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feat: add solutions to lc problem: No.1349
No.1349.Maximum Students Taking Exam
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‎solution/1300-1399/1349.Maximum Students Taking Exam/README.md

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@@ -63,22 +63,204 @@
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<!-- 这里可写通用的实现逻辑 -->
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**方法一：状态压缩 + 记忆化搜索**
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我们注意到，每个座位有两种状态：可选和不可选。因此，我们可以使用二进制数来表示每一行的座位状态，其中 $1$ 表示可选，而 $0$ 表示不可选。例如，对于示例 $1$ 中的第一行，我们可以表示为 $010010$。因此，我们将初始座位转换为一个一维数组 $ss$，其中 $ss[i]$ 表示第 $i$ 行的座位状态。
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接下来，我们设计一个函数 $dfs(seat, i)$，表示从第 $i$ 行开始，当前行的座位状态为 $seat$，可以容纳的最多学生人数。
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我们可以枚举第 $i$ 行的所有选座状态 $mask$，并且判断 $mask$ 是否满足以下条件：
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- 状态 $mask$ 不能选择 $seat$ 之外的座位；
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- 状态 $mask$ 不能选择相邻的座位。
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如果满足条件，我们求出当前行选择的座位个数 $cnt$，如果当前是最后一行，则更新函数的返回值，即 $ans = max(ans, cnt)$。否则，我们继续递归地求解下一行的最大人数，下一行的座位状态 $nxt = ss[i + 1]$，并且需要排除当前行已选座位的左右两侧。然后我们递归地求解下一行的最大人数，即 $ans = max(ans, cnt + dfs(nxt, i + 1))$。
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最后，我们将 $ans$ 作为函数的返回值返回。
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为了避免重复计算，我们可以使用记忆化搜索，将函数 $dfs(seat, i)$ 的返回值保存在一个二维数组 $f$ 中，其中 $f[seat][i]$ 表示从第 $i$ 行开始，当前行的座位状态为 $seat$，可以容纳的最多学生人数。
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时间复杂度 $O(4^n \times n \times m)$，空间复杂度 $O(2^n \times m)$。其中 $m$ 和 $n$ 分别为座位的行数和列数。
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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class Solution:
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def maxStudents(self, seats: List[List[str]]) -> int:
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def f(seat: List[str]) -> int:
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mask = 0
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for i, c in enumerate(seat):
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if c == '.':
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mask |= 1 << i
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return mask
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@cache
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def dfs(seat: int, i: int) -> int:
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ans = 0
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for mask in range(1 << n):
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if (seat | mask) != seat or (mask & (mask << 1)):
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continue
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cnt = mask.bit_count()
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if i == len(ss) - 1:
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ans = max(ans, cnt)
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else:
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nxt = ss[i + 1]
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nxt &= ~(mask << 1)
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nxt &= ~(mask >> 1)
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ans = max(ans, cnt + dfs(nxt, i + 1))
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return ans
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n = len(seats[0])
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ss = [f(s) for s in seats]
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return dfs(ss[0], 0)
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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class Solution {
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private Integer[][] f;
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private int n;
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private int[] ss;
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public int maxStudents(char[][] seats) {
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int m = seats.length;
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n = seats[0].length;
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ss = new int[m];
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f = new Integer[1 << n][m];
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for (int i = 0; i < m; ++i) {
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for (int j = 0; j < n; ++j) {
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if (seats[i][j] == '.') {
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ss[i] |= 1 << j;
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}
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}
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}
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return dfs(ss[0], 0);
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}
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private int dfs(int seat, int i) {
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if (f[seat][i] != null) {
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return f[seat][i];
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}
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int ans = 0;
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for (int mask = 0; mask < 1 << n; ++mask) {
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if ((seat | mask) != seat || (mask & (mask << 1)) != 0) {
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continue;
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}
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int cnt = Integer.bitCount(mask);
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if (i == ss.length - 1) {
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ans = Math.max(ans, cnt);
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} else {
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int nxt = ss[i + 1];
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nxt &= ~(mask << 1);
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nxt &= ~(mask >> 1);
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ans = Math.max(ans, cnt + dfs(nxt, i + 1));
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}
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}
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return f[seat][i] = ans;
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int maxStudents(vector<vector<char>>& seats) {
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int m = seats.size();
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int n = seats[0].size();
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vector<int> ss(m);
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vector<vector<int>> f(1 << n, vector<int>(m, -1));
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for (int i = 0; i < m; ++i) {
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for (int j = 0; j < n; ++j) {
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if (seats[i][j] == '.') {
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ss[i] |= 1 << j;
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}
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}
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}
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function<int(int, int)> dfs = [&](int seat, int i) -> int {
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if (f[seat][i] != -1) {
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return f[seat][i];
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}
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int ans = 0;
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for (int mask = 0; mask < 1 << n; ++mask) {
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if ((seat | mask) != seat || (mask & (mask << 1)) != 0) {
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continue;
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}
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int cnt = __builtin_popcount(mask);
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if (i == m - 1) {
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ans = max(ans, cnt);
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} else {
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int nxt = ss[i + 1];
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nxt &= ~(mask >> 1);
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nxt &= ~(mask << 1);
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ans = max(ans, cnt + dfs(nxt, i + 1));
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}
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}
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return f[seat][i] = ans;
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};
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return dfs(ss[0], 0);
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}
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};
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```
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### **Go**
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```go
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func maxStudents(seats [][]byte) int {
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m, n := len(seats), len(seats[0])
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ss := make([]int, m)
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f := make([][]int, 1<<n)
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for i, seat := range seats {
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for j, c := range seat {
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if c == '.' {
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ss[i] |= 1 << j
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}
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}
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}
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for i := range f {
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f[i] = make([]int, m)
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for j := range f[i] {
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f[i][j] = -1
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}
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}
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var dfs func(int, int) int
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dfs = func(seat, i int) int {
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if f[seat][i] != -1 {
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return f[seat][i]
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}
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ans := 0
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for mask := 0; mask < 1<<n; mask++ {
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if (seat|mask) != seat || (mask&(mask<<1)) != 0 {
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continue
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}
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cnt := bits.OnesCount(uint(mask))
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if i == m-1 {
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ans = max(ans, cnt)
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} else {
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nxt := ss[i+1] & ^(mask >> 1) & ^(mask << 1)
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ans = max(ans, cnt+dfs(nxt, i+1))
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}
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}
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f[seat][i] = ans
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return ans
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}
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return dfs(ss[0], 0)
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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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### **...**

‎solution/1300-1399/1349.Maximum Students Taking Exam/README_EN.md

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### **Python3**
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```python
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class Solution:
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def maxStudents(self, seats: List[List[str]]) -> int:
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def f(seat: List[str]) -> int:
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mask = 0
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for i, c in enumerate(seat):
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if c == '.':
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mask |= 1 << i
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return mask
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@cache
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def dfs(seat: int, i: int) -> int:
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ans = 0
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for mask in range(1 << n):
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if (seat | mask) != seat or (mask & (mask << 1)):
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continue
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cnt = mask.bit_count()
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if i == len(ss) - 1:
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ans = max(ans, cnt)
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else:
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nxt = ss[i + 1]
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nxt &= ~(mask << 1)
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nxt &= ~(mask >> 1)
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ans = max(ans, cnt + dfs(nxt, i + 1))
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return ans
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n = len(seats[0])
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ss = [f(s) for s in seats]
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return dfs(ss[0], 0)
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```
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### **Java**
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```java
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class Solution {
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private Integer[][] f;
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private int n;
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private int[] ss;
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public int maxStudents(char[][] seats) {
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int m = seats.length;
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n = seats[0].length;
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ss = new int[m];
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f = new Integer[1 << n][m];
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for (int i = 0; i < m; ++i) {
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for (int j = 0; j < n; ++j) {
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if (seats[i][j] == '.') {
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ss[i] |= 1 << j;
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}
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}
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}
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return dfs(ss[0], 0);
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}
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private int dfs(int seat, int i) {
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if (f[seat][i] != null) {
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return f[seat][i];
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}
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int ans = 0;
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for (int mask = 0; mask < 1 << n; ++mask) {
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if ((seat | mask) != seat || (mask & (mask << 1)) != 0) {
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continue;
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}
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int cnt = Integer.bitCount(mask);
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if (i == ss.length - 1) {
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ans = Math.max(ans, cnt);
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} else {
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int nxt = ss[i + 1];
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nxt &= ~(mask << 1);
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nxt &= ~(mask >> 1);
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ans = Math.max(ans, cnt + dfs(nxt, i + 1));
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}
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}
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return f[seat][i] = ans;
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int maxStudents(vector<vector<char>>& seats) {
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int m = seats.size();
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int n = seats[0].size();
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vector<int> ss(m);
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vector<vector<int>> f(1 << n, vector<int>(m, -1));
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for (int i = 0; i < m; ++i) {
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for (int j = 0; j < n; ++j) {
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if (seats[i][j] == '.') {
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ss[i] |= 1 << j;
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}
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}
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}
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function<int(int, int)> dfs = [&](int seat, int i) -> int {
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if (f[seat][i] != -1) {
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return f[seat][i];
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}
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int ans = 0;
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for (int mask = 0; mask < 1 << n; ++mask) {
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if ((seat | mask) != seat || (mask & (mask << 1)) != 0) {
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continue;
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}
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int cnt = __builtin_popcount(mask);
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if (i == m - 1) {
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ans = max(ans, cnt);
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} else {
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int nxt = ss[i + 1];
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nxt &= ~(mask >> 1);
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nxt &= ~(mask << 1);
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ans = max(ans, cnt + dfs(nxt, i + 1));
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}
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}
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return f[seat][i] = ans;
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};
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return dfs(ss[0], 0);
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}
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};
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```
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### **Go**
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```go
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func maxStudents(seats [][]byte) int {
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m, n := len(seats), len(seats[0])
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ss := make([]int, m)
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f := make([][]int, 1<<n)
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for i, seat := range seats {
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for j, c := range seat {
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if c == '.' {
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ss[i] |= 1 << j
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}
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}
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}
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for i := range f {
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f[i] = make([]int, m)
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for j := range f[i] {
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f[i][j] = -1
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}
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}
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var dfs func(int, int) int
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dfs = func(seat, i int) int {
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if f[seat][i] != -1 {
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return f[seat][i]
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}
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ans := 0
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for mask := 0; mask < 1<<n; mask++ {
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if (seat|mask) != seat || (mask&(mask<<1)) != 0 {
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continue
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}
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cnt := bits.OnesCount(uint(mask))
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if i == m-1 {
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ans = max(ans, cnt)
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} else {
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nxt := ss[i+1] & ^(mask >> 1) & ^(mask << 1)
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ans = max(ans, cnt+dfs(nxt, i+1))
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}
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}
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f[seat][i] = ans
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return ans
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}
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return dfs(ss[0], 0)
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}
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func max(a, b int) int {
232+
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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### **...**

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