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Formatted question description: https://leetcode.ca/all/2536.html

2536. Increment Submatrices by One

Description

You are given a positive integer n, indicating that we initially have an n x n 0-indexed integer matrix mat filled with zeroes.

You are also given a 2D integer array query. For each query[i] = [row1i, col1i, row2i, col2i], you should do the following operation:

  • Add 1 to every element in the submatrix with the top left corner (row1i, col1i) and the bottom right corner (row2i, col2i). That is, add 1 to mat[x][y] for all row1i <= x <= row2i and col1i <= y <= col2i.

Return the matrix mat after performing every query.

 

Example 1:

Input: n = 3, queries = [[1,1,2,2],[0,0,1,1]]
Output: [[1,1,0],[1,2,1],[0,1,1]]
Explanation: The diagram above shows the initial matrix, the matrix after the first query, and the matrix after the second query.
- In the first query, we add 1 to every element in the submatrix with the top left corner (1, 1) and bottom right corner (2, 2).
- In the second query, we add 1 to every element in the submatrix with the top left corner (0, 0) and bottom right corner (1, 1).

Example 2:

Input: n = 2, queries = [[0,0,1,1]]
Output: [[1,1],[1,1]]
Explanation: The diagram above shows the initial matrix and the matrix after the first query.
- In the first query we add 1 to every element in the matrix.

 

Constraints:

  • 1 <= n <= 500
  • 1 <= queries.length <= 104
  • 0 <= row1i <= row2i < n
  • 0 <= col1i <= col2i < n

Solutions

  • class Solution {
        public int[][] rangeAddQueries(int n, int[][] queries) {
            int[][] mat = new int[n][n];
            for (var q : queries) {
                int x1 = q[0], y1 = q[1], x2 = q[2], y2 = q[3];
                mat[x1][y1]++;
                if (x2 + 1 < n) {
                    mat[x2 + 1][y1]--;
                }
                if (y2 + 1 < n) {
                    mat[x1][y2 + 1]--;
                }
                if (x2 + 1 < n && y2 + 1 < n) {
                    mat[x2 + 1][y2 + 1]++;
                }
            }
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    if (i > 0) {
                        mat[i][j] += mat[i - 1][j];
                    }
                    if (j > 0) {
                        mat[i][j] += mat[i][j - 1];
                    }
                    if (i > 0 && j > 0) {
                        mat[i][j] -= mat[i - 1][j - 1];
                    }
                }
            }
            return mat;
        }
    }
    
  • class Solution {
    public:
        vector<vector<int>> rangeAddQueries(int n, vector<vector<int>>& queries) {
            vector<vector<int>> mat(n, vector<int>(n));
            for (auto& q : queries) {
                int x1 = q[0], y1 = q[1], x2 = q[2], y2 = q[3];
                mat[x1][y1]++;
                if (x2 + 1 < n) {
                    mat[x2 + 1][y1]--;
                }
                if (y2 + 1 < n) {
                    mat[x1][y2 + 1]--;
                }
                if (x2 + 1 < n && y2 + 1 < n) {
                    mat[x2 + 1][y2 + 1]++;
                }
            }
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < n; ++j) {
                    if (i > 0) {
                        mat[i][j] += mat[i - 1][j];
                    }
                    if (j > 0) {
                        mat[i][j] += mat[i][j - 1];
                    }
                    if (i > 0 && j > 0) {
                        mat[i][j] -= mat[i - 1][j - 1];
                    }
                }
            }
            return mat;
        }
    };
    
  • class Solution:
        def rangeAddQueries(self, n: int, queries: List[List[int]]) -> List[List[int]]:
            mat = [[0] * n for _ in range(n)]
            for x1, y1, x2, y2 in queries:
                mat[x1][y1] += 1
                if x2 + 1 < n:
                    mat[x2 + 1][y1] -= 1
                if y2 + 1 < n:
                    mat[x1][y2 + 1] -= 1
                if x2 + 1 < n and y2 + 1 < n:
                    mat[x2 + 1][y2 + 1] += 1
    
            for i in range(n):
                for j in range(n):
                    if i:
                        mat[i][j] += mat[i - 1][j]
                    if j:
                        mat[i][j] += mat[i][j - 1]
                    if i and j:
                        mat[i][j] -= mat[i - 1][j - 1]
            return mat
    
    
  • func rangeAddQueries(n int, queries [][]int) [][]int {
    	mat := make([][]int, n)
    	for i := range mat {
    		mat[i] = make([]int, n)
    	}
    	for _, q := range queries {
    		x1, y1, x2, y2 := q[0], q[1], q[2], q[3]
    		mat[x1][y1]++
    		if x2+1 < n {
    			mat[x2+1][y1]--
    		}
    		if y2+1 < n {
    			mat[x1][y2+1]--
    		}
    		if x2+1 < n && y2+1 < n {
    			mat[x2+1][y2+1]++
    		}
    	}
    	for i := 0; i < n; i++ {
    		for j := 0; j < n; j++ {
    			if i > 0 {
    				mat[i][j] += mat[i-1][j]
    			}
    			if j > 0 {
    				mat[i][j] += mat[i][j-1]
    			}
    			if i > 0 && j > 0 {
    				mat[i][j] -= mat[i-1][j-1]
    			}
    		}
    	}
    	return mat
    }
    

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