feat: add solutions to lcci problem: No.10.10

No.10.10.Rank from Stream

Author: yanglbme

lcci/10.10.Rank from Stream/README.md

@@ -33,22 +33,241 @@
 
 <!-- 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)`。
+
+树状数组最基本的功能就是求比某点 x 小的点的个数（这里的比较是抽象的概念，可以是数的大小、坐标的大小、质量的大小等等）。
+
+比如给定数组 `a[5] = {2, 5, 3, 4, 1}`，求 `b[i] = 位置 i 左边小于等于 a[i] 的数的个数`。对于此例，`b[5] = {0, 1, 1, 2, 0}`。
+
+解决方案是直接遍历数组，每个位置先求出 `query(a[i])`，然后再修改树状数组 `update(a[i], 1)` 即可。当数的范围比较大时，需要进行离散化，即先进行去重并排序，然后对每个数字进行编号。
+
 <!-- 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 StreamRank:
+
+    def __init__(self):
+        self.tree = BinaryIndexedTree(50010)
+
+    def track(self, x: int) -> None:
+        self.tree.update(x + 1, 1)
+
+    def getRankOfNumber(self, x: int) -> int:
+        return self.tree.query(x + 1)
+
+
+# Your StreamRank object will be instantiated and called as such:
+# obj = StreamRank()
+# obj.track(x)
+# param_2 = obj.getRankOfNumber(x)
 ```
 
 ### **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 static int lowbit(int x) {
+        return x & -x;
+    }
+
+    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;
+    }
+}
+
+class StreamRank {
+    private BinaryIndexedTree tree;
+
+    public StreamRank() {
+        tree = new BinaryIndexedTree(50010);
+    }
+    
+    public void track(int x) {
+        tree.update(x + 1, 1);
+    }
+    
+    public int getRankOfNumber(int x) {
+        return tree.query(x + 1);
+    }
+}
+
+/**
+ * Your StreamRank object will be instantiated and called as such:
+ * StreamRank obj = new StreamRank();
+ * obj.track(x);
+ * int param_2 = obj.getRankOfNumber(x);
+ */
+```
+
+### **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 StreamRank {
+public:
+    BinaryIndexedTree* tree;
+
+    StreamRank() {
+        tree = new BinaryIndexedTree(50010);
+    }
+    
+    void track(int x) {
+        tree->update(x + 1, 1);
+    }
+    
+    int getRankOfNumber(int x) {
+        return tree->query(x + 1);
+    }
+};
+
+/**
+ * Your StreamRank object will be instantiated and called as such:
+ * StreamRank* obj = new StreamRank();
+ * obj->track(x);
+ * int param_2 = obj->getRankOfNumber(x);
+ */
+```
+
+### **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 StreamRank struct {
+	tree *BinaryIndexedTree
+}
+
+func Constructor() StreamRank {
+	tree := newBinaryIndexedTree(50010)
+	return StreamRank{tree}
+}
+
+func (this *StreamRank) Track(x int) {
+	this.tree.update(x+1, 1)
+}
+
+func (this *StreamRank) GetRankOfNumber(x int) int {
+	return this.tree.query(x + 1)
+}
 
+/**
+ * Your StreamRank object will be instantiated and called as such:
+ * obj := Constructor();
+ * obj.Track(x);
+ * param_2 := obj.GetRankOfNumber(x);
+ */
 ```
 
 ### **...**