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Sep 11, 2024
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feat: add solutions to lc problem: No.2145 #3511

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62 changes: 41 additions & 21 deletions solution/2100-2199/2145.Count the Hidden Sequences/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -85,7 +85,13 @@ tags:

<!-- solution:start -->

### 方法一
### 方法一：前缀和

由于数组 $\textit{differences}$ 已经确定，那么数组 $\textit{hidden}$ 的元素最大值与最小值之差也是固定的，我们只要确保差值不超过 $\textit{upper} - \textit{lower}$ 即可。

我们不妨假设数组 $\textit{hidden}$ 的第一个元素为 $0$，那么 $\textit{hidden}[i] = \textit{hidden}[i - 1] + \textit{differences}[i - 1]$，其中 $1 \leq i \leq n$。记数组 $\textit{hidden}$ 的最大值为 $mx$，最小值为 $mi$，如果 $mx - mi \leq \textit{upper} - \textit{lower}$，那么我们就可以构造出一个合法的 $\textit{hidden}$ 数组，可以构造的个数为 $\textit{upper} - \textit{lower} - (mx - mi) + 1$。否则，无法构造出合法的 $\textit{hidden}$ 数组，返回 $0$。

时间复杂度 $O(n)$，其中 $n$ 是数组 $\textit{differences}$ 的长度。空间复杂度 $O(1)$。

<!-- tabs:start -->

Expand All @@ -94,26 +100,26 @@ tags:
```python
class Solution:
def numberOfArrays(self, differences: List[int], lower: int, upper: int) -> int:
num = mi = mx = 0
x = mi = mx = 0
for d in differences:
num += d
mi = min(mi, num)
mx = max(mx, num)
return max(0, upper - lower - (mx - mi) + 1)
x += d
mi = min(mi, x)
mx = max(mx, x)
return max(upper - lower - (mx - mi) + 1, 0)
```

#### Java

```java
class Solution {
public int numberOfArrays(int[] differences, int lower, int upper) {
long num = 0, mi = 0, mx = 0;
long x = 0, mi = 0, mx = 0;
for (int d : differences) {
num += d;
mi = Math.min(mi, num);
mx = Math.max(mx, num);
x += d;
mi = Math.min(mi, x);
mx = Math.max(mx, x);
}
return Math.max(0, (int) (upper - lower - (mx - mi) + 1));
return (int) Math.max(upper - lower - (mx - mi) + 1, 0);
}
}
```
Expand All @@ -124,13 +130,13 @@ class Solution {
class Solution {
public:
int numberOfArrays(vector<int>& differences, int lower, int upper) {
long long num = 0, mi = 0, mx = 0;
for (int& d : differences) {
num += d;
mi = min(mi, num);
mx = max(mx, num);
long long x = 0, mi = 0, mx = 0;
for (int d : differences) {
x += d;
mi = min(mi, x);
mx = max(mx, x);
}
return max(0, (int) (upper - lower - (mx - mi) + 1));
return max(upper - lower - (mx - mi) + 1, 0LL);
}
};
```
Expand All @@ -139,16 +145,30 @@ public:

```go
func numberOfArrays(differences []int, lower int, upper int) int {
num, mi, mx := 0, 0, 0
x, mi, mx := 0, 0, 0
for _, d := range differences {
num += d
mi = min(mi, num)
mx = max(mx, num)
x += d
mi = min(mi, x)
mx = max(mx, x)
}
return max(0, upper-lower-(mx-mi)+1)
}
```

#### TypeScript

```ts
function numberOfArrays(differences: number[], lower: number, upper: number): number {
let [x, mi, mx] = [0, 0, 0];
for (const d of differences) {
x += d;
mi = Math.min(mi, x);
mx = Math.max(mx, x);
}
return Math.max(0, upper - lower - (mx - mi) + 1);
}
```

<!-- tabs:end -->

<!-- solution:end -->
Expand Down
62 changes: 41 additions & 21 deletions solution/2100-2199/2145.Count the Hidden Sequences/README_EN.md
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Original file line number Diff line number Diff line change
Expand Up @@ -86,7 +86,13 @@ Thus, we return 4.

<!-- solution:start -->

### Solution 1
### Solution 1: Prefix Sum

Since the array $\textit{differences}$ is already determined, the difference between the maximum and minimum values of the elements in the array $\textit{hidden}$ is also fixed. We just need to ensure that this difference does not exceed $\textit{upper} - \textit{lower}$.

Let's assume the first element of the array $\textit{hidden}$ is $0$. Then, $\textit{hidden}[i] = \textit{hidden}[i - 1] + \textit{differences}[i - 1]$, where $1 \leq i \leq n$. Let the maximum value of the array $\textit{hidden}$ be $mx$ and the minimum value be $mi$. If $mx - mi \leq \textit{upper} - \textit{lower}$, then we can construct a valid $\textit{hidden}$ array. The number of possible constructions is $\textit{upper} - \textit{lower} - (mx - mi) + 1$. Otherwise, it is impossible to construct a valid $\textit{hidden}$ array, and we return $0$.

The time complexity is $O(n)$, where $n$ is the length of the array $\textit{differences}$. The space complexity is $O(1)$.

<!-- tabs:start -->

Expand All @@ -95,26 +101,26 @@ Thus, we return 4.
```python
class Solution:
def numberOfArrays(self, differences: List[int], lower: int, upper: int) -> int:
num = mi = mx = 0
x = mi = mx = 0
for d in differences:
num += d
mi = min(mi, num)
mx = max(mx, num)
return max(0, upper - lower - (mx - mi) + 1)
x += d
mi = min(mi, x)
mx = max(mx, x)
return max(upper - lower - (mx - mi) + 1, 0)
```

#### Java

```java
class Solution {
public int numberOfArrays(int[] differences, int lower, int upper) {
long num = 0, mi = 0, mx = 0;
long x = 0, mi = 0, mx = 0;
for (int d : differences) {
num += d;
mi = Math.min(mi, num);
mx = Math.max(mx, num);
x += d;
mi = Math.min(mi, x);
mx = Math.max(mx, x);
}
return Math.max(0, (int) (upper - lower - (mx - mi) + 1));
return (int) Math.max(upper - lower - (mx - mi) + 1, 0);
}
}
```
Expand All @@ -125,13 +131,13 @@ class Solution {
class Solution {
public:
int numberOfArrays(vector<int>& differences, int lower, int upper) {
long long num = 0, mi = 0, mx = 0;
for (int& d : differences) {
num += d;
mi = min(mi, num);
mx = max(mx, num);
long long x = 0, mi = 0, mx = 0;
for (int d : differences) {
x += d;
mi = min(mi, x);
mx = max(mx, x);
}
return max(0, (int) (upper - lower - (mx - mi) + 1));
return max(upper - lower - (mx - mi) + 1, 0LL);
}
};
```
Expand All @@ -140,16 +146,30 @@ public:

```go
func numberOfArrays(differences []int, lower int, upper int) int {
num, mi, mx := 0, 0, 0
x, mi, mx := 0, 0, 0
for _, d := range differences {
num += d
mi = min(mi, num)
mx = max(mx, num)
x += d
mi = min(mi, x)
mx = max(mx, x)
}
return max(0, upper-lower-(mx-mi)+1)
}
```

#### TypeScript

```ts
function numberOfArrays(differences: number[], lower: number, upper: number): number {
let [x, mi, mx] = [0, 0, 0];
for (const d of differences) {
x += d;
mi = Math.min(mi, x);
mx = Math.max(mx, x);
}
return Math.max(0, upper - lower - (mx - mi) + 1);
}
```

<!-- tabs:end -->

<!-- solution:end -->
Expand Down
14 changes: 7 additions & 7 deletions solution/2100-2199/2145.Count the Hidden Sequences/Solution.cpp
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Original file line number Diff line number Diff line change
@@ -1,12 +1,12 @@
class Solution {
public:
int numberOfArrays(vector<int>& differences, int lower, int upper) {
long long num = 0, mi = 0, mx = 0;
for (int& d : differences) {
num += d;
mi = min(mi, num);
mx = max(mx, num);
long long x = 0, mi = 0, mx = 0;
for (int d : differences) {
x += d;
mi = min(mi, x);
mx = max(mx, x);
}
return max(0, (int) (upper - lower - (mx - mi) + 1));
return max(upper - lower - (mx - mi) + 1, 0LL);
}
};
};
10 changes: 5 additions & 5 deletions solution/2100-2199/2145.Count the Hidden Sequences/Solution.go
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Open in desktop
Original file line number Diff line number Diff line change
@@ -1,9 +1,9 @@
func numberOfArrays(differences []int, lower int, upper int) int {
num, mi, mx := 0, 0, 0
x, mi, mx := 0, 0, 0
for _, d := range differences {
num += d
mi = min(mi, num)
mx = max(mx, num)
x += d
mi = min(mi, x)
mx = max(mx, x)
}
return max(0, upper-lower-(mx-mi)+1)
}
}
12 changes: 6 additions & 6 deletions solution/2100-2199/2145.Count the Hidden Sequences/Solution.java
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Original file line number Diff line number Diff line change
@@ -1,11 +1,11 @@
class Solution {
public int numberOfArrays(int[] differences, int lower, int upper) {
long num = 0, mi = 0, mx = 0;
long x = 0, mi = 0, mx = 0;
for (int d : differences) {
num += d;
mi = Math.min(mi, num);
mx = Math.max(mx, num);
x += d;
mi = Math.min(mi, x);
mx = Math.max(mx, x);
}
return Math.max(0, (int) (upper - lower - (mx - mi) + 1));
return (int) Math.max(upper - lower - (mx - mi) + 1, 0);
}
}
}
10 changes: 5 additions & 5 deletions solution/2100-2199/2145.Count the Hidden Sequences/Solution.py
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,8 +1,8 @@
class Solution:
def numberOfArrays(self, differences: List[int], lower: int, upper: int) -> int:
num = mi = mx = 0
x = mi = mx = 0
for d in differences:
num += d
mi = min(mi, num)
mx = max(mx, num)
return max(0, upper - lower - (mx - mi) + 1)
x += d
mi = min(mi, x)
mx = max(mx, x)
return max(upper - lower - (mx - mi) + 1, 0)
9 changes: 9 additions & 0 deletions solution/2100-2199/2145.Count the Hidden Sequences/Solution.ts
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Original file line number Diff line number Diff line change
@@ -0,0 +1,9 @@
function numberOfArrays(differences: number[], lower: number, upper: number): number {
let [x, mi, mx] = [0, 0, 0];
for (const d of differences) {
x += d;
mi = Math.min(mi, x);
mx = Math.max(mx, x);
}
return Math.max(0, upper - lower - (mx - mi) + 1);
}
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