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feat: add solutions to lc problem: No.0568
No.0568.Maximum Vacation Days
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‎solution/0500-0599/0568.Maximum Vacation Days/README.md

Lines changed: 120 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -80,22 +80,141 @@ Ans = 7 + 7 + 7 = 21
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<!-- 这里可写通用的实现逻辑 -->
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**方法一：动态规划**
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我们定义 $f[k][j]$ 表示前 $k$ 周，且最后一周在城市 $j$ 休假的最长天数。初始时 $f[0][0]=0$，其它 $f[0][j]=-\infty$。答案为 $\max_{j=0}^{n-1} f[K][j]$。
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接下来，我们考虑如何计算 $f[k][j]$。对于当前这一周，我们可以枚举上一周所在的城市 $i$，城市 $i$ 可以和城市 $j$ 相等，那么 $f[k][j] = f[k-1][i]$；也可以和城市 $j$ 不相等，如果不相等，我们需要判断是否可以从城市 $i$ 飞到城市 $j$，如果可以，那么 $f[k][j] = max(f[k][j], f[k-1][i])$。最后，我们还需要加上这一周在城市 $j$ 休假的天数 $days[j][k-1]$。
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最终的答案即为 $\max_{j=0}^{n-1} f[K][j]$。
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时间复杂度 $O(K \times n^2)$，空间复杂度 $O(K \times n)$。其中 $K$ 和 $n$ 分别为周数和城市数。
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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 maxVacationDays(self, flights: List[List[int]], days: List[List[int]]) -> int:
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n = len(flights)
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K = len(days[0])
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f = [[-inf] * n for _ in range(K + 1)]
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f[0][0] = 0
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for k in range(1, K + 1):
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for j in range(n):
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f[k][j] = f[k - 1][j]
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for i in range(n):
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if flights[i][j]:
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f[k][j] = max(f[k][j], f[k - 1][i])
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f[k][j] += days[j][k - 1]
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return max(f[-1][j] for j in range(n))
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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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public int maxVacationDays(int[][] flights, int[][] days) {
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int n = flights.length;
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int K = days[0].length;
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final int inf = 1 << 30;
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int[][] f = new int[K + 1][n];
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for (var g : f) {
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Arrays.fill(g, -inf);
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}
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f[0][0] = 0;
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for (int k = 1; k <= K; ++k) {
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for (int j = 0; j < n; ++j) {
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f[k][j] = f[k - 1][j];
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for (int i = 0; i < n; ++i) {
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if (flights[i][j] == 1) {
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f[k][j] = Math.max(f[k][j], f[k - 1][i]);
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}
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}
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f[k][j] += days[j][k - 1];
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}
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}
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int ans = 0;
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for (int j = 0; j < n; ++j) {
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ans = Math.max(ans, f[K][j]);
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}
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return 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 maxVacationDays(vector<vector<int>>& flights, vector<vector<int>>& days) {
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int n = flights.size();
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int K = days[0].size();
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int f[K + 1][n];
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memset(f, -0x3f, sizeof(f));
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f[0][0] = 0;
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for (int k = 1; k <= K; ++k) {
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for (int j = 0; j < n; ++j) {
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f[k][j] = f[k - 1][j];
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for (int i = 0; i < n; ++i) {
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if (flights[i][j] == 1) {
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f[k][j] = max(f[k][j], f[k - 1][i]);
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}
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}
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f[k][j] += days[j][k - 1];
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}
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}
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int ans = 0;
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for (int j = 0; j < n; ++j) {
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ans = max(ans, f[K][j]);
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}
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return ans;
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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 maxVacationDays(flights [][]int, days [][]int) (ans int) {
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n, K := len(flights), len(days[0])
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f := make([][]int, K+1)
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for i := range f {
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f[i] = make([]int, n)
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for j := range f[i] {
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f[i][j] = -(1 << 30)
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}
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}
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f[0][0] = 0
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for k := 1; k <= K; k++ {
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for j := 0; j < n; j++ {
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f[k][j] = f[k-1][j]
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for i := 0; i < n; i++ {
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if flights[i][j] == 1 {
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f[k][j] = max(f[k][j], f[k-1][i])
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}
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}
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f[k][j] += days[j][k-1]
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}
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}
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for j := 0; j < n; j++ {
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ans = max(ans, f[K][j])
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}
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return
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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/0500-0599/0568.Maximum Vacation Days/README_EN.md

Lines changed: 110 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -80,13 +80,122 @@ Ans = 7 + 7 + 7 = 21
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### **Python3**
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```python
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class Solution:
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def maxVacationDays(self, flights: List[List[int]], days: List[List[int]]) -> int:
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n = len(flights)
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K = len(days[0])
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f = [[-inf] * n for _ in range(K + 1)]
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f[0][0] = 0
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for k in range(1, K + 1):
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for j in range(n):
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f[k][j] = f[k - 1][j]
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for i in range(n):
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if flights[i][j]:
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f[k][j] = max(f[k][j], f[k - 1][i])
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f[k][j] += days[j][k - 1]
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return max(f[-1][j] for j in range(n))
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```
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### **Java**
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```java
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class Solution {
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public int maxVacationDays(int[][] flights, int[][] days) {
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int n = flights.length;
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int K = days[0].length;
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final int inf = 1 << 30;
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int[][] f = new int[K + 1][n];
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for (var g : f) {
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Arrays.fill(g, -inf);
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}
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f[0][0] = 0;
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for (int k = 1; k <= K; ++k) {
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for (int j = 0; j < n; ++j) {
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f[k][j] = f[k - 1][j];
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for (int i = 0; i < n; ++i) {
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if (flights[i][j] == 1) {
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f[k][j] = Math.max(f[k][j], f[k - 1][i]);
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}
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}
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f[k][j] += days[j][k - 1];
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}
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}
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int ans = 0;
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for (int j = 0; j < n; ++j) {
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ans = Math.max(ans, f[K][j]);
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}
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return 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 maxVacationDays(vector<vector<int>>& flights, vector<vector<int>>& days) {
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int n = flights.size();
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int K = days[0].size();
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int f[K + 1][n];
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memset(f, -0x3f, sizeof(f));
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f[0][0] = 0;
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for (int k = 1; k <= K; ++k) {
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for (int j = 0; j < n; ++j) {
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f[k][j] = f[k - 1][j];
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for (int i = 0; i < n; ++i) {
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if (flights[i][j] == 1) {
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f[k][j] = max(f[k][j], f[k - 1][i]);
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}
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}
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f[k][j] += days[j][k - 1];
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}
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}
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int ans = 0;
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for (int j = 0; j < n; ++j) {
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ans = max(ans, f[K][j]);
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}
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return ans;
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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 maxVacationDays(flights [][]int, days [][]int) (ans int) {
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n, K := len(flights), len(days[0])
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f := make([][]int, K+1)
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for i := range f {
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f[i] = make([]int, n)
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for j := range f[i] {
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f[i][j] = -(1 << 30)
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}
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}
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f[0][0] = 0
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for k := 1; k <= K; k++ {
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for j := 0; j < n; j++ {
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f[k][j] = f[k-1][j]
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for i := 0; i < n; i++ {
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if flights[i][j] == 1 {
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f[k][j] = max(f[k][j], f[k-1][i])
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}
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}
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f[k][j] += days[j][k-1]
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}
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}
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for j := 0; j < n; j++ {
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ans = max(ans, f[K][j])
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}
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return
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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/0500-0599/0568.Maximum Vacation Days/Solution.cpp

Lines changed: 26 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,26 @@
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class Solution {
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public:
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int maxVacationDays(vector<vector<int>>& flights, vector<vector<int>>& days) {
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int n = flights.size();
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int K = days[0].size();
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int f[K + 1][n];
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memset(f, -0x3f, sizeof(f));
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f[0][0] = 0;
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for (int k = 1; k <= K; ++k) {
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for (int j = 0; j < n; ++j) {
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f[k][j] = f[k - 1][j];
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for (int i = 0; i < n; ++i) {
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if (flights[i][j] == 1) {
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f[k][j] = max(f[k][j], f[k - 1][i]);
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}
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}
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f[k][j] += days[j][k - 1];
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}
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}
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int ans = 0;
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for (int j = 0; j < n; ++j) {
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ans = max(ans, f[K][j]);
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}
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return ans;
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}
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};

‎solution/0500-0599/0568.Maximum Vacation Days/Solution.go

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,33 @@
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func maxVacationDays(flights [][]int, days [][]int) (ans int) {
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n, K := len(flights), len(days[0])
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f := make([][]int, K+1)
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for i := range f {
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f[i] = make([]int, n)
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for j := range f[i] {
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f[i][j] = -(1 << 30)
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}
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}
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f[0][0] = 0
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for k := 1; k <= K; k++ {
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for j := 0; j < n; j++ {
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f[k][j] = f[k-1][j]
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for i := 0; i < n; i++ {
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if flights[i][j] == 1 {
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f[k][j] = max(f[k][j], f[k-1][i])
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}
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}
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f[k][j] += days[j][k-1]
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}
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}
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for j := 0; j < n; j++ {
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ans = max(ans, f[K][j])
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}
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return
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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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}

‎solution/0500-0599/0568.Maximum Vacation Days/Solution.java

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@@ -0,0 +1,28 @@
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class Solution {
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public int maxVacationDays(int[][] flights, int[][] days) {
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int n = flights.length;
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int K = days[0].length;
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final int inf = 1 << 30;
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int[][] f = new int[K + 1][n];
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for (var g : f) {
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Arrays.fill(g, -inf);
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}
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f[0][0] = 0;
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for (int k = 1; k <= K; ++k) {
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for (int j = 0; j < n; ++j) {
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f[k][j] = f[k - 1][j];
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for (int i = 0; i < n; ++i) {
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if (flights[i][j] == 1) {
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f[k][j] = Math.max(f[k][j], f[k - 1][i]);
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}
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}
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f[k][j] += days[j][k - 1];
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}
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}
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int ans = 0;
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for (int j = 0; j < n; ++j) {
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ans = Math.max(ans, f[K][j]);
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}
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return ans;
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}
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}

‎solution/0500-0599/0568.Maximum Vacation Days/Solution.py

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class Solution:
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def maxVacationDays(self, flights: List[List[int]], days: List[List[int]]) -> int:
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n = len(flights)
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K = len(days[0])
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f = [[-inf] * n for _ in range(K + 1)]
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f[0][0] = 0
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for k in range(1, K + 1):
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for j in range(n):
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f[k][j] = f[k - 1][j]
10+
for i in range(n):
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if flights[i][j]:
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f[k][j] = max(f[k][j], f[k - 1][i])
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f[k][j] += days[j][k - 1]
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return max(f[-1][j] for j in range(n))

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