feat: add solutions to lc problem: No.0308

No.0308.Range Sum Query 2D - Mutable

Author: yanglbme

solution/0300-0399/0308.Range Sum Query 2D - Mutable/README.md

@@ -61,22 +61,291 @@ numMatrix.sumRegion(2, 1, 4, 3); // 返回 10 (即，右侧红色矩形的和)
 
 <!-- 这里可写通用的实现逻辑 -->
 
+树状数组。
+
+树状数组，也称作“二叉索引树”（Binary Indexed Tree）或 Fenwick 树。 它可以高效地实现如下两个操作：
+
+1. **单点更新** `update(x, delta)`： 把序列 x 位置的数加上一个值 delta；
+1. **前缀和查询** `query(x)`：查询序列 `[1,...x]` 区间的区间和，即位置 x 的前缀和。
+
+这两个操作的时间复杂度均为 `O(log n)`。
+
+对于本题，可以构建二维树状数组。
+
 <!-- tabs:start -->
 
 ### **Python3**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```python
+class BinaryIndexedTree:
+    def __init__(self, n):
+        self.n = n
+        self.c = [0] * (n + 1)
+
+    @staticmethod
+    def lowbit(x):
+        return x & -x
+
+    def update(self, x, delta):
+        while x <= self.n:
+            self.c[x] += delta
+            x += BinaryIndexedTree.lowbit(x)
+
+    def query(self, x):
+        s = 0
+        while x > 0:
+            s += self.c[x]
+            x -= BinaryIndexedTree.lowbit(x)
+        return s
+
+
+class NumMatrix:
+
+    def __init__(self, matrix: List[List[int]]):
+        self.trees = []
+        n = len(matrix[0])
+        for row in matrix:
+            tree = BinaryIndexedTree(n)
+            for j, v in enumerate(row):
+                tree.update(j + 1, v)
+            self.trees.append(tree)
 
+    def update(self, row: int, col: int, val: int) -> None:
+        tree = self.trees[row]
+        prev = tree.query(col + 1) - tree.query(col)
+        tree.update(col + 1, val - prev)
+
+    def sumRegion(self, row1: int, col1: int, row2: int, col2: int) -> int:
+        return sum(tree.query(col2 + 1) - tree.query(col1) for tree in self.trees[row1: row2 + 1])
+
+
+# Your NumMatrix object will be instantiated and called as such:
+# obj = NumMatrix(matrix)
+# obj.update(row,col,val)
+# param_2 = obj.sumRegion(row1,col1,row2,col2)
 ```
 
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```java
+class BinaryIndexedTree {
+    private int n;
+    private int[] c;
+
+    public BinaryIndexedTree(int n) {
+        this.n = n;
+        c = new int[n + 1];
+    }
+
+    public void update(int x, int delta) {
+        while (x <= n) {
+            c[x] += delta;
+            x += lowbit(x);
+        }
+    }
+
+    public int query(int x) {
+        int s = 0;
+        while (x > 0) {
+            s += c[x];
+            x -= lowbit(x);
+        }
+        return s;
+    }
+
+    public static int lowbit(int x) {
+        return x & -x;
+    }
+}
+
+class NumMatrix {
+    private BinaryIndexedTree[] trees;
+
+    public NumMatrix(int[][] matrix) {
+        int m = matrix.length;
+        int n = matrix[0].length;
+        trees = new BinaryIndexedTree[m];
+        for (int i = 0; i < m; ++i) {
+            BinaryIndexedTree tree = new BinaryIndexedTree(n);
+            for (int j = 0; j < n; ++j) {
+                tree.update(j + 1, matrix[i][j]);
+            }
+            trees[i] = tree;
+        }
+    }
+    
+    public void update(int row, int col, int val) {
+        BinaryIndexedTree tree = trees[row];
+        int prev = tree.query(col + 1) - tree.query(col);
+        tree.update(col + 1, val - prev);
+    }
+    
+    public int sumRegion(int row1, int col1, int row2, int col2) {
+        int s = 0;
+        for (int i = row1; i <= row2; ++i) {
+            BinaryIndexedTree tree = trees[i];
+            s += tree.query(col2 + 1) - tree.query(col1);
+        }
+        return s;
+    }
+}
+
+/**
+ * Your NumMatrix object will be instantiated and called as such:
+ * NumMatrix obj = new NumMatrix(matrix);
+ * obj.update(row,col,val);
+ * int param_2 = obj.sumRegion(row1,col1,row2,col2);
+ */
+```
+
+### **C++**
+
+```cpp
+class BinaryIndexedTree {
+public:
+    int n;
+    vector<int> c;
+
+    BinaryIndexedTree(int _n): n(_n), c(_n + 1){}
+
+    void update(int x, int delta) {
+        while (x <= n)
+        {
+            c[x] += delta;
+            x += lowbit(x);
+        }
+    }
+
+    int query(int x) {
+        int s = 0;
+        while (x > 0)
+        {
+            s += c[x];
+            x -= lowbit(x);
+        }
+        return s;
+    }
+
+    int lowbit(int x) {
+        return x & -x;
+    }
+};
+
+class NumMatrix {
+public:
+    vector<BinaryIndexedTree*> trees;
+
+    NumMatrix(vector<vector<int>>& matrix) {
+        int m = matrix.size();
+        int n = matrix[0].size();
+        trees.resize(m);
+        for (int i = 0; i < m; ++i) {
+            BinaryIndexedTree* tree = new BinaryIndexedTree(n);
+            for (int j = 0; j < n; ++j) tree->update(j + 1, matrix[i][j]);
+            trees[i] = tree;
+        }
+    }
+    
+    void update(int row, int col, int val) {
+        BinaryIndexedTree* tree = trees[row];
+        int prev = tree->query(col + 1) - tree->query(col);
+        tree->update(col + 1, val - prev);
+    }
+    
+    int sumRegion(int row1, int col1, int row2, int col2) {
+        int s = 0;
+        for (int i = row1; i <= row2; ++i)
+        {
+            BinaryIndexedTree* tree = trees[i];
+            s += tree->query(col2 + 1) - tree->query(col1);
+        }
+        return s;
+    }
+};
+
+/**
+ * Your NumMatrix object will be instantiated and called as such:
+ * NumMatrix* obj = new NumMatrix(matrix);
+ * obj->update(row,col,val);
+ * int param_2 = obj->sumRegion(row1,col1,row2,col2);
+ */
+```
+
+### **Go**
+
+```go
+type BinaryIndexedTree struct {
+	n int
+	c []int
+}
+
+func newBinaryIndexedTree(n int) *BinaryIndexedTree {
+	c := make([]int, n+1)
+	return &BinaryIndexedTree{n, c}
+}
+
+func (this *BinaryIndexedTree) lowbit(x int) int {
+	return x & -x
+}
+
+func (this *BinaryIndexedTree) update(x, delta int) {
+	for x <= this.n {
+		this.c[x] += delta
+		x += this.lowbit(x)
+	}
+}
+
+func (this *BinaryIndexedTree) query(x int) int {
+	s := 0
+	for x > 0 {
+		s += this.c[x]
+		x -= this.lowbit(x)
+	}
+	return s
+}
+
+type NumMatrix struct {
+	trees []*BinaryIndexedTree
+}
+
+func Constructor(matrix [][]int) NumMatrix {
+	n := len(matrix[0])
+	var trees []*BinaryIndexedTree
+	for _, row := range matrix {
+		tree := newBinaryIndexedTree(n)
+		for j, v := range row {
+			tree.update(j+1, v)
+		}
+		trees = append(trees, tree)
+	}
+	return NumMatrix{trees}
+}
+
+func (this *NumMatrix) Update(row int, col int, val int) {
+	tree := this.trees[row]
+	prev := tree.query(col+1) - tree.query(col)
+	tree.update(col+1, val-prev)
+}
+
+func (this *NumMatrix) SumRegion(row1 int, col1 int, row2 int, col2 int) int {
+	s := 0
+	for i := row1; i <= row2; i++ {
+		tree := this.trees[i]
+		s += tree.query(col2+1) - tree.query(col1)
+	}
+	return s
+}
 
+/**
+ * Your NumMatrix object will be instantiated and called as such:
+ * obj := Constructor(matrix);
+ * obj.Update(row,col,val);
+ * param_2 := obj.SumRegion(row1,col1,row2,col2);
+ */
 ```
 
 ### **...**