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feat: add solutions to lc problem: No.1994
No.1994.The Number of Good Subsets
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‎solution/1900-1999/1994.The Number of Good Subsets/README.md

Lines changed: 141 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -61,22 +61,162 @@
6161

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<!-- 这里可写通用的实现逻辑 -->
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状态压缩 DP。
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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
71-
73+
class Solution:
74+
def numberOfGoodSubsets(self, nums: List[int]) -> int:
75+
counter = Counter(nums)
76+
mod = 10**9 + 7
77+
prime = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
78+
n = len(prime)
79+
dp = [0] * (1 << n)
80+
dp[0] = 1
81+
for x in range(2, 31):
82+
if counter[x] == 0 or x % 4 == 0 or x % 9 == 0 or x % 25 == 0:
83+
continue
84+
mask = 0
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for i, p in enumerate(prime):
86+
if x % p == 0:
87+
mask |= (1 << i)
88+
for state in range(1 << n):
89+
if mask & state:
90+
continue
91+
dp[mask | state] = (dp[mask | state] + counter[x] * dp[state]) % mod
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ans = 0
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for i in range(1, 1 << n):
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ans = (ans + dp[i]) % mod
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for i in range(counter[1]):
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ans = (ans << 1) % mod
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return ans
7298
```
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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 static final int MOD = (int) 1e9 + 7;
107+
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public int numberOfGoodSubsets(int[] nums) {
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int[] counter = new int[31];
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for (int x : nums) {
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++counter[x];
112+
}
113+
int[] prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29};
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int n = prime.length;
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long[] dp = new long[1 << n];
116+
dp[0] = 1;
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for (int x = 2; x <= 30; ++x) {
118+
if (counter[x] == 0 || x % 4 == 0 || x % 9 == 0 || x % 25 == 0) {
119+
continue;
120+
}
121+
int mask = 0;
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for (int i = 0; i < n; ++i) {
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if (x % prime[i] == 0) {
124+
mask |= (1 << i);
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}
126+
}
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for (int state = 0; state < 1 << n; ++state) {
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if ((mask & state) > 0) {
129+
continue;
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}
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dp[mask | state] = (dp[mask | state] + counter[x] * dp[state]) % MOD;
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}
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}
134+
long ans = 0;
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for (int i = 1; i < 1 << n; ++i) {
136+
ans = (ans + dp[i]) % MOD;
137+
}
138+
while (counter[1]-- > 0) {
139+
ans = (ans << 1) % MOD;
140+
}
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return (int) ans;
142+
}
143+
}
144+
```
145+
146+
### **C++**
147+
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```cpp
149+
class Solution {
150+
public:
151+
int numberOfGoodSubsets(vector<int>& nums) {
152+
vector<int> counter(31);
153+
for (int& x : nums) ++counter[x];
154+
vector<int> prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29};
155+
const int MOD = 1e9 + 7;
156+
int n = prime.size();
157+
vector<long long> dp(1 << n);
158+
dp[0] = 1;
159+
for (int x = 2; x <= 30; ++x)
160+
{
161+
if (counter[x] == 0 || x % 4 == 0 || x % 9 == 0 || x % 25 == 0) continue;
162+
int mask = 0;
163+
for (int i = 0; i < n; ++i)
164+
if (x % prime[i] == 0)
165+
mask |= (1 << i);
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for (int state = 0; state < 1 << n; ++state)
167+
{
168+
if ((mask & state) > 0) continue;
169+
dp[mask | state] = (dp[mask | state] + counter[x] * dp[state]) % MOD;
170+
}
171+
}
172+
long long ans = 0;
173+
for (int i = 1; i < 1 << n; ++i) ans = (ans + dp[i]) % MOD;
174+
while (counter[1]--) ans = (ans << 1) % MOD;
175+
return (int) ans;
176+
}
177+
};
178+
```
79179
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### **Go**
181+
182+
```go
183+
func numberOfGoodSubsets(nums []int) int {
184+
counter := make([]int, 31)
185+
for _, x := range nums {
186+
counter[x]++
187+
}
188+
const mod int = 1e9 + 7
189+
prime := []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
190+
n := len(prime)
191+
dp := make([]int, 1<<n)
192+
dp[0] = 1
193+
for x := 2; x <= 30; x++ {
194+
if counter[x] == 0 || x%4 == 0 || x%9 == 0 || x%25 == 0 {
195+
continue
196+
}
197+
mask := 0
198+
for i, p := range prime {
199+
if x%p == 0 {
200+
mask |= (1 << i)
201+
}
202+
}
203+
for state := 0; state < 1<<n; state++ {
204+
if (mask & state) > 0 {
205+
continue
206+
}
207+
dp[mask|state] = (dp[mask|state] + counter[x]*dp[state]) % mod
208+
}
209+
}
210+
ans := 0
211+
for i := 1; i < 1<<n; i++ {
212+
ans = (ans + dp[i]) % mod
213+
}
214+
for counter[1] > 0 {
215+
ans = (ans << 1) % mod
216+
counter[1]--
217+
}
218+
return ans
219+
}
80220
```
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### **...**

‎solution/1900-1999/1994.The Number of Good Subsets/README_EN.md

Lines changed: 139 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -62,13 +62,151 @@
6262
### **Python3**
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```python
65-
65+
class Solution:
66+
def numberOfGoodSubsets(self, nums: List[int]) -> int:
67+
counter = Counter(nums)
68+
mod = 10**9 + 7
69+
prime = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
70+
n = len(prime)
71+
dp = [0] * (1 << n)
72+
dp[0] = 1
73+
for x in range(2, 31):
74+
if counter[x] == 0 or x % 4 == 0 or x % 9 == 0 or x % 25 == 0:
75+
continue
76+
mask = 0
77+
for i, p in enumerate(prime):
78+
if x % p == 0:
79+
mask |= (1 << i)
80+
for state in range(1 << n):
81+
if mask & state:
82+
continue
83+
dp[mask | state] = (dp[mask | state] + counter[x] * dp[state]) % mod
84+
ans = 0
85+
for i in range(1, 1 << n):
86+
ans = (ans + dp[i]) % mod
87+
for i in range(counter[1]):
88+
ans = (ans << 1) % mod
89+
return ans
6690
```
6791

6892
### **Java**
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7094
```java
95+
class Solution {
96+
private static final int MOD = (int) 1e9 + 7;
97+
98+
public int numberOfGoodSubsets(int[] nums) {
99+
int[] counter = new int[31];
100+
for (int x : nums) {
101+
++counter[x];
102+
}
103+
int[] prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29};
104+
int n = prime.length;
105+
long[] dp = new long[1 << n];
106+
dp[0] = 1;
107+
for (int x = 2; x <= 30; ++x) {
108+
if (counter[x] == 0 || x % 4 == 0 || x % 9 == 0 || x % 25 == 0) {
109+
continue;
110+
}
111+
int mask = 0;
112+
for (int i = 0; i < n; ++i) {
113+
if (x % prime[i] == 0) {
114+
mask |= (1 << i);
115+
}
116+
}
117+
for (int state = 0; state < 1 << n; ++state) {
118+
if ((mask & state) > 0) {
119+
continue;
120+
}
121+
dp[mask | state] = (dp[mask | state] + counter[x] * dp[state]) % MOD;
122+
}
123+
}
124+
long ans = 0;
125+
for (int i = 1; i < 1 << n; ++i) {
126+
ans = (ans + dp[i]) % MOD;
127+
}
128+
while (counter[1]-- > 0) {
129+
ans = (ans << 1) % MOD;
130+
}
131+
return (int) ans;
132+
}
133+
}
134+
```
135+
136+
### **C++**
137+
138+
```cpp
139+
class Solution {
140+
public:
141+
int numberOfGoodSubsets(vector<int>& nums) {
142+
vector<int> counter(31);
143+
for (int& x : nums) ++counter[x];
144+
vector<int> prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29};
145+
const int MOD = 1e9 + 7;
146+
int n = prime.size();
147+
vector<long long> dp(1 << n);
148+
dp[0] = 1;
149+
for (int x = 2; x <= 30; ++x)
150+
{
151+
if (counter[x] == 0 || x % 4 == 0 || x % 9 == 0 || x % 25 == 0) continue;
152+
int mask = 0;
153+
for (int i = 0; i < n; ++i)
154+
if (x % prime[i] == 0)
155+
mask |= (1 << i);
156+
for (int state = 0; state < 1 << n; ++state)
157+
{
158+
if ((mask & state) > 0) continue;
159+
dp[mask | state] = (dp[mask | state] + counter[x] * dp[state]) % MOD;
160+
}
161+
}
162+
long long ans = 0;
163+
for (int i = 1; i < 1 << n; ++i) ans = (ans + dp[i]) % MOD;
164+
while (counter[1]--) ans = (ans << 1) % MOD;
165+
return (int) ans;
166+
}
167+
};
168+
```
71169
170+
### **Go**
171+
172+
```go
173+
func numberOfGoodSubsets(nums []int) int {
174+
counter := make([]int, 31)
175+
for _, x := range nums {
176+
counter[x]++
177+
}
178+
const mod int = 1e9 + 7
179+
prime := []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
180+
n := len(prime)
181+
dp := make([]int, 1<<n)
182+
dp[0] = 1
183+
for x := 2; x <= 30; x++ {
184+
if counter[x] == 0 || x%4 == 0 || x%9 == 0 || x%25 == 0 {
185+
continue
186+
}
187+
mask := 0
188+
for i, p := range prime {
189+
if x%p == 0 {
190+
mask |= (1 << i)
191+
}
192+
}
193+
for state := 0; state < 1<<n; state++ {
194+
if (mask & state) > 0 {
195+
continue
196+
}
197+
dp[mask|state] = (dp[mask|state] + counter[x]*dp[state]) % mod
198+
}
199+
}
200+
ans := 0
201+
for i := 1; i < 1<<n; i++ {
202+
ans = (ans + dp[i]) % mod
203+
}
204+
for counter[1] > 0 {
205+
ans = (ans << 1) % mod
206+
counter[1]--
207+
}
208+
return ans
209+
}
72210
```
73211

74212
### **...**

‎solution/1900-1999/1994.The Number of Good Subsets/Solution.cpp

Lines changed: 29 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,29 @@
1+
class Solution {
2+
public:
3+
int numberOfGoodSubsets(vector<int>& nums) {
4+
vector<int> counter(31);
5+
for (int& x : nums) ++counter[x];
6+
vector<int> prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29};
7+
const int MOD = 1e9 + 7;
8+
int n = prime.size();
9+
vector<long long> dp(1 << n);
10+
dp[0] = 1;
11+
for (int x = 2; x <= 30; ++x)
12+
{
13+
if (counter[x] == 0 || x % 4 == 0 || x % 9 == 0 || x % 25 == 0) continue;
14+
int mask = 0;
15+
for (int i = 0; i < n; ++i)
16+
if (x % prime[i] == 0)
17+
mask |= (1 << i);
18+
for (int state = 0; state < 1 << n; ++state)
19+
{
20+
if ((mask & state) > 0) continue;
21+
dp[mask | state] = (dp[mask | state] + counter[x] * dp[state]) % MOD;
22+
}
23+
}
24+
long long ans = 0;
25+
for (int i = 1; i < 1 << n; ++i) ans = (ans + dp[i]) % MOD;
26+
while (counter[1]--) ans = (ans << 1) % MOD;
27+
return (int) ans;
28+
}
29+
};

‎solution/1900-1999/1994.The Number of Good Subsets/Solution.go

Lines changed: 37 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,37 @@
1+
func numberOfGoodSubsets(nums []int) int {
2+
counter := make([]int, 31)
3+
for _, x := range nums {
4+
counter[x]++
5+
}
6+
const mod int = 1e9 + 7
7+
prime := []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
8+
n := len(prime)
9+
dp := make([]int, 1<<n)
10+
dp[0] = 1
11+
for x := 2; x <= 30; x++ {
12+
if counter[x] == 0 || x%4 == 0 || x%9 == 0 || x%25 == 0 {
13+
continue
14+
}
15+
mask := 0
16+
for i, p := range prime {
17+
if x%p == 0 {
18+
mask |= (1 << i)
19+
}
20+
}
21+
for state := 0; state < 1<<n; state++ {
22+
if (mask & state) > 0 {
23+
continue
24+
}
25+
dp[mask|state] = (dp[mask|state] + counter[x]*dp[state]) % mod
26+
}
27+
}
28+
ans := 0
29+
for i := 1; i < 1<<n; i++ {
30+
ans = (ans + dp[i]) % mod
31+
}
32+
for counter[1] > 0 {
33+
ans = (ans << 1) % mod
34+
counter[1]--
35+
}
36+
return ans
37+
}

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