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feat: add solutions to lcof problem: No.11
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‎lcof/面试题11. 旋转数组的最小数字/README.md

Lines changed: 211 additions & 45 deletions
Original file line numberDiff line numberDiff line change
@@ -24,6 +24,22 @@
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## 解法
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**方法一：二分查找**
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二分查找的变种，需要考虑重复元素的情况。
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我们定义两个指针 $l$ 和 $r$ 分别指向数组的左右两端，每次取中间元素 `numbers[mid]` 与右端元素 `numbers[r]` 比较，有以下三种情况：
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- `numbers[mid] > numbers[r]`：中间元素一定不是最小值，因此 $l = mid + 1$；
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- `numbers[mid] < numbers[r]`：中间元素可能是最小值，因此 $r = mid$；
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- `numbers[mid] == numbers[r]`：中间元素一定不是最小值，因此 $r = r - 1$。
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循环结束时，指针 $l$ 和 $r$ 指向同一个元素，即为最小值。
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时间复杂度 $(\log n)$，空间复杂度 $O(1)$。其中 $n$ 为数组长度。
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注意，我们也可以每次取中间元素 `numbers[mid]` 与左端元素 `numbers[l]` 比较，但需要考虑当前 $[l,..r]$ 区间内的元素是否已经有序，即是否满足 `numbers[l] < numbers[r]`，如果满足，直接返回 `numbers[l]` 即可。其它情况与上述方法类似。
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<!-- tabs:start -->
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### **Python3**
@@ -43,6 +59,23 @@ class Solution:
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return numbers[l]
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```
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```python
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class Solution:
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def minArray(self, numbers: List[int]) -> int:
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l, r = 0, len(numbers) - 1
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while l < r:
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if numbers[l] < numbers[r]:
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return numbers[l]
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mid = (l + r) >> 1
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if numbers[mid] > numbers[l]:
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l = mid + 1
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elif numbers[mid] < numbers[l]:
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r = mid
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else:
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l += 1
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return numbers[l]
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```
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### **Java**
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```java
@@ -64,6 +97,112 @@ class Solution {
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}
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```
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```java
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class Solution {
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public int minArray(int[] numbers) {
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int l = 0, r = numbers.length - 1;
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while (l < r) {
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if (numbers[l] < numbers[r]) {
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break;
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}
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int m = (l + r) >>> 1;
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if (numbers[m] > numbers[l]) {
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l = m + 1;
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} else if (numbers[m] < numbers[l]) {
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r = m;
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} else {
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++l;
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}
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}
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return numbers[l];
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int minArray(vector<int>& numbers) {
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int l = 0, r = numbers.size() - 1;
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while (l < r) {
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int mid = (l + r) >> 1;
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if (numbers[mid] > numbers[r]) {
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l = mid + 1;
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} else if (numbers[mid] < numbers[r]) {
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r = mid;
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} else {
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--r;
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}
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}
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return numbers[l];
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}
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};
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```
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```cpp
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class Solution {
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public:
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int minArray(vector<int>& numbers) {
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int l = 0, r = numbers.size() - 1;
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while (l < r) {
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if (numbers[l] < numbers[r]) {
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break;
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}
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int mid = (l + r) >> 1;
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if (numbers[mid] > numbers[l]) {
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l = mid + 1;
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} else if (numbers[mid] < numbers[l]) {
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r = mid;
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} else {
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++l;
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}
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}
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return numbers[l];
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}
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};
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```
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### **Go**
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```go
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func minArray(numbers []int) int {
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l, r := 0, len(numbers)-1
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for l < r {
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mid := (l + r) >> 1
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if numbers[mid] > numbers[r] {
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l = mid + 1
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} else if numbers[mid] < numbers[r] {
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r = mid
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} else {
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r--
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}
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}
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return numbers[l]
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}
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```
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```go
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func minArray(numbers []int) int {
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l, r := 0, len(numbers)-1
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for l < r {
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if numbers[l] < numbers[r] {
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break
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}
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mid := (l + r) >> 1
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if numbers[mid] > numbers[l] {
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l = mid + 1
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} else if numbers[mid] < numbers[l] {
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r = mid
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} else {
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l++
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}
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}
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return numbers[l]
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}
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```
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### **JavaScript**
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```js
@@ -88,44 +227,28 @@ var minArray = function (numbers) {
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};
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```
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91-
### **Go**
92-
93-
```go
94-
func minArray(nums []int) int {
95-
l, r := 0, len(nums)-1
96-
for l < r {
97-
mid := l + (r-l)>>1
98-
if nums[mid] > nums[r] {
99-
l = mid + 1
100-
} else if nums[mid] < nums[r] {
101-
r = mid // r 本身不需要被排除
102-
} else {
103-
r--
104-
}
105-
}
106-
return nums[l]
107-
}
108-
```
109-
110-
### **C++**
111-
112-
```cpp
113-
class Solution {
114-
public:
115-
int minArray(vector<int>& numbers) {
116-
int left = 0, right = numbers.size() - 1;
117-
while (left + 1 < right) {
118-
int mid = left + (right - left) / 2;
119-
if (numbers[mid] > numbers[right]) {
120-
left = mid;
121-
} else if (numbers[mid] < numbers[right]) {
122-
right = mid;
123-
} else {
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--right;
125-
}
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```js
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/**
232+
* @param {number[]} numbers
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* @return {number}
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*/
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var minArray = function (numbers) {
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let l = 0,
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r = numbers.length - 1;
238+
while (l < r) {
239+
if (numbers[l] < numbers[r]) {
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break;
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}
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let m = (l + r) >>> 1;
243+
if (numbers[m] > numbers[l]) {
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l = m + 1;
245+
} else if (numbers[m] < numbers[l]) {
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r = m;
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} else {
248+
++l;
126249
}
127-
return min(numbers[left], numbers[right]);
128250
}
251+
return numbers[l];
129252
};
130253
```
131254

@@ -149,23 +272,66 @@ impl Solution {
149272
}
150273
```
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275+
```rust
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impl Solution {
277+
pub fn min_array(numbers: Vec<i32>) -> i32 {
278+
let mut l = 0;
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let mut r = numbers.len() - 1;
280+
while l < r {
281+
if numbers[l] < numbers[r] {
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break;
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}
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let mid = l + r >> 1;
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match numbers[mid].cmp(&numbers[l]) {
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std::cmp::Ordering::Less => r = mid,
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std::cmp::Ordering::Equal => l += 1,
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std::cmp::Ordering::Greater => l = mid + 1,
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}
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}
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numbers[l]
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}
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}
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```
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### **C#**
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154298
```cs
155299
public class Solution {
156300
public int MinArray(int[] numbers) {
157-
int left = 0, right = numbers.Length - 1, mid;
158-
while (left < right) {
159-
mid = (left + right) / 2;
160-
if (numbers[mid] > numbers[right]) {
161-
left = mid + 1;
162-
} else if (numbers[mid] < numbers[right]) {
163-
right = mid;
301+
int l = 0, r = numbers.Length - 1;
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while (l < r) {
303+
int m = (l + r) >> 1;
304+
if (numbers[m] > numbers[r]) {
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l = m + 1;
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} else if (numbers[m] < numbers[r]) {
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r = m;
164308
} else {
165-
right -= 1;
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--r;
166310
}
167311
}
168-
return numbers[left];
312+
return numbers[l];
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}
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}
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```
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```cs
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public class Solution {
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public int MinArray(int[] numbers) {
320+
int l = 0, r = numbers.Length - 1;
321+
while (l < r) {
322+
if (numbers[l] < numbers[r]) {
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break;
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}
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int m = (l + r) >> 1;
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if (numbers[m] > numbers[l]) {
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l = m + 1;
328+
} else if (numbers[m] < numbers[l]) {
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r = m;
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} else {
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++l;
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}
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}
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return numbers[l];
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}
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}
171337
```

‎lcof/面试题11. 旋转数组的最小数字/Solution.cpp

Lines changed: 10 additions & 10 deletions
Original file line numberDiff line numberDiff line change
@@ -1,17 +1,17 @@
11
class Solution {
22
public:
33
int minArray(vector<int>& numbers) {
4-
int left = 0, right = numbers.size() - 1;
5-
while (left + 1 < right) {
6-
int mid = left + (right - left) / 2;
7-
if (numbers[mid] > numbers[right]) {
8-
left = mid;
9-
} else if (numbers[mid] < numbers[right]) {
10-
right = mid;
4+
int l = 0, r = numbers.size() - 1;
5+
while (l < r) {
6+
int mid = (l + r) >> 1;
7+
if (numbers[mid] > numbers[r]) {
8+
l = mid + 1;
9+
} else if (numbers[mid] < numbers[r]) {
10+
r = mid;
1111
} else {
12-
--right;
12+
--r;
1313
}
1414
}
15-
return min(numbers[left], numbers[right]);
15+
return numbers[l];
1616
}
17-
};
17+
};

‎lcof/面试题11. 旋转数组的最小数字/Solution.cs

Lines changed: 9 additions & 9 deletions
Original file line numberDiff line numberDiff line change
@@ -1,16 +1,16 @@
11
public class Solution {
22
public int MinArray(int[] numbers) {
3-
int left = 0, right = numbers.Length - 1, mid;
4-
while (left < right) {
5-
mid = (left + right) / 2;
6-
if (numbers[mid] > numbers[right]) {
7-
left = mid + 1;
8-
} else if (numbers[mid] < numbers[right]) {
9-
right = mid;
3+
int l = 0, r = numbers.Length - 1;
4+
while (l < r) {
5+
int m = (l + r) >> 1;
6+
if (numbers[m] > numbers[r]) {
7+
l = m + 1;
8+
} else if (numbers[m] < numbers[r]) {
9+
r = m;
1010
} else {
11-
right -= 1;
11+
--r;
1212
}
1313
}
14-
return numbers[left];
14+
return numbers[l];
1515
}
1616
}

‎lcof/面试题11. 旋转数组的最小数字/Solution.go

Lines changed: 7 additions & 7 deletions
Original file line numberDiff line numberDiff line change
@@ -1,14 +1,14 @@
1-
func minArray(nums []int) int {
2-
l, r := 0, len(nums)-1
1+
func minArray(numbers []int) int {
2+
l, r := 0, len(numbers)-1
33
for l < r {
4-
mid := l + (r-l)>>1
5-
if nums[mid] > nums[r] {
4+
mid := (l + r) >> 1
5+
if numbers[mid] > numbers[r] {
66
l = mid + 1
7-
} else if nums[mid] < nums[r] {
8-
r = mid // r 本身不需要被排除
7+
} else if numbers[mid] < numbers[r] {
8+
r = mid
99
} else {
1010
r--
1111
}
1212
}
13-
return nums[l]
13+
return numbers[l]
1414
}

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