LeetCode: 304. Range Sum Query 2D - Immutable

LeetCode: 304. Range Sum Query 2D - Immutable

题目描述

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.

解题思路 —— 动态规划

1. 记 ​​topLeftSums[i][j]​​​ 表示矩阵 ​​(0, 0, i, j)​​ 的和
2. 则 ​​topLeftSums[i+1][j+1] = topLeftSums[i+1][j] + sum(matrix[i+1][k])​​​， 其中 ​​k​​​ 是 ​​[0, j+1)​​​ 区间的整数。如图：
   
   3.如下图，矩阵 ​​​(row1, col1, row2, col2)​​​ 的和就是 ​​(0, 0, row2, col2) - (0, 0, row1-1, col2) - (0, 0, row2, col1-1) + (0, 0, row1-1, col1-1)​​

• ​​(row1, col1, row2, col2)​​:
• ​​(0, 0, row2, col2) - (0, 0, row1-1, col2) - (0, 0, row2, col1-1) + (0, 0, row1-1, col1-1)​​:

AC 代码

type NumMatrix struct {
    topLeftSums [][]int
}

func (this *NumMatrix) initNumMatrix(matrix [][]int) bool{
    if len(matrix) == 0 {
        return false
    }
    
    this.topLeftSums = make([][]int, len(matrix)+1)
    
    for i := 0; i <= len(matrix); i++{
        this.topLeftSums[i] = make([]int, len(matrix[0])+1)
    }
    
    return true
}

func Constructor(matrix [][]int) NumMatrix {
    var sumMatrix NumMatrix 
    
    if len(matrix) == 0 {
        return sumMatrix
    }
    
    sumMatrix.initNumMatrix(matrix)
    
    for i := 0; i < len(matrix); i++{
        for j := 0; j < len(matrix[i]); j++{
            sumMatrix.topLeftSums[i+1][j+1] = sumMatrix.topLeftSums[i][j+1]
            for k := 0; k < j+1; k++{
                sumMatrix.topLeftSums[i+1][j+1] += matrix[i][k]
            }
        }
    }
    
    return sumMatrix
}


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


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