feat: add solutions to lc problem: No.0370

No.0370.Range Addition

Author: yanglbme

solution/0300-0399/0370.Range Addition/README.md

@@ -37,14 +37,29 @@
 
 <!-- 这里可写通用的实现逻辑 -->
 
-差分数组。
+**方法一：差分数组**
+
+时间复杂度 O(n)。
+
+**方法二：树状数组 + 差分思想**
+
+时间复杂度 O(nlogn)。
+
+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)`。
 
 <!-- tabs:start -->
 
 ### **Python3**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
+差分数组：
+
 ```python
 class Solution:
     def getModifiedArray(self, length: int, updates: List[List[int]]) -> List[int]:
@@ -58,10 +73,46 @@ class Solution:
         return delta
 ```
 
+树状数组：
+
+```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:
+            s += self.c[x]
+            x -= BinaryIndexedTree.lowbit(x)
+        return s
+
+
+class Solution:
+    def getModifiedArray(self, length: int, updates: List[List[int]]) -> List[int]:
+        tree = BinaryIndexedTree(length)
+        for start, end, inc in updates:
+            tree.update(start + 1, inc)
+            tree.update(end + 2, -inc)
+        return [tree.query(i + 1) for i in range(length)]
+```
+
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
+差分数组：
+
 ```java
 class Solution {
     public int[] getModifiedArray(int length, int[][] updates) {
@@ -80,8 +131,60 @@ class Solution {
 }
 ```
 
+树状数组：
+
+```java
+class Solution {
+    public int[] getModifiedArray(int length, int[][] updates) {
+        BinaryIndexedTree tree = new BinaryIndexedTree(length);
+        for (int[] e : updates) {
+            int start = e[0], end = e[1], inc = e[2];
+            tree.update(start + 1, inc);
+            tree.update(end + 2, -inc);
+        }
+        int[] ans = new int[length];
+        for (int i = 0; i < length; ++i) {
+            ans[i] = tree.query(i + 1);
+        }
+        return ans;
+    }
+}
+
+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;
+    }
+}
+```
+
 ### **C++**
 
+差分数组：
+
 ```cpp
 class Solution {
 public:
@@ -97,8 +200,60 @@ public:
 };
 ```
 
+树状数组：
+
+```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 Solution {
+public:
+    vector<int> getModifiedArray(int length, vector<vector<int>>& updates) {
+        BinaryIndexedTree* tree = new BinaryIndexedTree(length);
+        for (auto& e : updates)
+        {
+            int start = e[0], end = e[1], inc = e[2];
+            tree->update(start + 1, inc);
+            tree->update(end + 2, -inc);
+        }
+        vector<int> ans;
+        for (int i = 0; i < length; ++i) ans.push_back(tree->query(i + 1));
+        return ans;
+    }
+};
+```
+
 ### **Go**
 
+差分数组：
+
 ```go
 func getModifiedArray(length int, updates [][]int) []int {
 	delta := make([]int, length)
@@ -115,6 +270,54 @@ func getModifiedArray(length int, updates [][]int) []int {
 }
 ```
 
+树状数组：
+
+```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
+}
+
+func getModifiedArray(length int, updates [][]int) []int {
+	tree := newBinaryIndexedTree(length)
+	for _, e := range updates {
+		start, end, inc := e[0], e[1], e[2]
+		tree.update(start+1, inc)
+		tree.update(end+2, -inc)
+	}
+	ans := make([]int, length)
+	for i := range ans {
+		ans[i] = tree.query(i + 1)
+	}
+	return ans
+}
+```
+
 ### **...**
 
 ```