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Original file line number Diff line number Diff line change
Expand Up @@ -180,4 +180,90 @@ function maxEnergyBoost(energyDrinkA: number[], energyDrinkB: number[]): number

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<!-- solution:start -->

### 方法二:动态规划(空间优化)

我们注意到,状态 $f[i]$ 至于 $f[i - 1]$ 有关,而与 $f[i - 2]$ 无关。因此我们可以只使用两个变量 $f$ 和 $g$ 来维护状态,从而将空间复杂度优化到 $O(1)$。

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

<!-- tabs:start -->

#### Python3

```python
class Solution:
def maxEnergyBoost(self, energyDrinkA: List[int], energyDrinkB: List[int]) -> int:
f, g = energyDrinkA[0], energyDrinkB[0]
for a, b in zip(energyDrinkA[1:], energyDrinkB[1:]):
f, g = max(f + a, g), max(g + b, f)
return max(f, g)
```

#### Java

```java
class Solution {
public long maxEnergyBoost(int[] energyDrinkA, int[] energyDrinkB) {
int n = energyDrinkA.length;
long f = energyDrinkA[0], g = energyDrinkB[0];
for (int i = 1; i < n; ++i) {
long ff = Math.max(f + energyDrinkA[i], g);
g = Math.max(g + energyDrinkB[i], f);
f = ff;
}
return Math.max(f, g);
}
}
```

#### C++

```cpp
class Solution {
public:
long long maxEnergyBoost(vector<int>& energyDrinkA, vector<int>& energyDrinkB) {
int n = energyDrinkA.size();
long long f = energyDrinkA[0], g = energyDrinkB[0];
for (int i = 1; i < n; ++i) {
long long ff = max(f + energyDrinkA[i], g);
g = max(g + energyDrinkB[i], f);
f = ff;
}
return max(f, g);
}
};
```

#### Go

```go
func maxEnergyBoost(energyDrinkA []int, energyDrinkB []int) int64 {
n := len(energyDrinkA)
f, g := energyDrinkA[0], energyDrinkB[0]
for i := 1; i < n; i++ {
f, g = max(f+energyDrinkA[i], g), max(g+energyDrinkB[i], f)
}
return int64(max(f, g))
}
```

#### TypeScript

```ts
function maxEnergyBoost(energyDrinkA: number[], energyDrinkB: number[]): number {
const n = energyDrinkA.length;
let [f, g] = [energyDrinkA[0], energyDrinkB[0]];
for (let i = 1; i < n; ++i) {
[f, g] = [Math.max(f + energyDrinkA[i], g), Math.max(g + energyDrinkB[i], f)];
}
return Math.max(f, g);
}
```

<!-- tabs:end -->

<!-- solution:end -->

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Original file line number Diff line number Diff line change
Expand Up @@ -180,4 +180,90 @@ function maxEnergyBoost(energyDrinkA: number[], energyDrinkB: number[]): number

<!-- solution:end -->

<!-- solution:start -->

### Solution 2: Dynamic Programming (Space Optimization)

We notice that the state $f[i]$ is only related to $f[i - 1]$ and not to $f[i - 2]$. Therefore, we can use only two variables $f$ and $g$ to maintain the state, thus optimizing the space complexity to $O(1)$.

The time complexity is $O(n)$, where $n$ is the length of the array. The space complexity is $O(1)$.

<!-- tabs:start -->

#### Python3

```python
class Solution:
def maxEnergyBoost(self, energyDrinkA: List[int], energyDrinkB: List[int]) -> int:
f, g = energyDrinkA[0], energyDrinkB[0]
for a, b in zip(energyDrinkA[1:], energyDrinkB[1:]):
f, g = max(f + a, g), max(g + b, f)
return max(f, g)
```

#### Java

```java
class Solution {
public long maxEnergyBoost(int[] energyDrinkA, int[] energyDrinkB) {
int n = energyDrinkA.length;
long f = energyDrinkA[0], g = energyDrinkB[0];
for (int i = 1; i < n; ++i) {
long ff = Math.max(f + energyDrinkA[i], g);
g = Math.max(g + energyDrinkB[i], f);
f = ff;
}
return Math.max(f, g);
}
}
```

#### C++

```cpp
class Solution {
public:
long long maxEnergyBoost(vector<int>& energyDrinkA, vector<int>& energyDrinkB) {
int n = energyDrinkA.size();
long long f = energyDrinkA[0], g = energyDrinkB[0];
for (int i = 1; i < n; ++i) {
long long ff = max(f + energyDrinkA[i], g);
g = max(g + energyDrinkB[i], f);
f = ff;
}
return max(f, g);
}
};
```

#### Go

```go
func maxEnergyBoost(energyDrinkA []int, energyDrinkB []int) int64 {
n := len(energyDrinkA)
f, g := energyDrinkA[0], energyDrinkB[0]
for i := 1; i < n; i++ {
f, g = max(f+energyDrinkA[i], g), max(g+energyDrinkB[i], f)
}
return int64(max(f, g))
}
```

#### TypeScript

```ts
function maxEnergyBoost(energyDrinkA: number[], energyDrinkB: number[]): number {
const n = energyDrinkA.length;
let [f, g] = [energyDrinkA[0], energyDrinkB[0]];
for (let i = 1; i < n; ++i) {
[f, g] = [Math.max(f + energyDrinkA[i], g), Math.max(g + energyDrinkB[i], f)];
}
return Math.max(f, g);
}
```

<!-- tabs:end -->

<!-- solution:end -->

<!-- problem:end -->
Original file line number Diff line number Diff line change
@@ -0,0 +1,13 @@
class Solution {
public:
long long maxEnergyBoost(vector<int>& energyDrinkA, vector<int>& energyDrinkB) {
int n = energyDrinkA.size();
long long f = energyDrinkA[0], g = energyDrinkB[0];
for (int i = 1; i < n; ++i) {
long long ff = max(f + energyDrinkA[i], g);
g = max(g + energyDrinkB[i], f);
f = ff;
}
return max(f, g);
}
};
Original file line number Diff line number Diff line change
@@ -0,0 +1,8 @@
func maxEnergyBoost(energyDrinkA []int, energyDrinkB []int) int64 {
n := len(energyDrinkA)
f, g := energyDrinkA[0], energyDrinkB[0]
for i := 1; i < n; i++ {
f, g = max(f+energyDrinkA[i], g), max(g+energyDrinkB[i], f)
}
return int64(max(f, g))
}
Original file line number Diff line number Diff line change
@@ -0,0 +1,12 @@
class Solution {
public long maxEnergyBoost(int[] energyDrinkA, int[] energyDrinkB) {
int n = energyDrinkA.length;
long f = energyDrinkA[0], g = energyDrinkB[0];
for (int i = 1; i < n; ++i) {
long ff = Math.max(f + energyDrinkA[i], g);
g = Math.max(g + energyDrinkB[i], f);
f = ff;
}
return Math.max(f, g);
}
}
Original file line number Diff line number Diff line change
@@ -0,0 +1,6 @@
class Solution:
def maxEnergyBoost(self, energyDrinkA: List[int], energyDrinkB: List[int]) -> int:
f, g = energyDrinkA[0], energyDrinkB[0]
for a, b in zip(energyDrinkA[1:], energyDrinkB[1:]):
f, g = max(f + a, g), max(g + b, f)
return max(f, g)
Original file line number Diff line number Diff line change
@@ -0,0 +1,8 @@
function maxEnergyBoost(energyDrinkA: number[], energyDrinkB: number[]): number {
const n = energyDrinkA.length;
let [f, g] = [energyDrinkA[0], energyDrinkB[0]];
for (let i = 1; i < n; ++i) {
[f, g] = [Math.max(f + energyDrinkA[i], g), Math.max(g + energyDrinkB[i], f)];
}
return Math.max(f, g);
}
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