Range sum query 2d mutable

Array Design Binary Indexed Tree Segment Tree Matrix

45.4% acceptance

Mar 31, 2026

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Given a 2D matrix matrix, handle multiple queries of the following types: Update the value of a cell in matrix. Calculate the sum of the elements of matrix 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. void update(int row, int col, int val) Updates the value of matrix[row][col] to be val. int sumRegion(int row1, int col1, int row2, int col2) Returns the sum of the elements of matrix inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

Solution

Rust

Time O(n * m)

Space O(n * m)

LeetCode

solution.rs

struct NumMatrix {
  bit: Vec<Vec<i32>>,
  matrix: Vec<Vec<i32>>,
  m: usize,
  n: usize,
}

impl NumMatrix {

  fn new(matrix: Vec<Vec<i32>>) -> Self {
    let m = matrix.len();
    let n = matrix[0].len();
    let mut nm = NumMatrix {
      bit: vec![vec![0; n + 1]; m + 1],
      matrix: vec![vec![0; n]; m],
      m,
      n,
    };
    for i in 0..m {
      for j in 0..n {
        nm.add(i, j, matrix[i][j]);
        nm.matrix[i][j] = matrix[i][j];
      }
    }
    nm
  }
  
  fn update(&mut self, row: i32, col: i32, val: i32) {
    let r = row as usize;
    let c = col as usize;
    let diff = val - self.matrix[r][c];
    self.matrix[r][c] = val;
    self.add(r, c, diff);
  }
  
  fn sum_region(&self, row1: i32, col1: i32, row2: i32, col2: i32) -> i32 {
    let (r1, c1, r2, c2) = (row1 as usize, col1 as usize, row2 as usize, col2 as usize);
    self.prefix_sum(r2 + 1, c2 + 1) - self.prefix_sum(r1, c2 + 1) - self.prefix_sum(r2 + 1, c1) + self.prefix_sum(r1, c1)
  }

  fn add(&mut self, row: usize, col: usize, val: i32) {
    let mut i = row + 1;
    while i <= self.m {
      let mut j = col + 1;
      while j <= self.n {
        self.bit[i][j] += val;
        j += j & j.wrapping_neg();
      }
      i += i & i.wrapping_neg();
    }
  }

  fn prefix_sum(&self, row: usize, col: usize) -> i32 {
    let mut sum = 0;
    let mut i = row;
    while i > 0 {
      let mut j = col;
      while j > 0 {
        sum += self.bit[i][j];
        j -= j & j.wrapping_neg();
      }
      i -= i & i.wrapping_neg();
    }
    sum
  }
}