[Swift]LeetCode304. 二维区域和检索

★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★
➤微信公众号：山青咏芝（shanqingyongzhi）
➤博客园地址：山青咏芝（https://www.cnblogs.com/strengthen/）
➤GitHub地址：https://github.com/strengthen/LeetCode
➤原文地址：https://www.cnblogs.com/strengthen/p/10246925.html 
➤如果链接不是山青咏芝的博客园地址，则可能是爬取作者的文章。
➤原文已修改更新！强烈建议点击原文地址阅读！支持作者！支持原创！
★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★

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.

---

给定一个二维矩阵，计算其子矩形范围内元素的总和，该子矩阵的左上角为 (row1, col1) ，右下角为 (row2, col2)。

上图子矩阵左上角 (row1, col1) = (2, 1) ，右下角(row2, col2) = (4, 3)，该子矩形内元素的总和为 8。

示例:

给定 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

说明:

1. 你可以假设矩阵不可变。
2. 会多次调用 sumRegion 方法。
3. 你可以假设 row1 ≤ row2 且 col1 ≤ col2。

---

140ms

class NumMatrix {

    var matrix: [[Int]]
    var sumMatrix = [[Int]]()
    
    init(_ matrix: [[Int]]) {
        self.matrix = matrix
        sumMatrix = matrix
        let m = matrix.count
        if m == 0 { return }
        let n = matrix[0].count
        
        for i in 0 ..< m { 
            for j in 1 ..< n {
                sumMatrix[i][j] = sumMatrix[i][j - 1] + sumMatrix[i][j]
            }
        }
        for j in 0 ..< n {
            for i in 1 ..< m {
                sumMatrix[i][j] = sumMatrix[i - 1][j] + sumMatrix[i][j]    
            }
            
        }
    }
    
    func sumRegion(_ row1: Int, _ col1: Int, _ row2: Int, _ col2: Int) -> Int {
        if row1 == 0 && col1 == 0 {
            return sumMatrix[row2][col2]
        } else if row1 == 0 {
            return sumMatrix[row2][col2] - sumMatrix[row2][col1 - 1]
        } else if col1 == 0 {
            return sumMatrix[row2][col2] - sumMatrix[row1 - 1][col2]
        } else {
            return sumMatrix[row2][col2] - sumMatrix[row1 - 1][col2] - sumMatrix[row2][col1 - 1] + sumMatrix[row1 - 1][col1 - 1] 
        }
        
    }
}

/**
 * Your NumMatrix object will be instantiated and called as such:
 * let obj = NumMatrix(matrix)
 * let ret_1: Int = obj.sumRegion(row1, col1, row2, col2)
 */
 

---

180ms

class NumMatrix {
    
    let _matrix : [[Int]]
    var sums : [[Int]]
    
    init(_ matrix: [[Int]]) {
        _matrix = matrix
        sums = matrix
        
        if matrix.isEmpty {
            return
        }
        
        for i in 0..<matrix.count {
            for j in 0..<matrix[0].count {
                if i == 0 && j == 0 {
                    continue
                }
                if i > 0 && j > 0 {
                    sums[i][j] += sums[i-1][j] + sums[i][j-1] - sums[i-1][j-1]
                }
                if i == 0 {
                    sums[i][j] += sums[i][j-1]
                }
                
                if j == 0 {
                    sums[i][j] += sums[i-1][j]
                }
            }
        }
        
    }
    
    @inline(__always)  func sumRegion(_ row1: Int, _ col1: Int, _ row2: Int, _ col2: Int) -> Int {
        if row1 == 0 && col1 == 0 {
            return sums[row2][col2]
        }
        
        if row1 == 0 {
            return sums[row2][col2] - sums[row2][col1-1]
        }
        
        if col1 == 0 {
            return sums[row2][col2] - sums[row1-1][col2]
        }
        
        return sums[row2][col2] - sums[row2][col1-1] - sums[row1-1][col2] + sums[row1-1][col1-1]
    }
}