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Jan 21, 2025
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feat: add solutions to lc problem: No.2219 #3976

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105 changes: 69 additions & 36 deletions solution/2200-2299/2219.Maximum Sum Score of Array/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -70,7 +70,15 @@ nums 可取得的最大总分是 -3 。

<!-- solution:start -->

### 方法一
### 方法一：前缀和

我们可以使用两个变量 $l$ 和 $r$ 分别表示数组的前缀和和后缀和，初始时 $l = 0$, $r = \sum_{i=0}^{n-1} \textit{nums}[i]$。

接下来，我们遍历数组 $\textit{nums}$，对于每个元素 $x$，我们将 $l$ 增加 $x$，并更新答案 $\textit{ans} = \max(\textit{ans}, l, r)$，然后将 $r$ 减少 $x$。

遍历结束后，返回答案 $\textit{ans}$ 即可。

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

<!-- tabs:start -->

Expand All @@ -79,23 +87,29 @@ nums 可取得的最大总分是 -3 。
```python
class Solution:
def maximumSumScore(self, nums: List[int]) -> int:
s = [0] + list(accumulate(nums))
return max(max(s[i + 1], s[-1] - s[i]) for i in range(len(nums)))
l, r = 0, sum(nums)
ans = -inf
for x in nums:
l += x
ans = max(ans, l, r)
r -= x
return ans
```

#### Java

```java
class Solution {
public long maximumSumScore(int[] nums) {
int n = nums.length;
long[] s = new long[n + 1];
for (int i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
long l = 0, r = 0;
for (int x : nums) {
r += x;
}
long ans = Long.MIN_VALUE;
for (int i = 0; i < n; ++i) {
ans = Math.max(ans, Math.max(s[i + 1], s[n] - s[i]));
for (int x : nums) {
l += x;
ans = Math.max(ans, Math.max(l, r));
r -= x;
}
return ans;
}
Expand All @@ -108,11 +122,13 @@ class Solution {
class Solution {
public:
long long maximumSumScore(vector<int>& nums) {
int n = nums.size();
vector<long long> s(n + 1);
for (int i = 0; i < n; ++i) s[i + 1] = s[i] + nums[i];
long long ans = INT_MIN;
for (int i = 0; i < n; ++i) ans = max(ans, max(s[i + 1], s[n] - s[i]));
long long l = 0, r = accumulate(nums.begin(), nums.end(), 0LL);
long long ans = -1e18;
for (int x : nums) {
l += x;
ans = max({ans, l, r});
r -= x;
}
return ans;
}
};
Expand All @@ -122,36 +138,54 @@ public:

```go
func maximumSumScore(nums []int) int64 {
n := len(nums)
s := make([]int64, n+1)
for i, v := range nums {
s[i+1] = s[i] + int64(v)
l, r := 0, 0
for _, x := range nums {
r += x
}
var ans int64 = math.MinInt64
for i := 0; i < n; i++ {
ans = max(ans, max(s[i+1], s[n]-s[i]))
ans := math.MinInt64
for _, x := range nums {
l += x
ans = max(ans, max(l, r))
r -= x
}
return ans
return int64(ans)
}
```

#### TypeScript

```ts
function maximumSumScore(nums: number[]): number {
const n = nums.length;
let s = new Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
}
let l = 0;
let r = nums.reduce((a, b) => a + b, 0);
let ans = -Infinity;
for (let i = 0; i < n; ++i) {
ans = Math.max(ans, Math.max(s[i + 1], s[n] - s[i]));
for (const x of nums) {
l += x;
ans = Math.max(ans, l, r);
r -= x;
}
return ans;
}
```

#### Rust

```rust
impl Solution {
pub fn maximum_sum_score(nums: Vec<i32>) -> i64 {
let mut l = 0;
let mut r: i64 = nums.iter().map(|&x| x as i64).sum();
let mut ans = std::i64::MIN;
for &x in &nums {
l += x as i64;
ans = ans.max(l).max(r);
r -= x as i64;
}
ans
}
}
```

#### JavaScript

```js
Expand All @@ -160,14 +194,13 @@ function maximumSumScore(nums: number[]): number {
* @return {number}
*/
var maximumSumScore = function (nums) {
const n = nums.length;
let s = new Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
}
let l = 0;
let r = nums.reduce((a, b) => a + b, 0);
let ans = -Infinity;
for (let i = 0; i < n; ++i) {
ans = Math.max(ans, Math.max(s[i + 1], s[n] - s[i]));
for (const x of nums) {
l += x;
ans = Math.max(ans, l, r);
r -= x;
}
return ans;
};
Expand Down
105 changes: 69 additions & 36 deletions solution/2200-2299/2219.Maximum Sum Score of Array/README_EN.md
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -68,7 +68,15 @@ The maximum sum score of nums is -3.

<!-- solution:start -->

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

We can use two variables $l$ and $r$ to represent the prefix sum and suffix sum of the array, respectively. Initially, $l = 0$ and $r = \sum_{i=0}^{n-1} \textit{nums}[i]$.

Next, we traverse the array $\textit{nums}$. For each element $x$, we add $x$ to $l$ and update the answer $\textit{ans} = \max(\textit{ans}, l, r)$, then subtract $x$ from $r$.

After the traversal, return the answer $\textit{ans}$.

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

<!-- tabs:start -->

Expand All @@ -77,23 +85,29 @@ The maximum sum score of nums is -3.
```python
class Solution:
def maximumSumScore(self, nums: List[int]) -> int:
s = [0] + list(accumulate(nums))
return max(max(s[i + 1], s[-1] - s[i]) for i in range(len(nums)))
l, r = 0, sum(nums)
ans = -inf
for x in nums:
l += x
ans = max(ans, l, r)
r -= x
return ans
```

#### Java

```java
class Solution {
public long maximumSumScore(int[] nums) {
int n = nums.length;
long[] s = new long[n + 1];
for (int i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
long l = 0, r = 0;
for (int x : nums) {
r += x;
}
long ans = Long.MIN_VALUE;
for (int i = 0; i < n; ++i) {
ans = Math.max(ans, Math.max(s[i + 1], s[n] - s[i]));
for (int x : nums) {
l += x;
ans = Math.max(ans, Math.max(l, r));
r -= x;
}
return ans;
}
Expand All @@ -106,11 +120,13 @@ class Solution {
class Solution {
public:
long long maximumSumScore(vector<int>& nums) {
int n = nums.size();
vector<long long> s(n + 1);
for (int i = 0; i < n; ++i) s[i + 1] = s[i] + nums[i];
long long ans = INT_MIN;
for (int i = 0; i < n; ++i) ans = max(ans, max(s[i + 1], s[n] - s[i]));
long long l = 0, r = accumulate(nums.begin(), nums.end(), 0LL);
long long ans = -1e18;
for (int x : nums) {
l += x;
ans = max({ans, l, r});
r -= x;
}
return ans;
}
};
Expand All @@ -120,36 +136,54 @@ public:

```go
func maximumSumScore(nums []int) int64 {
n := len(nums)
s := make([]int64, n+1)
for i, v := range nums {
s[i+1] = s[i] + int64(v)
l, r := 0, 0
for _, x := range nums {
r += x
}
var ans int64 = math.MinInt64
for i := 0; i < n; i++ {
ans = max(ans, max(s[i+1], s[n]-s[i]))
ans := math.MinInt64
for _, x := range nums {
l += x
ans = max(ans, max(l, r))
r -= x
}
return ans
return int64(ans)
}
```

#### TypeScript

```ts
function maximumSumScore(nums: number[]): number {
const n = nums.length;
let s = new Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
}
let l = 0;
let r = nums.reduce((a, b) => a + b, 0);
let ans = -Infinity;
for (let i = 0; i < n; ++i) {
ans = Math.max(ans, Math.max(s[i + 1], s[n] - s[i]));
for (const x of nums) {
l += x;
ans = Math.max(ans, l, r);
r -= x;
}
return ans;
}
```

#### Rust

```rust
impl Solution {
pub fn maximum_sum_score(nums: Vec<i32>) -> i64 {
let mut l = 0;
let mut r: i64 = nums.iter().map(|&x| x as i64).sum();
let mut ans = std::i64::MIN;
for &x in &nums {
l += x as i64;
ans = ans.max(l).max(r);
r -= x as i64;
}
ans
}
}
```

#### JavaScript

```js
Expand All @@ -158,14 +192,13 @@ function maximumSumScore(nums: number[]): number {
* @return {number}
*/
var maximumSumScore = function (nums) {
const n = nums.length;
let s = new Array(n + 1).fill(0);
for (let i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
}
let l = 0;
let r = nums.reduce((a, b) => a + b, 0);
let ans = -Infinity;
for (let i = 0; i < n; ++i) {
ans = Math.max(ans, Math.max(s[i + 1], s[n] - s[i]));
for (const x of nums) {
l += x;
ans = Math.max(ans, l, r);
r -= x;
}
return ans;
};
Expand Down
14 changes: 8 additions & 6 deletions solution/2200-2299/2219.Maximum Sum Score of Array/Solution.cpp
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Open in desktop
Original file line number Diff line number Diff line change
@@ -1,11 +1,13 @@
class Solution {
public:
long long maximumSumScore(vector<int>& nums) {
int n = nums.size();
vector<long long> s(n + 1);
for (int i = 0; i < n; ++i) s[i + 1] = s[i] + nums[i];
long long ans = INT_MIN;
for (int i = 0; i < n; ++i) ans = max(ans, max(s[i + 1], s[n] - s[i]));
long long l = 0, r = accumulate(nums.begin(), nums.end(), 0LL);
long long ans = -1e18;
for (int x : nums) {
l += x;
ans = max({ans, l, r});
r -= x;
}
return ans;
}
};
};
19 changes: 10 additions & 9 deletions solution/2200-2299/2219.Maximum Sum Score of Array/Solution.go
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,12 +1,13 @@
func maximumSumScore(nums []int) int64 {
n := len(nums)
s := make([]int64, n+1)
for i, v := range nums {
s[i+1] = s[i] + int64(v)
l, r := 0, 0
for _, x := range nums {
r += x
}
var ans int64 = math.MinInt64
for i := 0; i < n; i++ {
ans = max(ans, max(s[i+1], s[n]-s[i]))
ans := math.MinInt64
for _, x := range nums {
l += x
ans = max(ans, max(l, r))
r -= x
}
return ans
}
return int64(ans)
}
15 changes: 8 additions & 7 deletions solution/2200-2299/2219.Maximum Sum Score of Array/Solution.java
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Original file line number Diff line number Diff line change
@@ -1,14 +1,15 @@
class Solution {
public long maximumSumScore(int[] nums) {
int n = nums.length;
long[] s = new long[n + 1];
for (int i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
long l = 0, r = 0;
for (int x : nums) {
r += x;
}
long ans = Long.MIN_VALUE;
for (int i = 0; i < n; ++i) {
ans = Math.max(ans, Math.max(s[i + 1], s[n] - s[i]));
for (int x : nums) {
l += x;
ans = Math.max(ans, Math.max(l, r));
r -= x;
}
return ans;
}
}
}
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