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feat: add solutions to lc/lcci problems #1660

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Sep 22, 2023
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feat: add solutions to lc/lcci problems #1660

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165 changes: 164 additions & 1 deletion lcci/10.03.Search Rotate Array/README.md
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Expand Up @@ -5,6 +5,7 @@
## 题目描述

<!-- 这里写题目描述 -->

<p>搜索旋转数组。给定一个排序后的数组，包含n个整数，但这个数组已被旋转过很多次了，次数不详。请编写代码找出数组中的某个元素，假设数组元素原先是按升序排列的。若有多个相同元素，返回索引值最小的一个。</p>
<p><strong>示例1:</strong></p>
<pre><strong> 输入</strong>: arr = [15, 16, 19, 20, 25, 1, 3, 4, 5, 7, 10, 14], target = 5
Expand All @@ -22,22 +23,184 @@
## 解法

<!-- 这里可写通用的实现逻辑 -->

**方法一：二分查找**

我们定义二分查找的左边界 $l=0$，右边界 $r=n-1$，其中 $n$ 为数组的长度。

每次在二分查找的过程中，我们会得到当前的中点 $mid=(l+r)/2$。

- 如果 $nums[mid] \gt nums[r]$，说明 $[l,mid]$ 是有序的，此时如果 $nums[l] \le target \le nums[mid]$，说明 $target$ 位于 $[l,mid]$，否则 $target$ 位于 $[mid+1,r]$。
- 如果 $nums[mid] \lt nums[r]$，说明 $[mid+1,r]$ 是有序的，此时如果 $nums[mid] \lt target \le nums[r]$，说明 $target$ 位于 $[mid+1,r]$，否则 $target$ 位于 $[l,mid]$。
- 如果 $nums[mid] = nums[r]$，说明元素 $nums[mid]$ 和 $nums[r]$ 相等，此时无法判断 $target$ 位于哪个区间，我们只能将 $r$ 减少 $1$。

二分查找结束后，如果 $nums[l] = target$，则说明数组中存在目标值 $target$，否则说明不存在。

注意，如果一开始 $nums[l] = nums[r]$，我们循环将 $r$ 减少 $1$，直到 $nums[l] \ne nums[r]$。

时间复杂度近似 $O(\log n)$，空间复杂度 $O(1)$。其中 $n$ 为数组的长度。

相似题目：

- [81. 搜索旋转排序数组 II](/solution/0000-0099/0081.Search%20in%20Rotated%20Sorted%20Array%20II/README.md)

<!-- tabs:start -->

### **Python3**

<!-- 这里可写当前语言的特殊实现逻辑 -->

```python

class Solution:
def search(self, arr: List[int], target: int) -> int:
l, r = 0, len(arr) - 1
while arr[l] == arr[r]:
r -= 1
while l < r:
mid = (l + r) >> 1
if arr[mid] > arr[r]:
if arr[l] <= target <= arr[mid]:
r = mid
else:
l = mid + 1
elif arr[mid] < arr[r]:
if arr[mid] < target <= arr[r]:
l = mid + 1
else:
r = mid
else:
r -= 1
return l if arr[l] == target else -1
```

### **Java**

<!-- 这里可写当前语言的特殊实现逻辑 -->

```java
class Solution {
public int search(int[] arr, int target) {
int l = 0, r = arr.length - 1;
while (arr[l] == arr[r]) {
--r;
}
while (l < r) {
int mid = (l + r) >> 1;
if (arr[mid] > arr[r]) {
if (arr[l] <= target && target <= arr[mid]) {
r = mid;
} else {
l = mid + 1;
}
} else if (arr[mid] < arr[r]) {
if (arr[mid] < target && target <= arr[r]) {
l = mid + 1;
} else {
r = mid;
}
} else {
--r;
}
}
return arr[l] == target ? l : -1;
}
}
```

### **C++**

```cpp
class Solution {
public:
int search(vector<int>& arr, int target) {
int l = 0, r = arr.size() - 1;
while (arr[l] == arr[r]) {
--r;
}
while (l < r) {
int mid = (l + r) >> 1;
if (arr[mid] > arr[r]) {
if (arr[l] <= target && target <= arr[mid]) {
r = mid;
} else {
l = mid + 1;
}
} else if (arr[mid] < arr[r]) {
if (arr[mid] < target && target <= arr[r]) {
l = mid + 1;
} else {
r = mid;
}
} else {
--r;
}
}
return arr[l] == target ? l : -1;
}
};
```

### **Go**

```go
func search(arr []int, target int) int {
l, r := 0, len(arr)-1
for arr[l] == arr[r] {
r--
}
for l < r {
mid := (l + r) >> 1
if arr[mid] > arr[r] {
if arr[l] <= target && target <= arr[mid] {
r = mid
} else {
l = mid + 1
}
} else if arr[mid] < arr[r] {
if arr[mid] < target && target <= arr[r] {
l = mid + 1
} else {
r = mid
}
} else {
r--
}
}
if arr[l] == target {
return l
}
return -1
}
```

### **TypeScript**

```ts
function search(arr: number[], target: number): number {
let [l, r] = [0, arr.length - 1];
while (arr[l] === arr[r]) {
--r;
}
while (l < r) {
const mid = (l + r) >> 1;
if (arr[mid] > arr[r]) {
if (arr[l] <= target && target <= arr[mid]) {
r = mid;
} else {
l = mid + 1;
}
} else if (arr[mid] < arr[r]) {
if (arr[mid] < target && target <= arr[r]) {
l = mid + 1;
} else {
r = mid;
}
} else {
--r;
}
}
return arr[l] === target ? l : -1;
}
```

### **...**
Expand Down
143 changes: 142 additions & 1 deletion lcci/10.03.Search Rotate Array/README_EN.md
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Expand Up @@ -33,13 +33,154 @@
### **Python3**

```python

class Solution:
def search(self, arr: List[int], target: int) -> int:
l, r = 0, len(arr) - 1
while arr[l] == arr[r]:
r -= 1
while l < r:
mid = (l + r) >> 1
if arr[mid] > arr[r]:
if arr[l] <= target <= arr[mid]:
r = mid
else:
l = mid + 1
elif arr[mid] < arr[r]:
if arr[mid] < target <= arr[r]:
l = mid + 1
else:
r = mid
else:
r -= 1
return l if arr[l] == target else -1
```

### **Java**

```java
class Solution {
public int search(int[] arr, int target) {
int l = 0, r = arr.length - 1;
while (arr[l] == arr[r]) {
--r;
}
while (l < r) {
int mid = (l + r) >> 1;
if (arr[mid] > arr[r]) {
if (arr[l] <= target && target <= arr[mid]) {
r = mid;
} else {
l = mid + 1;
}
} else if (arr[mid] < arr[r]) {
if (arr[mid] < target && target <= arr[r]) {
l = mid + 1;
} else {
r = mid;
}
} else {
--r;
}
}
return arr[l] == target ? l : -1;
}
}
```

### **C++**

```cpp
class Solution {
public:
int search(vector<int>& arr, int target) {
int l = 0, r = arr.size() - 1;
while (arr[l] == arr[r]) {
--r;
}
while (l < r) {
int mid = (l + r) >> 1;
if (arr[mid] > arr[r]) {
if (arr[l] <= target && target <= arr[mid]) {
r = mid;
} else {
l = mid + 1;
}
} else if (arr[mid] < arr[r]) {
if (arr[mid] < target && target <= arr[r]) {
l = mid + 1;
} else {
r = mid;
}
} else {
--r;
}
}
return arr[l] == target ? l : -1;
}
};
```

### **Go**

```go
func search(arr []int, target int) int {
l, r := 0, len(arr)-1
for arr[l] == arr[r] {
r--
}
for l < r {
mid := (l + r) >> 1
if arr[mid] > arr[r] {
if arr[l] <= target && target <= arr[mid] {
r = mid
} else {
l = mid + 1
}
} else if arr[mid] < arr[r] {
if arr[mid] < target && target <= arr[r] {
l = mid + 1
} else {
r = mid
}
} else {
r--
}
}
if arr[l] == target {
return l
}
return -1
}
```

### **TypeScript**

```ts
function search(arr: number[], target: number): number {
let [l, r] = [0, arr.length - 1];
while (arr[l] === arr[r]) {
--r;
}
while (l < r) {
const mid = (l + r) >> 1;
if (arr[mid] > arr[r]) {
if (arr[l] <= target && target <= arr[mid]) {
r = mid;
} else {
l = mid + 1;
}
} else if (arr[mid] < arr[r]) {
if (arr[mid] < target && target <= arr[r]) {
l = mid + 1;
} else {
r = mid;
}
} else {
--r;
}
}
return arr[l] === target ? l : -1;
}
```

### **...**
Expand Down
28 changes: 28 additions & 0 deletions lcci/10.03.Search Rotate Array/Solution.cpp
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Original file line number Diff line number Diff line change
@@ -0,0 +1,28 @@
class Solution {
public:
int search(vector<int>& arr, int target) {
int l = 0, r = arr.size() - 1;
while (arr[l] == arr[r]) {
--r;
}
while (l < r) {
int mid = (l + r) >> 1;
if (arr[mid] > arr[r]) {
if (arr[l] <= target && target <= arr[mid]) {
r = mid;
} else {
l = mid + 1;
}
} else if (arr[mid] < arr[r]) {
if (arr[mid] < target && target <= arr[r]) {
l = mid + 1;
} else {
r = mid;
}
} else {
--r;
}
}
return arr[l] == target ? l : -1;
}
};
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