Range Sum Query 2D - Immutable

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).

The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.

Example:

Given matrix = [
  [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]
]
sumRegion(2, 1, 4, 3) -> 8
sumRegion(1, 1, 2, 2) -> 11
sumRegion(1, 2, 2, 4) -> 12

Note:

1. You may assume that the matrix does not change.
2. There are many calls to sumRegion function.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

Solution(javascript)

/*
 * @lc app=leetcode id=304 lang=javascript
 *
 * [304] Range Sum Query 2D - Immutable
 */

// @lc code=start
/**
 * @param {number[][]} matrix
 */
const NumMatrix = function (matrix) {
  const sum = (i, j) => {
    let top = 0
    let left = 0
    let topLeft = 0
    if (matrix[i - 1] && matrix[i - 1][j] !== undefined) {
      top = matrix[i - 1][j]
    }
    if (matrix[i - 1] && matrix[i - 1][j - 1] !== undefined) {
      topLeft = matrix[i - 1][j - 1]
    }
    if (matrix[i][j - 1] !== undefined) {
      left = matrix[i][j - 1]
    }
    return matrix[i][j] + left + top - topLeft
  }
  for (let i = 0; i < matrix.length; i++) {
    for (let j = 0; j < matrix[i].length; j++) {
      matrix[i][j] = sum(i, j)
    }
  }
  this.dp = matrix
}

/**
 * @param {number} row1
 * @param {number} col1
 * @param {number} row2
 * @param {number} col2
 * @return {number}
 */
NumMatrix.prototype.sumRegion = function (row1, col1, row2, col2) {
  const get = (row, column) => {
    if (row < 0 || column < 0) {
      return 0
    }
    return this.dp[row][column]
  }
  return get(row2, col2) - get(row1 - 1, col2) - get(row2, col1 - 1) + get(row1 - 1, col1 - 1)
}

/**
 * Your NumMatrix object will be instantiated and called as such:
 * var obj = new NumMatrix(matrix)
 * var param_1 = obj.sumRegion(row1,col1,row2,col2)
 */
// @lc code=end