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feat: add solutions to lc/lcof problems (#1444)
* lc No.0198 & lcof2 No.089.House Robber * lc No.0213 & lcof2 No.090.House Robber II
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‎lcof2/剑指 Offer II 089. 房屋偷盗/README.md

+142-40
Original file line numberDiff line numberDiff line change
@@ -44,7 +44,31 @@
4444

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<!-- 这里可写通用的实现逻辑 -->
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简单动态规划，用 `dp[i]` 表示 `0 ~ i` 的房子能偷到的最高金额
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**方法一：动态规划**
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我们定义 $f[i]$ 表示前 $i$ 间房屋能偷窃到的最高总金额，初始时 $f[0]=0$, $f[1]=nums[0]$。
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考虑 $i \gt 1$ 的情况，第 $i$ 间房屋有两个选项：
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- 不偷窃第 $i$ 间房屋，偷窃总金额为 $f[i-1]$；
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- 偷窃第 $i$ 间房屋，偷窃总金额为 $f[i-2]+nums[i-1]$；
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因此，我们可以得到状态转移方程：
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$$
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f[i]=
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\begin{cases}
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0, & i=0 \\
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nums[0], & i=1 \\
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\max(f[i-1],f[i-2]+nums[i-1]), & i \gt 1
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\end{cases}
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$$
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最终的答案即为 $f[n]$，其中 $n$ 是数组的长度。
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时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 是数组长度。
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注意到当 $i \gt 2$ 时，$f[i]$ 只和 $f[i-1]$ 与 $f[i-2]$ 有关，因此我们可以使用两个变量代替数组，将空间复杂度降到 $O(1)$。
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<!-- tabs:start -->
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@@ -55,15 +79,21 @@
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```python
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class Solution:
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def rob(self, nums: List[int]) -> int:
58-
if len(nums) == 1:
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return nums[0]
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n = len(nums)
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dp = [0] * n
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dp[0], dp[1] = nums[0], max(nums[0], nums[1])
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for i in range(2, n):
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dp[i] = max(dp[i - 2] + nums[i], dp[i - 1])
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return dp[n - 1]
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f = [0] * (n + 1)
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f[1] = nums[0]
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for i in range(2, n + 1):
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f[i] = max(f[i - 1], f[i - 2] + nums[i - 1])
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return f[n]
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```
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```python
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class Solution:
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def rob(self, nums: List[int]) -> int:
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f = g = 0
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for x in nums:
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f, g = max(f, g), f + x
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return max(f, g)
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```
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### **Java**
@@ -73,17 +103,27 @@ class Solution:
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```java
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class Solution {
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public int rob(int[] nums) {
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if (nums.length == 1) {
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return nums[0];
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}
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int n = nums.length;
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int[] dp = new int[n];
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dp[0] = nums[0];
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dp[1] = Math.max(nums[0], nums[1]);
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for (int i = 2; i < n; i++) {
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dp[i] = Math.max(dp[i - 2] + nums[i], dp[i - 1]);
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int[] f = new int[n + 1];
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f[1] = nums[0];
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for (int i = 2; i <= n; ++i) {
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f[i] = Math.max(f[i - 1], f[i - 2] + nums[i - 1]);
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}
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return dp[n - 1];
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return f[n];
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}
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}
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```
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```java
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class Solution {
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public int rob(int[] nums) {
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int f = 0, g = 0;
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for (int x : nums) {
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int ff = Math.max(f, g);
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g = f + x;
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f = ff;
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}
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return Math.max(f, g);
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}
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}
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```
@@ -94,17 +134,29 @@ class Solution {
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class Solution {
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public:
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int rob(vector<int>& nums) {
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if (nums.size() == 1) {
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return nums[0];
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}
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int n = nums.size();
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vector<int> dp(n, 0);
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dp[0] = nums[0];
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dp[1] = max(nums[0], nums[1]);
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for (int i = 2; i < n; i++) {
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dp[i] = max(dp[i - 2] + nums[i], dp[i - 1]);
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int f[n + 1];
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memset(f, 0, sizeof(f));
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f[1] = nums[0];
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for (int i = 2; i <= n; ++i) {
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f[i] = max(f[i - 1], f[i - 2] + nums[i - 1]);
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}
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return dp[n - 1];
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return f[n];
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}
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};
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```
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```cpp
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class Solution {
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public:
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int rob(vector<int>& nums) {
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int f = 0, g = 0;
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for (int& x : nums) {
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int ff = max(f, g);
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g = f + x;
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f = ff;
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}
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return max(f, g);
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}
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};
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```
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```go
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func rob(nums []int) int {
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if len(nums) == 1 {
117-
return nums[0]
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n := len(nums)
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f := make([]int, n+1)
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f[1] = nums[0]
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for i := 2; i <= n; i++ {
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f[i] = max(f[i-1], f[i-2]+nums[i-1])
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}
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return f[n]
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}
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n := len(nums)
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dp := make([]int, n)
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dp[0] = nums[0]
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dp[1] = max(nums[0], nums[1])
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for i := 2; i < n; i++ {
125-
dp[i] = max(dp[i-2]+nums[i], dp[i-1])
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func max(a, b int) int {
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if a > b {
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return a
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}
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return dp[n-1]
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return b
128182
}
183+
```
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130-
func max(x, y int) int {
131-
if x > y {
132-
return x
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```go
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func rob(nums []int) int {
187+
f, g := 0, 0
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for _, x := range nums {
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f, g = max(f, g), f+x
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}
134-
return y
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return max(f, g)
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}
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```
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### **TypeScript**
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```ts
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function rob(nums: number[]): number {
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const n = nums.length;
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const f: number[] = Array(n + 1).fill(0);
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f[1] = nums[0];
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for (let i = 2; i <= n; ++i) {
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f[i] = Math.max(f[i - 1], f[i - 2] + nums[i - 1]);
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}
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return f[n];
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}
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```
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```ts
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function rob(nums: number[]): number {
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let [f, g] = [0, 0];
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for (const x of nums) {
220+
[f, g] = [Math.max(f, g), f + x];
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}
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return Math.max(f, g);
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}
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```
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### **Rust**
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```rust
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impl Solution {
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pub fn rob(nums: Vec<i32>) -> i32 {
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let mut f = [0, 0];
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for x in nums {
233+
f = [f[0].max(f[1]), f[0] + x]
234+
}
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f[0].max(f[1])
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}
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}
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```
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‎lcof2/剑指 Offer II 089. 房屋偷盗/Solution.cpp

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@@ -1,16 +1,12 @@
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class Solution {
2-
public:
3-
int rob(vector<int>& nums) {
4-
if (nums.size() == 1) {
5-
return nums[0];
6-
}
7-
int n = nums.size();
8-
vector<int> dp(n, 0);
9-
dp[0] = nums[0];
10-
dp[1] = max(nums[0], nums[1]);
11-
for (int i = 2; i < n; i++) {
12-
dp[i] = max(dp[i - 2] + nums[i], dp[i - 1]);
13-
}
14-
return dp[n - 1];
15-
}
16-
};
1+
class Solution {
2+
public:
3+
int rob(vector<int>& nums) {
4+
int f = 0, g = 0;
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for (int& x : nums) {
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int ff = max(f, g);
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g = f + x;
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f = ff;
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}
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return max(f, g);
11+
}
12+
};

‎lcof2/剑指 Offer II 089. 房屋偷盗/Solution.go

+8-15
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@@ -1,21 +1,14 @@
11
func rob(nums []int) int {
2-
if len(nums) == 1 {
3-
return nums[0]
2+
f, g := 0, 0
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for _, x := range nums {
4+
f, g = max(f, g), f+x
45
}
5-
6-
n := len(nums)
7-
dp := make([]int, n)
8-
dp[0] = nums[0]
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dp[1] = max(nums[0], nums[1])
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for i := 2; i < n; i++ {
11-
dp[i] = max(dp[i-2]+nums[i], dp[i-1])
12-
}
13-
return dp[n-1]
6+
return max(f, g)
147
}
158

16-
func max(x, y int) int {
17-
if x > y {
18-
return x
9+
func max(a, b int) int {
10+
if a > b {
11+
return a
1912
}
20-
return y
13+
return b
2114
}

‎lcof2/剑指 Offer II 089. 房屋偷盗/Solution.java

+11-15
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@@ -1,15 +1,11 @@
1-
class Solution {
2-
public int rob(int[] nums) {
3-
if (nums.length == 1) {
4-
return nums[0];
5-
}
6-
int n = nums.length;
7-
int[] dp = new int[n];
8-
dp[0] = nums[0];
9-
dp[1] = Math.max(nums[0], nums[1]);
10-
for (int i = 2; i < n; i++) {
11-
dp[i] = Math.max(dp[i - 2] + nums[i], dp[i - 1]);
12-
}
13-
return dp[n - 1];
14-
}
15-
}
1+
class Solution {
2+
public int rob(int[] nums) {
3+
int f = 0, g = 0;
4+
for (int x : nums) {
5+
int ff = Math.max(f, g);
6+
g = f + x;
7+
f = ff;
8+
}
9+
return Math.max(f, g);
10+
}
11+
}

‎lcof2/剑指 Offer II 089. 房屋偷盗/Solution.py

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Original file line numberDiff line numberDiff line change
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1-
class Solution:
2-
def rob(self, nums: List[int]) -> int:
3-
if len(nums) == 1:
4-
return nums[0]
5-
6-
n = len(nums)
7-
dp = [0] * n
8-
dp[0], dp[1] = nums[0], max(nums[0], nums[1])
9-
for i in range(2, n):
10-
dp[i] = max(dp[i - 2] + nums[i], dp[i - 1])
11-
return dp[n - 1]
1+
class Solution:
2+
def rob(self, nums: List[int]) -> int:
3+
f = g = 0
4+
for x in nums:
5+
f, g = max(f, g), f + x
6+
return max(f, g)

‎lcof2/剑指 Offer II 089. 房屋偷盗/Solution.rs

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Original file line numberDiff line numberDiff line change
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1+
impl Solution {
2+
pub fn rob(nums: Vec<i32>) -> i32 {
3+
let mut f = [0, 0];
4+
for x in nums {
5+
f = [f[0].max(f[1]), f[0] + x]
6+
}
7+
f[0].max(f[1])
8+
}
9+
}

‎lcof2/剑指 Offer II 089. 房屋偷盗/Solution.ts

+7
Original file line numberDiff line numberDiff line change
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1+
function rob(nums: number[]): number {
2+
let [f, g] = [0, 0];
3+
for (const x of nums) {
4+
[f, g] = [Math.max(f, g), f + x];
5+
}
6+
return Math.max(f, g);
7+
}

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