Skip to content

Navigation Menu

Sign in
Appearance settings

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly
Sign up
Appearance settings

Commit 77d2ea0

Browse files
committed
feat: update solutions to lc problem: No.0204
No.0204.Count Primes
1 parent c3636ba commit 77d2ea0

File tree

12 files changed

+380
-117
lines changed

12 files changed

+380
-117
lines changed

‎solution/0200-0299/0204.Count Primes/README.md‎

Lines changed: 102 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -44,11 +44,13 @@
4444

4545
<!-- 这里可写通用的实现逻辑 -->
4646

47-
如果 x 是质数,那么大于 x 的 x 的倍数 2x,3x,... 一定不是质数,因此我们可以从这里入手。
47+
**方法一:埃氏筛**
4848

49-
我们设 `primes[i]` 表示数 i 是不是质数,如果是质数则为 true,否则为 false。从小到大遍历每个数,如果这个数为质数,则将其所有的倍数都标记为合数(除了该质数本身),即 false,这样在运行结束的时候我们即能知道质数的个数。
49+
如果 $x$ 是质数,那么大于 $x$ 的 $x$ 的倍数 2ドルx,ドル3ドルx,ドル... 一定不是质数,因此我们可以从这里入手。
5050

51-
对于一个质数 x,我们从 2x 开始标记其实是冗余的,应该直接从 x⋅x 开始标记,因为 2x,3x,... 这些数一定在 x 之前就被其他数的倍数标记过了,例如 2 的所有倍数,3 的所有倍数等。
51+
我们设 $primes[i]$ 表示数 $i$ 是不是质数,如果是质数则为 $true,ドル否则为 $false$。从小到大遍历每个数,如果这个数为质数,则将其所有的倍数都标记为合数(除了该质数本身),即 $false,ドル这样在运行结束的时候我们即能知道质数的个数。
52+
53+
时间复杂度 $O(nloglogn)$。
5254

5355
<!-- tabs:start -->
5456

@@ -59,16 +61,14 @@
5961
```python
6062
class Solution:
6163
def countPrimes(self, n: int) -> int:
62-
if n < 2:
63-
return 0
64-
res = 0
65-
primes = [True for _ in range(n)]
64+
primes = [True] * n
65+
ans = 0
6666
for i in range(2, n):
6767
if primes[i]:
68-
res += 1
69-
for j in range(i * i, n, i):
68+
ans += 1
69+
for j in range(i + i, n, i):
7070
primes[j] = False
71-
return res
71+
return ans
7272
```
7373

7474
### **Java**
@@ -78,21 +78,105 @@ class Solution:
7878
```java
7979
class Solution {
8080
public int countPrimes(int n) {
81-
if (n < 2) return 0;
8281
boolean[] primes = new boolean[n];
8382
Arrays.fill(primes, true);
84-
int res = 0;
83+
int ans = 0;
8584
for (int i = 2; i < n; ++i) {
8685
if (primes[i]) {
87-
++res;
88-
if ((long) i * i < n) {
89-
for (int j = i * i; j < n; j += i) {
90-
primes[j] = false;
91-
}
86+
++ans;
87+
for (int j = i + i; j < n; j += i) {
88+
primes[j] = false;
89+
}
90+
}
91+
}
92+
return ans;
93+
}
94+
}
95+
```
96+
97+
### **C++**
98+
99+
```cpp
100+
class Solution {
101+
public:
102+
int countPrimes(int n) {
103+
vector<bool> primes(n, true);
104+
int ans = 0;
105+
for (int i = 2; i < n; ++i)
106+
{
107+
if (primes[i])
108+
{
109+
++ans;
110+
for (int j = i + i; j < n; j += i) primes[j] = false;
111+
}
112+
}
113+
return ans;
114+
}
115+
};
116+
```
117+
118+
### **Go**
119+
120+
```go
121+
func countPrimes(n int) int {
122+
primes := make([]bool, n)
123+
for i := range primes {
124+
primes[i] = true
125+
}
126+
ans := 0
127+
for i := 2; i < n; i++ {
128+
if primes[i] {
129+
ans++
130+
for j := i + i; j < n; j += i {
131+
primes[j] = false
132+
}
133+
}
134+
}
135+
return ans
136+
}
137+
```
138+
139+
### **JavaScript**
140+
141+
```js
142+
/**
143+
* @param {number} n
144+
* @return {number}
145+
*/
146+
var countPrimes = function (n) {
147+
let primes = new Array(n).fill(true);
148+
let ans = 0;
149+
for (let i = 2; i < n; ++i) {
150+
if (primes[i]) {
151+
++ans;
152+
for (let j = i + i; j < n; j += i) {
153+
primes[j] = false;
154+
}
155+
}
156+
}
157+
return ans;
158+
};
159+
```
160+
161+
### **C#**
162+
163+
```cs
164+
public class Solution {
165+
public int CountPrimes(int n) {
166+
var notPrimes = new bool[n];
167+
int ans = 0;
168+
for (int i = 2; i < n; ++i)
169+
{
170+
if (!notPrimes[i])
171+
{
172+
++ans;
173+
for (int j = i + i; j < n; j += i)
174+
{
175+
notPrimes[j] = true;
92176
}
93177
}
94178
}
95-
return res;
179+
return ans;
96180
}
97181
}
98182
```

‎solution/0200-0299/0204.Count Primes/README_EN.md‎

Lines changed: 97 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -45,38 +45,120 @@
4545
```python
4646
class Solution:
4747
def countPrimes(self, n: int) -> int:
48-
if n < 2:
49-
return 0
50-
res = 0
51-
primes = [True for _ in range(n)]
48+
primes = [True] * n
49+
ans = 0
5250
for i in range(2, n):
5351
if primes[i]:
54-
res += 1
55-
for j in range(i * i, n, i):
52+
ans += 1
53+
for j in range(i + i, n, i):
5654
primes[j] = False
57-
return res
55+
return ans
5856
```
5957

6058
### **Java**
6159

6260
```java
6361
class Solution {
6462
public int countPrimes(int n) {
65-
if (n < 2) return 0;
6663
boolean[] primes = new boolean[n];
6764
Arrays.fill(primes, true);
68-
int res = 0;
65+
int ans = 0;
6966
for (int i = 2; i < n; ++i) {
7067
if (primes[i]) {
71-
++res;
72-
if ((long) i * i < n) {
73-
for (int j = i * i; j < n; j += i) {
74-
primes[j] = false;
75-
}
68+
++ans;
69+
for (int j = i + i; j < n; j += i) {
70+
primes[j] = false;
7671
}
7772
}
7873
}
79-
return res;
74+
return ans;
75+
}
76+
}
77+
```
78+
79+
### **C++**
80+
81+
```cpp
82+
class Solution {
83+
public:
84+
int countPrimes(int n) {
85+
vector<bool> primes(n, true);
86+
int ans = 0;
87+
for (int i = 2; i < n; ++i)
88+
{
89+
if (primes[i])
90+
{
91+
++ans;
92+
for (int j = i + i; j < n; j += i) primes[j] = false;
93+
}
94+
}
95+
return ans;
96+
}
97+
};
98+
```
99+
100+
### **Go**
101+
102+
```go
103+
func countPrimes(n int) int {
104+
primes := make([]bool, n)
105+
for i := range primes {
106+
primes[i] = true
107+
}
108+
ans := 0
109+
for i := 2; i < n; i++ {
110+
if primes[i] {
111+
ans++
112+
for j := i + i; j < n; j += i {
113+
primes[j] = false
114+
}
115+
}
116+
}
117+
return ans
118+
}
119+
```
120+
121+
### **JavaScript**
122+
123+
```js
124+
/**
125+
* @param {number} n
126+
* @return {number}
127+
*/
128+
var countPrimes = function (n) {
129+
let primes = new Array(n).fill(true);
130+
let ans = 0;
131+
for (let i = 2; i < n; ++i) {
132+
if (primes[i]) {
133+
++ans;
134+
for (let j = i + i; j < n; j += i) {
135+
primes[j] = false;
136+
}
137+
}
138+
}
139+
return ans;
140+
};
141+
```
142+
143+
### **C#**
144+
145+
```cs
146+
public class Solution {
147+
public int CountPrimes(int n) {
148+
var notPrimes = new bool[n];
149+
int ans = 0;
150+
for (int i = 2; i < n; ++i)
151+
{
152+
if (!notPrimes[i])
153+
{
154+
++ans;
155+
for (int j = i + i; j < n; j += i)
156+
{
157+
notPrimes[j] = true;
158+
}
159+
}
160+
}
161+
return ans;
80162
}
81163
}
82164
```
Lines changed: 12 additions & 25 deletions
Original file line numberDiff line numberDiff line change
@@ -1,29 +1,16 @@
11
class Solution {
2-
public:
3-
4-
vector<int> primes;
5-
6-
int isPrime(int num){
7-
8-
int i = 1;
9-
while( i < primes.size() && sqrt(num) >= primes[i] ){
10-
if( num % primes[i] == 0 ) return 0;
11-
i++;
12-
}
13-
return 1;
14-
}
15-
2+
public:
163
int countPrimes(int n) {
17-
18-
if( n <= 2 ) return 0;
19-
20-
primes.push_back(2);
21-
22-
for(int i = 3; i < n; i += 2){
23-
if( isPrime(i) )
24-
primes.push_back(i);
4+
vector<bool> primes(n, true);
5+
int ans = 0;
6+
for (int i = 2; i < n; ++i)
7+
{
8+
if (primes[i])
9+
{
10+
++ans;
11+
for (int j = i; j < n; j += i) primes[j] = false;
12+
}
2513
}
26-
27-
return primes.size();
14+
return ans;
2815
}
29-
};
16+
};
Lines changed: 8 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -1,18 +1,18 @@
11
public class Solution {
22
public int CountPrimes(int n) {
3-
var count = 0;
4-
varnotPrime = newbool[n];
5-
for (var i = 2; i < n; ++i)
3+
var notPrimes = newbool[n];
4+
intans = 0;
5+
for (int i = 2; i < n; ++i)
66
{
7-
if (!notPrime[i])
7+
if (!notPrimes[i])
88
{
9-
++count;
10-
for (var j = i + i; j < n; j += i)
9+
++ans;
10+
for (int j = i + i; j < n; j += i)
1111
{
12-
notPrime[j] = true;
12+
notPrimes[j] = true;
1313
}
1414
}
1515
}
16-
return count;
16+
return ans;
1717
}
1818
}
Lines changed: 16 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,16 @@
1+
func countPrimes(n int) int {
2+
primes := make([]bool, n)
3+
for i := range primes {
4+
primes[i] = true
5+
}
6+
ans := 0
7+
for i := 2; i < n; i++ {
8+
if primes[i] {
9+
ans++
10+
for j := i + i; j < n; j += i {
11+
primes[j] = false
12+
}
13+
}
14+
}
15+
return ans
16+
}

0 commit comments

Comments
(0)

AltStyle によって変換されたページ (->オリジナル) /