[Swift]LeetCode304. 二維區域和檢索 - 矩陣不可變 | 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.

---

給定一個二維矩陣，計算其子矩形範圍內元素的總和，該子矩陣的左上角爲 (row1, col1) ，右下角爲 (row2, col2)。

上圖子矩陣左上角 (row1, col1) = (2, 1) ，右下角(row2, col2) = (4, 3)，該子矩形內元素的總和爲 8。

示例:

給定 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

說明:

1. 你能夠假設矩陣不可變。
2. 會屢次調用 sumRegion 方法。
3. 你能夠假設 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 }