README_EN.md

304. Range Sum Query 2D - Immutable

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Description

Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

Implement the NumMatrix class:

• NumMatrix(int[][] matrix) initializes the object with the integer matrix matrix.
• int sumRegion(int row1, int col1, int row2, int col2) returns the sum of the elements of the matrix array inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

 

Example 1:

Input
["NumMatrix", "sumRegion", "sumRegion", "sumRegion"]
[[[[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]]
Output
[null, 8, 11, 12]
Explanation
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 rectangele).
numMatrix.sumRegion(1, 1, 2, 2); // return 11 (i.e sum of the green rectangele).
numMatrix.sumRegion(1, 2, 2, 4); // return 12 (i.e sum of the blue rectangele).

 

Constraints:

• m == matrix.length
• n == matrix[i].length
• 1 <= m, n <= 200
• -105 <= matrix[i][j] <= 105
• 0 <= row1 <= row2 < m
• 0 <= col1 <= col2 < n
• At most 104 calls will be made to sumRegion.

Solutions

Dynamic programming - 2D preSum.

Python3

class NumMatrix:

    def __init__(self, matrix: List[List[int]]):
        m, n = len(matrix), len(matrix[0])
        self.pre = [[0] * (n + 1) for _ in range(m + 1)]
        for i in range(1, m + 1):
            for j in range(1, n + 1):
                self.pre[i][j] = self.pre[i - 1][j] + self.pre[i][j - 1] - self.pre[i - 1][j - 1] + matrix[i - 1][j - 1]

    def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
        return self.pre[row2 + 1][col2 + 1] - self.pre[row2 + 1][col1] - self.pre[row1][col2 + 1] + self.pre[row1][col1]


# Your NumMatrix object will be instantiated and called as such:
# obj = NumMatrix(matrix)
# param_1 = obj.sumRegion(row1,col1,row2,col2)

Java

class NumMatrix {
    private int[][] pre;

    public NumMatrix(int[][] matrix) {
        int m = matrix.length, n = matrix[0].length;
        pre = new int[m + 1][n + 1];
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                pre[i][j] = pre[i - 1][j] + pre[i][j - 1] - pre[i - 1][j - 1] + matrix[i - 1][j - 1];
            }
        }
    }
    
    public int sumRegion(int row1, int col1, int row2, int col2) {
        return pre[row2 + 1][col2 + 1] - pre[row2 + 1][col1] - pre[row1][col2 + 1] + pre[row1][col1];
    }
}

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix obj = new NumMatrix(matrix);
 * int param_1 = obj.sumRegion(row1,col1,row2,col2);
 */

C++

class NumMatrix {
public:
    vector<vector<int>> pre;

    NumMatrix(vector<vector<int>>& matrix) {
        int m = matrix.size(), n = matrix[0].size();
        pre.resize(m + 1, vector<int>(n + 1));
        for (int i = 1; i <= m; ++i) {
            for (int j = 1; j <= n; ++j) {
                pre[i][j] = pre[i - 1][j] + pre[i][j - 1] - pre[i - 1][j - 1] + matrix[i - 1][j - 1];
            }
        }
    }
    
    int sumRegion(int row1, int col1, int row2, int col2) {
        return pre[row2 + 1][col2 + 1] - pre[row2 + 1][col1] - pre[row1][col2 + 1] + pre[row1][col1];
    }
};

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix* obj = new NumMatrix(matrix);
 * int param_1 = obj->sumRegion(row1,col1,row2,col2);
 */

C++

type NumMatrix struct {
	pre [][]int
}

func Constructor(matrix [][]int) NumMatrix {
	m, n := len(matrix), len(matrix[0])
	pre := make([][]int, m+1)
	for i := 0; i < m+1; i++ {
		pre[i] = make([]int, n+1)
	}
	for i := 1; i < m+1; i++ {
		for j := 1; j < n+1; j++ {
			pre[i][j] = pre[i-1][j] + pre[i][j-1] + -pre[i-1][j-1] + matrix[i-1][j-1]
		}
	}
	return NumMatrix{pre}
}

func (this *NumMatrix) SumRegion(row1 int, col1 int, row2 int, col2 int) int {
	return this.pre[row2+1][col2+1] - this.pre[row2+1][col1] - this.pre[row1][col2+1] + this.pre[row1][col1]
}

/**
 * Your NumMatrix object will be instantiated and called as such:
 * obj := Constructor(matrix);
 * param_1 := obj.SumRegion(row1,col1,row2,col2);
 */

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