feat: add solutions to lc problem: No.1649

No.1649.Create Sorted Array through Instructions

Author: yanglbme

solution/1600-1699/1649.Create Sorted Array through Instructions/README.md

@@ -74,22 +74,222 @@
 
 <!-- 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 Solution:
+    def createSortedArray(self, instructions: List[int]) -> int:
+        n = max(instructions)
+        tree = BinaryIndexedTree(n)
+        ans = 0
+        for num in instructions:
+            a = tree.query(num - 1)
+            b = tree.query(n) - tree.query(num)
+            ans += min(a, b)
+            tree.update(num, 1)
+        return ans % int((1e9 + 7))
 ```
 
 ### **Java**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
 ```java
+class Solution {
+    public int createSortedArray(int[] instructions) {
+        int n = 100010;
+        int mod = (int) 1e9 + 7;
+        BinaryIndexedTree tree = new BinaryIndexedTree(n);
+        int ans = 0;
+        for (int num : instructions) {
+            int a = tree.query(num - 1);
+            int b = tree.query(n) - tree.query(num);
+            ans += Math.min(a, b);
+            ans %= mod;
+            tree.update(num, 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++**
+
+```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:
+    int createSortedArray(vector<int>& instructions) {
+        int n = 100010;
+        int mod = 1e9 + 7;
+        BinaryIndexedTree* tree = new BinaryIndexedTree(n);
+        int ans = 0;
+        for (int num : instructions)
+        {
+            int a = tree->query(num - 1);
+            int b = tree->query(n) - tree->query(num);
+            ans += min(a, b);
+            ans %= mod;
+            tree->update(num, 1);
+        }
+        return ans;
+    }
+};
+```
 
+### **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
+}
+
+func createSortedArray(instructions []int) int {
+	n := 100010
+	mod := int(1e9 + 7)
+	tree := newBinaryIndexedTree(n)
+	ans := 0
+	for _, num := range instructions {
+		a, b := tree.query(num-1), tree.query(n)-tree.query(num)
+		ans += min(a, b)
+		ans %= mod
+		tree.update(num, 1)
+	}
+	return ans
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
 ```
 
 ### **...**