[Swift]LeetCode304. 二维区域和检索 - 矩阵不可变 | Range Sum Query 2D - Immutable

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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. 你能够假设矩阵不可变。
2. 会屡次调用 sumRegion 方法。
3. 你能够假设 row1 ≤ row2 且 col1 ≤ col2。

---

140ms

 1 class NumMatrix {
 2 
 3     var matrix: [[Int]]
 4     var sumMatrix = [[Int]]()
 5     
 6     init(_ matrix: [[Int]]) {
 7         self.matrix = matrix
 8         sumMatrix = matrix
 9         let m = matrix.count
10         if m == 0 { return }
11         let n = matrix[0].count
12         
13         for i in 0 ..< m { 
14             for j in 1 ..< n {
15                 sumMatrix[i][j] = sumMatrix[i][j - 1] + sumMatrix[i][j]
16             }
17         }
18         for j in 0 ..< n {
19             for i in 1 ..< m {
20                 sumMatrix[i][j] = sumMatrix[i - 1][j] + sumMatrix[i][j]    
21             }
22             
23         }
24     }
25     
26     func sumRegion(_ row1: Int, _ col1: Int, _ row2: Int, _ col2: Int) -> Int {
27         if row1 == 0 && col1 == 0 {
28             return sumMatrix[row2][col2]
29         } else if row1 == 0 {
30             return sumMatrix[row2][col2] - sumMatrix[row2][col1 - 1]
31         } else if col1 == 0 {
32             return sumMatrix[row2][col2] - sumMatrix[row1 - 1][col2]
33         } else {
34             return sumMatrix[row2][col2] - sumMatrix[row1 - 1][col2] - sumMatrix[row2][col1 - 1] + sumMatrix[row1 - 1][col1 - 1] 
35         }
36         
37     }
38 }
39 
40 /**
41  * Your NumMatrix object will be instantiated and called as such:
42  * let obj = NumMatrix(matrix)
43  * let ret_1: Int = obj.sumRegion(row1, col1, row2, col2)
44  */
45  

---

180ms

 1 class NumMatrix {
 2     
 3     let _matrix : [[Int]]
 4     var sums : [[Int]]
 5     
 6     init(_ matrix: [[Int]]) {
 7         _matrix = matrix
 8         sums = matrix
 9         
10         if matrix.isEmpty {
11             return
12         }
13         
14         for i in 0..<matrix.count {
15             for j in 0..<matrix[0].count {
16                 if i == 0 && j == 0 {
17                     continue
18                 }
19                 if i > 0 && j > 0 {
20                     sums[i][j] += sums[i-1][j] + sums[i][j-1] - sums[i-1][j-1]
21                 }
22                 if i == 0 {
23                     sums[i][j] += sums[i][j-1]
24                 }
25                 
26                 if j == 0 {
27                     sums[i][j] += sums[i-1][j]
28                 }
29             }
30         }
31         
32     }
33     
34     @inline(__always)  func sumRegion(_ row1: Int, _ col1: Int, _ row2: Int, _ col2: Int) -> Int {
35         if row1 == 0 && col1 == 0 {
36             return sums[row2][col2]
37         }
38         
39         if row1 == 0 {
40             return sums[row2][col2] - sums[row2][col1-1]
41         }
42         
43         if col1 == 0 {
44             return sums[row2][col2] - sums[row1-1][col2]
45         }
46         
47         return sums[row2][col2] - sums[row2][col1-1] - sums[row1-1][col2] + sums[row1-1][col1-1]
48     }
49 }