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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

• Java
• C++
• Python
• Go

• 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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