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Mar 27, 2023
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[pull] main from doocs:main #500

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252 changes: 202 additions & 50 deletions solution/0800-0899/0845.Longest Mountain in Array/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -60,6 +60,18 @@

<!-- 这里可写通用的实现逻辑 -->

**方法一：预处理 + 枚举**

我们定义两个数组 $f$ 和 $g$，其中 $f[i]$ 表示以 $arr[i]$ 结尾的最长上升子序列的长度，而 $g[i]$ 表示以 $arr[i]$ 开头的最长下降子序列的长度。那么对于每个下标 $i$，如果 $f[i] \gt 1$ 且 $g[i] \gt 1$，那么以 $arr[i]$ 为山顶的山脉的长度为 $f[i] + g[i] - 1$，我们只需要枚举所有的 $i$，找出最大的那个值即可。

时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 为数组 $arr$ 的长度。

**方法二：一次遍历（枚举左侧山脚）**

我们可以枚举山脉的左侧山脚，然后向右寻找山脉的右侧山脚。我们可以使用两个指针 $l$ 和 $r$，其中 $l$ 表示左侧山脚的下标，$r$ 表示右侧山脚的下标，初始时 $l=0$,$r=0$，然后我们向右移动 $r$，找到山顶的位置，此时判断 $r$ 是否满足 $r + 1 \lt n$ 并且 $arr[r] \gt arr[r + 1]$，如果满足，我们向右继续移动 $r$，直到找到右侧山脚的位置，此时山脉的长度为 $r - l + 1$，我们更新答案，然后将 $l$ 的值更新为 $r$，继续寻找下一个山脉。

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

<!-- tabs:start -->

### **Python3**
Expand All @@ -69,32 +81,38 @@
```python
class Solution:
def longestMountain(self, arr: List[int]) -> int:
left, right = 0, 1
status = -1
n = len(arr)
f = [1] * n
g = [1] * n
for i in range(1, n):
if arr[i] > arr[i - 1]:
f[i] = f[i - 1] + 1
ans = 0
while right < len(arr):
if status == -1 or status == 1:
if arr[right] == arr[right - 1]:
status = -1
if status == -1:
if arr[right] > arr[right - 1]:
status = 1
else:
left = right
if status == 1 and arr[right] < arr[right - 1]:
status = 2
else:
if arr[right] == arr[right - 1]:
status = -1
ans = max(ans, right - left)
left = right
elif arr[right] > arr[right - 1]:
status = 1
ans = max(ans, right - left)
left = right - 1
right += 1
if status == 2:
ans = max(right - left, ans)
for i in range(n - 2, -1, -1):
if arr[i] > arr[i + 1]:
g[i] = g[i + 1] + 1
if f[i] > 1:
ans = max(ans, f[i] + g[i] - 1)
return ans
```

```python
class Solution:
def longestMountain(self, arr: List[int]) -> int:
n = len(arr)
ans = l = 0
while l + 2 < n:
r = l + 1
if arr[l] < arr[r]:
while r + 1 < n and arr[r] < arr[r + 1]:
r += 1
if r < n - 1 and arr[r] > arr[r + 1]:
while r < n - 1 and arr[r] > arr[r + 1]:
r += 1
ans = max(ans, r - l + 1)
else:
r += 1
l = r
return ans
```

Expand All @@ -105,41 +123,175 @@ class Solution:
```java
class Solution {
public int longestMountain(int[] arr) {
int left = 0, right = 0;
int n = arr.length;
int[] f = new int[n];
int[] g = new int[n];
Arrays.fill(f, 1);
Arrays.fill(g, 1);
for (int i = 1; i < n; ++i) {
if (arr[i] > arr[i - 1]) {
f[i] = f[i - 1] + 1;
}
}
int ans = 0;
int status = -1;
while (++right < arr.length) {
if (status == -1 || status == 1) {
if (arr[right] == arr[right - 1]) {
status = -1;
for (int i = n - 2; i >= 0; --i) {
if (arr[i] > arr[i + 1]) {
g[i] = g[i + 1] + 1;
if (f[i] > 1) {
ans = Math.max(ans, f[i] + g[i] - 1);
}
if (status == -1) {
if (arr[right] > arr[right - 1]) {
status = 1;
} else {
left = right;
}
}
}
return ans;
}
}
```

```java
class Solution {
public int longestMountain(int[] arr) {
int n = arr.length;
int ans = 0;
for (int l = 0, r = 0; l + 2 < n; l = r) {
r = l + 1;
if (arr[l] < arr[r]) {
while (r + 1 < n && arr[r] < arr[r + 1]) {
++r;
}
if (status == 1 && arr[right] < arr[right - 1]) {
status = 2;
if (r + 1 < n && arr[r] > arr[r + 1]) {
while (r + 1 < n && arr[r] > arr[r + 1]) {
++r;
}
ans = Math.max(ans, r - l + 1);
} else {
++r;
}
} else {
if (arr[right] > arr[right - 1]) {
status = 1;
ans = Math.max(right - left, ans);
left = right - 1;
} else if (arr[right] == arr[right - 1]) {
status = -1;
ans = Math.max(right - left, ans);
left = right;
}
}
return ans;
}
}
```

### **C++**

```cpp
class Solution {
public:
int longestMountain(vector<int>& arr) {
int n = arr.size();
int f[n];
int g[n];
fill(f, f + n, 1);
fill(g, g + n, 1);
for (int i = 1; i < n; ++i) {
if (arr[i] > arr[i - 1]) {
f[i] = f[i - 1] + 1;
}
}
int ans = 0;
for (int i = n - 2; ~i; --i) {
if (arr[i] > arr[i + 1]) {
g[i] = g[i + 1] + 1;
if (f[i] > 1) {
ans = max(ans, f[i] + g[i] - 1);
}
}
}
if (status == 2) {
ans = Math.max(ans, right - left);
return ans;
}
};
```

```cpp
class Solution {
public:
int longestMountain(vector<int>& arr) {
int n = arr.size();
int ans = 0;
for (int l = 0, r = 0; l + 2 < n; l = r) {
r = l + 1;
if (arr[l] < arr[r]) {
while (r + 1 < n && arr[r] < arr[r + 1]) {
++r;
}
if (r + 1 < n && arr[r] > arr[r + 1]) {
while (r + 1 < n && arr[r] > arr[r + 1]) {
++r;
}
ans = max(ans, r - l + 1);
} else {
++r;
}
}
}
return ans;
}
};
```

### **Go**

```go
func longestMountain(arr []int) (ans int) {
n := len(arr)
f := make([]int, n)
g := make([]int, n)
for i := range f {
f[i] = 1
g[i] = 1
}
for i := 1; i < n; i++ {
if arr[i] > arr[i-1] {
f[i] = f[i-1] + 1
}
}
for i := n - 2; i >= 0; i-- {
if arr[i] > arr[i+1] {
g[i] = g[i+1] + 1
if f[i] > 1 {
ans = max(ans, f[i]+g[i]-1)
}
}
}
return
}

func max(a, b int) int {
if a > b {
return a
}
return b
}
```

```go
func longestMountain(arr []int) (ans int) {
n := len(arr)
for l, r := 0, 0; l+2 < n; l = r {
r = l + 1
if arr[l] < arr[r] {
for r+1 < n && arr[r] < arr[r+1] {
r++
}
if r+1 < n && arr[r] > arr[r+1] {
for r+1 < n && arr[r] > arr[r+1] {
r++
}
ans = max(ans, r-l+1)
} else {
r++
}
}
}
return
}

func max(a, b int) int {
if a > b {
return a
}
return b
}
```

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