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Mar 31, 2023
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Original file line number Diff line number Diff line change
Expand Up @@ -55,22 +55,115 @@

<!-- 这里可写通用的实现逻辑 -->

**方法一:二分查找**

我们设计一个函数 $missing(i)$,表示 $nums[i]$ 与 $nums[0]$ 之间缺失的元素个数。那么 $missing(i)$ 就等于 $nums[i] - nums[0] - i$。我们可以通过二分查找找到最小的 $i$,使得 $missing(i) \geq k$,那么 $nums[i - 1] + k - missing(i - 1)$ 就是第 $k$ 个缺失的元素。

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

<!-- tabs:start -->

### **Python3**

<!-- 这里可写当前语言的特殊实现逻辑 -->

```python

class Solution:
def missingElement(self, nums: List[int], k: int) -> int:
def missing(i: int) -> int:
return nums[i] - nums[0] - i

n = len(nums)
if k > missing(n - 1):
return nums[n - 1] + k - missing(n - 1)
l, r = 0, n - 1
while l < r:
mid = (l + r) >> 1
if missing(mid) >= k:
r = mid
else:
l = mid + 1
return nums[l - 1] + k - missing(l - 1)
```

### **Java**

<!-- 这里可写当前语言的特殊实现逻辑 -->

```java
class Solution {
public int missingElement(int[] nums, int k) {
int n = nums.length;
if (k > missing(nums, n - 1)) {
return nums[n - 1] + k - missing(nums, n - 1);
}
int l = 0, r = n - 1;
while (l < r) {
int mid = (l + r) >> 1;
if (missing(nums, mid) >= k) {
r = mid;
} else {
l = mid + 1;
}
}
return nums[l - 1] + k - missing(nums, l - 1);
}

private int missing(int[] nums, int i) {
return nums[i] - nums[0] - i;
}
}
```

### **C++**

```cpp
class Solution {
public:
int missingElement(vector<int>& nums, int k) {
auto missing = [&](int i) {
return nums[i] - nums[0] - i;
};
int n = nums.size();
if (k > missing(n - 1)) {
return nums[n - 1] + k - missing(n - 1);
}
int l = 0, r = n - 1;
while (l < r) {
int mid = (l + r) >> 1;
if (missing(mid) >= k) {
r = mid;
} else {
l = mid + 1;
}
}
return nums[l - 1] + k - missing(l - 1);
}
};
```

### **Go**

```go
func missingElement(nums []int, k int) int {
missing := func(i int) int {
return nums[i] - nums[0] - i
}
n := len(nums)
if k > missing(n-1) {
return nums[n-1] + k - missing(n-1)
}
l, r := 0, n-1
for l < r {
mid := (l + r) >> 1
if missing(mid) >= k {
r = mid
} else {
l = mid + 1
}
}
return nums[l-1] + k - missing(l-1)
}
```

### **...**
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -51,13 +51,100 @@
### **Python3**

```python

class Solution:
def missingElement(self, nums: List[int], k: int) -> int:
def missing(i: int) -> int:
return nums[i] - nums[0] - i

n = len(nums)
if k > missing(n - 1):
return nums[n - 1] + k - missing(n - 1)
l, r = 0, n - 1
while l < r:
mid = (l + r) >> 1
if missing(mid) >= k:
r = mid
else:
l = mid + 1
return nums[l - 1] + k - missing(l - 1)
```

### **Java**

```java
class Solution {
public int missingElement(int[] nums, int k) {
int n = nums.length;
if (k > missing(nums, n - 1)) {
return nums[n - 1] + k - missing(nums, n - 1);
}
int l = 0, r = n - 1;
while (l < r) {
int mid = (l + r) >> 1;
if (missing(nums, mid) >= k) {
r = mid;
} else {
l = mid + 1;
}
}
return nums[l - 1] + k - missing(nums, l - 1);
}

private int missing(int[] nums, int i) {
return nums[i] - nums[0] - i;
}
}
```

### **C++**

```cpp
class Solution {
public:
int missingElement(vector<int>& nums, int k) {
auto missing = [&](int i) {
return nums[i] - nums[0] - i;
};
int n = nums.size();
if (k > missing(n - 1)) {
return nums[n - 1] + k - missing(n - 1);
}
int l = 0, r = n - 1;
while (l < r) {
int mid = (l + r) >> 1;
if (missing(mid) >= k) {
r = mid;
} else {
l = mid + 1;
}
}
return nums[l - 1] + k - missing(l - 1);
}
};
```

### **Go**

```go
func missingElement(nums []int, k int) int {
missing := func(i int) int {
return nums[i] - nums[0] - i
}
n := len(nums)
if k > missing(n-1) {
return nums[n-1] + k - missing(n-1)
}
l, r := 0, n-1
for l < r {
mid := (l + r) >> 1
if missing(mid) >= k {
r = mid
} else {
l = mid + 1
}
}
return nums[l-1] + k - missing(l-1)
}
```

### **...**
Expand Down
Original file line number Diff line number Diff line change
@@ -0,0 +1,22 @@
class Solution {
public:
int missingElement(vector<int>& nums, int k) {
auto missing = [&](int i) {
return nums[i] - nums[0] - i;
};
int n = nums.size();
if (k > missing(n - 1)) {
return nums[n - 1] + k - missing(n - 1);
}
int l = 0, r = n - 1;
while (l < r) {
int mid = (l + r) >> 1;
if (missing(mid) >= k) {
r = mid;
} else {
l = mid + 1;
}
}
return nums[l - 1] + k - missing(l - 1);
}
};
Original file line number Diff line number Diff line change
@@ -0,0 +1,19 @@
func missingElement(nums []int, k int) int {
missing := func(i int) int {
return nums[i] - nums[0] - i
}
n := len(nums)
if k > missing(n-1) {
return nums[n-1] + k - missing(n-1)
}
l, r := 0, n-1
for l < r {
mid := (l + r) >> 1
if missing(mid) >= k {
r = mid
} else {
l = mid + 1
}
}
return nums[l-1] + k - missing(l-1)
}
Original file line number Diff line number Diff line change
@@ -0,0 +1,22 @@
class Solution {
public int missingElement(int[] nums, int k) {
int n = nums.length;
if (k > missing(nums, n - 1)) {
return nums[n - 1] + k - missing(nums, n - 1);
}
int l = 0, r = n - 1;
while (l < r) {
int mid = (l + r) >> 1;
if (missing(nums, mid) >= k) {
r = mid;
} else {
l = mid + 1;
}
}
return nums[l - 1] + k - missing(nums, l - 1);
}

private int missing(int[] nums, int i) {
return nums[i] - nums[0] - i;
}
}
Original file line number Diff line number Diff line change
@@ -0,0 +1,16 @@
class Solution:
def missingElement(self, nums: List[int], k: int) -> int:
def missing(i: int) -> int:
return nums[i] - nums[0] - i

n = len(nums)
if k > missing(n - 1):
return nums[n - 1] + k - missing(n - 1)
l, r = 0, n - 1
while l < r:
mid = (l + r) >> 1
if missing(mid) >= k:
r = mid
else:
l = mid + 1
return nums[l - 1] + k - missing(l - 1)
Original file line number Diff line number Diff line change
Expand Up @@ -112,6 +112,24 @@ var findSpecialInteger = function (arr) {
};
```

### **PHP**

```php
class Solution {
/**
* @param Integer[] $arr
* @return Integer
*/
function findSpecialInteger($arr) {
$len = count($arr);
for ($i = 0; $i < $len; $i++) {
if ($arr[$i] == $arr[$i + ($len >> 2)]) return $arr[$i];
}
return -1;
}
}
```

### **...**

```
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -107,6 +107,24 @@ var findSpecialInteger = function (arr) {
};
```

### **PHP**

```php
class Solution {
/**
* @param Integer[] $arr
* @return Integer
*/
function findSpecialInteger($arr) {
$len = count($arr);
for ($i = 0; $i < $len; $i++) {
if ($arr[$i] == $arr[$i + ($len >> 2)]) return $arr[$i];
}
return -1;
}
}
```

### **...**

```
Expand Down
Original file line number Diff line number Diff line change
@@ -0,0 +1,13 @@
class Solution {
/**
* @param Integer[] $arr
* @return Integer
*/
function findSpecialInteger($arr) {
$len = count($arr);
for ($i = 0; $i < $len; $i++) {
if ($arr[$i] == $arr[$i + ($len >> 2)]) return $arr[$i];
}
return -1;
}
}
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