": ["Ruby", "<p><code>Ruby 3.2</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 6.0</code>.</p>\r\n\r\n<p>You may use the following packages:<br/>\r\n<a href=\"https://github.com/apple/swift-algorithms/tree/1.2.0\" target=\"_blank\">swift-algorithms 1.2.0</a><br/>\r\n<a href=\"https://github.com/apple/swift-collections/tree/1.1.4\" target=\"_blank\">swift-collections 1.1.4</a><br/>\r\n<a href=\"https://github.com/apple/swift-numerics/tree/1.0.2\" target=\"_blank\">swift-numerics 1.0.2</a></p>"], "golang": ["Go", "<p><code>Go 1.23</code></p>\r\n<p>Support <a href=\"https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1</a> and <a href=\"https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha</a> library.</p>"], "python3": ["Python3", "<p><code>Python 3.11</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 3.3.1</code>.</p>"], "kotlin": ["Kotlin", "<p><code>Kotlin 2.1.10</code>.</p>"], "rust": ["Rust", "<p><code>Rust 1.85.0</code>. Your code will be compiled with <code>opt-level</code> 2.</p>\r\n\r\n<p>Supports <a href=\"https://crates.io/crates/rand\" target=\"_blank\">rand v0.8</a> and <a href=\"https://crates.io/crates/regex\" target=\"_blank\">regex\u00a0v1</a> and <a href=\"https://crates.io/crates/itertools\" target=\"_blank\">itertools\u00a0v0.14</a> from crates.io</p>"], "php": ["PHP", "<p><code>PHP 8.2</code>.</p>\r\n<p>With bcmath module</p>"], "typescript": ["Typescript", "<p><code>TypeScript 5.7.3, Node.js 22.14.0</code>.</p>\r\n\r\n<p>Compile Options: <code>--alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2024</code></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 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "racket": ["Racket", "<p><a href=\"https://docs.racket-lang.org/guide/performance.html#%28tech._c%29\" target=\"_blank\">Racket CS</a> v8.15</p>\r\n\r\n<p>Using <code>#lang racket</code></p>\r\n\r\n<p>Required <code>data/gvector data/queue data/order data/heap</code> automatically for your convenience</p>"], "erlang": ["Erlang", "Erlang/OTP 26"], "elixir": ["Elixir", "Elixir 1.17 with Erlang/OTP 26"], "dart": ["Dart", "<p>Dart 3.2. You may use package <a href=\"https://pub.dev/packages/collection/versions/1.18.0\" target=\"_blank\">collection</a></p>\r\n\r\n<p>Your code will be run directly without compiling</p>"]}
['Array', 'Design', 'Matrix', 'Prefix Sum']