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Mar 23, 2023
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10 changes: 5 additions & 5 deletions solution/0800-0899/0879.Profitable Schemes/Solution.py
Original file line number Diff line number Diff line change
@@ -1,16 +1,16 @@
class Solution:
def profitableSchemes(self, n: int, minProfit: int, group: List[int], profit: List[int]) -> int:
def profitableSchemes(
self, n: int, minProfit: int, group: List[int], profit: List[int]
) -> int:
mod = 10**9 + 7
m = len(group)
f = [[[0] * (minProfit + 1) for _ in range(n + 1)]
for _ in range(m + 1)]
f = [[[0] * (minProfit + 1) for _ in range(n + 1)] for _ in range(m + 1)]
for j in range(n + 1):
f[0][j][0] = 1
for i, (x, p) in enumerate(zip(group, profit), 1):
for j in range(n + 1):
for k in range(minProfit + 1):
f[i][j][k] = f[i - 1][j][k]
if j >= x:
f[i][j][k] = (f[i][j][k] + f[i - 1]
[j - x][max(0, k - p)]) % mod
f[i][j][k] = (f[i][j][k] + f[i - 1][j - x][max(0, k - p)]) % mod
return f[m][n][minProfit]
Original file line number Diff line number Diff line change
Expand Up @@ -15,8 +15,7 @@ def dfs(pos: int, mask: int, lead: bool, limit: bool) -> int:
if i == 0 and lead:
ans += dfs(pos - 1, mask, lead, limit and i == up)
else:
ans += dfs(pos - 1, mask | 1 << i,
False, limit and i == up)
ans += dfs(pos - 1, mask | 1 << i, False, limit and i == up)
return ans

nums = []
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -64,22 +64,95 @@

<!-- 这里可写通用的实现逻辑 -->

**方法一:动态规划**

我们定义 $f[i][j]$ 表示将 $i$ 个糖果分配给 $j$ 个手袋的不同分配方式的数量。初始时 $f[0][0]=1$,答案为 $f[n][k]$。

我们考虑第 $i$ 个糖果如何分配,如果第 $i$ 个糖果分配给一个新的手袋,那么 $f[i][j]=f[i-1][j-1]$;如果第 $i$ 个糖果分配给一个已有的手袋,那么 $f[i][j]=f[i-1][j]\times j$。因此,状态转移方程为:

$$
f[i][j]=f[i-1][j-1]+f[i-1][j]\times j
$$

最终的答案为 $f[n][k]$。

时间复杂度 $O(n \times k)$,空间复杂度 $O(n \times k)$。其中 $n$ 和 $k$ 分别为糖果的数量和手袋的数量。

<!-- tabs:start -->

### **Python3**

<!-- 这里可写当前语言的特殊实现逻辑 -->

```python

class Solution:
def waysToDistribute(self, n: int, k: int) -> int:
mod = 10**9 + 7
f = [[0] * (k + 1) for _ in range(n + 1)]
f[0][0] = 1
for i in range(1, n + 1):
for j in range(1, k + 1):
f[i][j] = (f[i - 1][j] * j + f[i - 1][j - 1]) % mod
return f[n][k]
```

### **Java**

<!-- 这里可写当前语言的特殊实现逻辑 -->

```java
class Solution {
public int waysToDistribute(int n, int k) {
final int mod = (int) 1e9 + 7;
int[][] f = new int[n + 1][k + 1];
f[0][0] = 1;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= k; j++) {
f[i][j] = (int) ((long) f[i - 1][j] * j % mod + f[i - 1][j - 1]) % mod;
}
}
return f[n][k];
}
}
```

### **C++**

```cpp
class Solution {
public:
int waysToDistribute(int n, int k) {
const int mod = 1e9 + 7;
int f[n + 1][k + 1];
memset(f, 0, sizeof(f));
f[0][0] = 1;
for (int i = 1; i <= n; ++i) {
for (int j = 1; j <= k; ++j) {
f[i][j] = (1LL * f[i - 1][j] * j + f[i - 1][j - 1]) % mod;
}
}
return f[n][k];
}
};
```

### **Go**

```go
func waysToDistribute(n int, k int) int {
f := make([][]int, n+1)
for i := range f {
f[i] = make([]int, k+1)
}
f[0][0] = 1
const mod = 1e9 + 7
for i := 1; i <= n; i++ {
for j := 1; j <= k; j++ {
f[i][j] = (f[i-1][j]*j + f[i-1][j-1]) % mod
}
}
return f[n][k]
}
```

### **...**
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -63,13 +63,72 @@
### **Python3**

```python

class Solution:
def waysToDistribute(self, n: int, k: int) -> int:
mod = 10**9 + 7
f = [[0] * (k + 1) for _ in range(n + 1)]
f[0][0] = 1
for i in range(1, n + 1):
for j in range(1, k + 1):
f[i][j] = (f[i - 1][j] * j + f[i - 1][j - 1]) % mod
return f[n][k]
```

### **Java**

```java
class Solution {
public int waysToDistribute(int n, int k) {
final int mod = (int) 1e9 + 7;
int[][] f = new int[n + 1][k + 1];
f[0][0] = 1;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= k; j++) {
f[i][j] = (int) ((long) f[i - 1][j] * j % mod + f[i - 1][j - 1]) % mod;
}
}
return f[n][k];
}
}
```

### **C++**

```cpp
class Solution {
public:
int waysToDistribute(int n, int k) {
const int mod = 1e9 + 7;
int f[n + 1][k + 1];
memset(f, 0, sizeof(f));
f[0][0] = 1;
for (int i = 1; i <= n; ++i) {
for (int j = 1; j <= k; ++j) {
f[i][j] = (1LL * f[i - 1][j] * j + f[i - 1][j - 1]) % mod;
}
}
return f[n][k];
}
};
```

### **Go**

```go
func waysToDistribute(n int, k int) int {
f := make([][]int, n+1)
for i := range f {
f[i] = make([]int, k+1)
}
f[0][0] = 1
const mod = 1e9 + 7
for i := 1; i <= n; i++ {
for j := 1; j <= k; j++ {
f[i][j] = (f[i-1][j]*j + f[i-1][j-1]) % mod
}
}
return f[n][k]
}
```

### **...**
Expand Down
Original file line number Diff line number Diff line change
@@ -0,0 +1,15 @@
class Solution {
public:
int waysToDistribute(int n, int k) {
const int mod = 1e9 + 7;
int f[n + 1][k + 1];
memset(f, 0, sizeof(f));
f[0][0] = 1;
for (int i = 1; i <= n; ++i) {
for (int j = 1; j <= k; ++j) {
f[i][j] = (1LL * f[i - 1][j] * j + f[i - 1][j - 1]) % mod;
}
}
return f[n][k];
}
};
Original file line number Diff line number Diff line change
@@ -0,0 +1,14 @@
func waysToDistribute(n int, k int) int {
f := make([][]int, n+1)
for i := range f {
f[i] = make([]int, k+1)
}
f[0][0] = 1
const mod = 1e9 + 7
for i := 1; i <= n; i++ {
for j := 1; j <= k; j++ {
f[i][j] = (f[i-1][j]*j + f[i-1][j-1]) % mod
}
}
return f[n][k]
}
Original file line number Diff line number Diff line change
@@ -0,0 +1,13 @@
class Solution {
public int waysToDistribute(int n, int k) {
final int mod = (int) 1e9 + 7;
int[][] f = new int[n + 1][k + 1];
f[0][0] = 1;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= k; j++) {
f[i][j] = (int) ((long) f[i - 1][j] * j % mod + f[i - 1][j - 1]) % mod;
}
}
return f[n][k];
}
}
Original file line number Diff line number Diff line change
@@ -0,0 +1,9 @@
class Solution:
def waysToDistribute(self, n: int, k: int) -> int:
mod = 10**9 + 7
f = [[0] * (k + 1) for _ in range(n + 1)]
f[0][0] = 1
for i in range(1, n + 1):
for j in range(1, k + 1):
f[i][j] = (f[i - 1][j] * j + f[i - 1][j - 1]) % mod
return f[n][k]
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