给定三个整数L , R和P ,其中P为质数,任务是计算范围[L,R]中所有数的质数分解中P发生的次数。
例子:
Input: L = 2, R = 8, P = 2
Output: 7
Element | Prime Factors | Time 2 occurs |
---|---|---|
2 | 2 | 1 |
3 | 3 | 0 |
4 | 2 * 2 | 2 |
5 | 5 | 0 |
6 | 2 * 3 | 1 |
7 | 7 | 0 |
8 | 2 * 2 * 2 | 3 |
1 + 0 + 2 + 0 + 1 + 0 + 3 = 7
Input: L = 5, R = 25, P = 7
Output: 3
天真的方法:简单地遍历该范围,并为每个值计数P将该值除以多少次并将其求和得出结果。时间复杂度O(R – L) 。
下面是上述方法的实现:
C++
// C++ implementation of the approach
#include
using namespace std;
// Function to return the highest
// power of p that divides n
int countFactors(int n, int p)
{
int pwr = 0;
while (n > 0 && n % p == 0) {
n /= p;
pwr++;
}
return pwr;
}
// Function to return the count of times p
// appaers in the prime factors of the
// elements from the range [l, r]
int getCount(int l, int r, int p)
{
// To store the required count
int cnt = 0;
// For every element of the range
for (int i = l; i <= r; i++) {
// Add the highest power of
// p that divides i
cnt += countFactors(i, p);
}
return cnt;
}
// Driver code
int main()
{
int l = 2, r = 8, p = 2;
cout << getCount(l, r, p);
return 0;
}
Java
// Java implementation of the approach
class GFG
{
// Function to return the highest
// power of p that divides n
static int countFactors(int n, int p)
{
int pwr = 0;
while (n > 0 && n % p == 0)
{
n /= p;
pwr++;
}
return pwr;
}
// Function to return the count of times p
// appaers in the prime factors of the
// elements from the range [l, r]
static int getCount(int l, int r, int p)
{
// To store the required count
int cnt = 0;
// For every element of the range
for (int i = l; i <= r; i++)
{
// Add the highest power of
// p that divides i
cnt += countFactors(i, p);
}
return cnt;
}
// Driver code
public static void main(String[] args)
{
int l = 2, r = 8, p = 2;
System.out.println(getCount(l, r, p));
}
}
// This code is contributed by Rajput-Ji
Python3
# Python3 implementation of the approach
# Function to return the highest
# power of p that divides n
def countFactors(n, p) :
pwr = 0;
while (n > 0 and n % p == 0) :
n //= p;
pwr += 1;
return pwr;
# Function to return the count of times p
# appaers in the prime factors of the
# elements from the range [l, r]
def getCount(l, r, p) :
# To store the required count
cnt = 0;
# For every element of the range
for i in range(l, r + 1) :
# Add the highest power of
# p that divides i
cnt += countFactors(i, p);
return cnt;
# Driver code
if __name__ == "__main__" :
l = 2; r = 8; p = 2;
print(getCount(l, r, p));
# This code is contributed by AnkitRai01
C#
// C# implementation of the approach
using System;
class GFG
{
// Function to return the highest
// power of p that divides n
static int countFactors(int n, int p)
{
int pwr = 0;
while (n > 0 && n % p == 0)
{
n /= p;
pwr++;
}
return pwr;
}
// Function to return the count of times p
// appaers in the prime factors of the
// elements from the range [l, r]
static int getCount(int l, int r, int p)
{
// To store the required count
int cnt = 0;
// For every element of the range
for (int i = l; i <= r; i++)
{
// Add the highest power of
// p that divides i
cnt += countFactors(i, p);
}
return cnt;
}
// Driver code
public static void Main(String[] args)
{
int l = 2, r = 8, p = 2;
Console.WriteLine(getCount(l, r, p));
}
}
// This code is contributed by 29AjayKumar
Javascript
C++
// C++ implementation of the approach
#include
using namespace std;
// Function to return the count of times p
// appaers in the prime factors of the
// elements from the range [l, r]
int getCount(int l, int r, int p)
{
// To store the requried count
int cnt = 0;
int val = p;
while (1) {
// Number of values in the range [0, r]
// that are divisible by val
int a = r / val;
// Number of values in the range [0, l - 1]
// that are divisible by val
int b = (l - 1) / val;
// Increment the power of the val
val *= p;
// (a - b) is the count of numbers in the
// range [l, r] that are divisible by val
if (a - b) {
cnt += (a - b);
}
// No values that are divisible by val
// thus exiting from the loop
else
break;
}
return cnt;
}
// Driver code
int main()
{
int l = 2, r = 8, p = 2;
cout << getCount(l, r, p);
return 0;
}
Java
// Java implementation of the approach
import java.util.*;
class GFG
{
// Function to return the count of times p
// appaers in the prime factors of the
// elements from the range [l, r]
static int getCount(int l, int r, int p)
{
// To store the requried count
int cnt = 0;
int val = p;
while (true)
{
// Number of values in the range [0, r]
// that are divisible by val
int a = r / val;
// Number of values in the range [0, l - 1]
// that are divisible by val
int b = (l - 1) / val;
// Increment the power of the val
val *= p;
// (a - b) is the count of numbers in the
// range [l, r] that are divisible by val
if ((a - b) > 0)
{
cnt += (a - b);
}
// No values that are divisible by val
// thus exiting from the loop
else
break;
}
return cnt;
}
// Driver code
public static void main(String[] args)
{
int l = 2, r = 8, p = 2;
System.out.println(getCount(l, r, p));
}
}
// This code is contributed by 29AjayKumar
Python3
# Python3 implementation of the approach
# Function to return the count of times p
# appaers in the prime factors of the
# elements from the range [l, r]
def getCount(l, r, p):
# To store the requried count
cnt = 0;
val = p;
while (True):
# Number of values in the range [0, r]
# that are divisible by val
a = r // val;
# Number of values in the range [0, l - 1]
# that are divisible by val
b = (l - 1) // val;
# Increment the power of the val
val *= p;
# (a - b) is the count of numbers in the
# range [l, r] that are divisible by val
if (a - b):
cnt += (a - b);
# No values that are divisible by val
# thus exiting from the loop
else:
break;
return int(cnt);
# Driver Code
l = 2;
r = 8;
p = 2;
print(getCount(l, r, p));
# This code is contributed by princiraj
C#
// C# implementation of the approach
using System;
class GFG
{
// Function to return the count of times p
// appaers in the prime factors of the
// elements from the range [l, r]
static int getCount(int l, int r, int p)
{
// To store the requried count
int cnt = 0;
int val = p;
while (true)
{
// Number of values in the range [0, r]
// that are divisible by val
int a = r / val;
// Number of values in the range [0, l - 1]
// that are divisible by val
int b = (l - 1) / val;
// Increment the power of the val
val *= p;
// (a - b) is the count of numbers in the
// range [l, r] that are divisible by val
if ((a - b) > 0)
{
cnt += (a - b);
}
// No values that are divisible by val
// thus exiting from the loop
else
break;
}
return cnt;
}
// Driver code
public static void Main(String[] args)
{
int l = 2, r = 8, p = 2;
Console.WriteLine(getCount(l, r, p));
}
}
// This code is contributed by PrinciRaj1992
Javascript
输出:
7
有效方法:计算在[L,R]范围内被P,P 2 ,P 3 ,…,P x整除的值,其中x是P的最大幂,以使P x处在上限( P x ≤N )。每次迭代花费O(1)时间,因此时间复杂度变为O(x) ,其中x =(log(R)/ log(P)) 。
下面是上述方法的实现:
C++
// C++ implementation of the approach
#include
using namespace std;
// Function to return the count of times p
// appaers in the prime factors of the
// elements from the range [l, r]
int getCount(int l, int r, int p)
{
// To store the requried count
int cnt = 0;
int val = p;
while (1) {
// Number of values in the range [0, r]
// that are divisible by val
int a = r / val;
// Number of values in the range [0, l - 1]
// that are divisible by val
int b = (l - 1) / val;
// Increment the power of the val
val *= p;
// (a - b) is the count of numbers in the
// range [l, r] that are divisible by val
if (a - b) {
cnt += (a - b);
}
// No values that are divisible by val
// thus exiting from the loop
else
break;
}
return cnt;
}
// Driver code
int main()
{
int l = 2, r = 8, p = 2;
cout << getCount(l, r, p);
return 0;
}
Java
// Java implementation of the approach
import java.util.*;
class GFG
{
// Function to return the count of times p
// appaers in the prime factors of the
// elements from the range [l, r]
static int getCount(int l, int r, int p)
{
// To store the requried count
int cnt = 0;
int val = p;
while (true)
{
// Number of values in the range [0, r]
// that are divisible by val
int a = r / val;
// Number of values in the range [0, l - 1]
// that are divisible by val
int b = (l - 1) / val;
// Increment the power of the val
val *= p;
// (a - b) is the count of numbers in the
// range [l, r] that are divisible by val
if ((a - b) > 0)
{
cnt += (a - b);
}
// No values that are divisible by val
// thus exiting from the loop
else
break;
}
return cnt;
}
// Driver code
public static void main(String[] args)
{
int l = 2, r = 8, p = 2;
System.out.println(getCount(l, r, p));
}
}
// This code is contributed by 29AjayKumar
Python3
# Python3 implementation of the approach
# Function to return the count of times p
# appaers in the prime factors of the
# elements from the range [l, r]
def getCount(l, r, p):
# To store the requried count
cnt = 0;
val = p;
while (True):
# Number of values in the range [0, r]
# that are divisible by val
a = r // val;
# Number of values in the range [0, l - 1]
# that are divisible by val
b = (l - 1) // val;
# Increment the power of the val
val *= p;
# (a - b) is the count of numbers in the
# range [l, r] that are divisible by val
if (a - b):
cnt += (a - b);
# No values that are divisible by val
# thus exiting from the loop
else:
break;
return int(cnt);
# Driver Code
l = 2;
r = 8;
p = 2;
print(getCount(l, r, p));
# This code is contributed by princiraj
C#
// C# implementation of the approach
using System;
class GFG
{
// Function to return the count of times p
// appaers in the prime factors of the
// elements from the range [l, r]
static int getCount(int l, int r, int p)
{
// To store the requried count
int cnt = 0;
int val = p;
while (true)
{
// Number of values in the range [0, r]
// that are divisible by val
int a = r / val;
// Number of values in the range [0, l - 1]
// that are divisible by val
int b = (l - 1) / val;
// Increment the power of the val
val *= p;
// (a - b) is the count of numbers in the
// range [l, r] that are divisible by val
if ((a - b) > 0)
{
cnt += (a - b);
}
// No values that are divisible by val
// thus exiting from the loop
else
break;
}
return cnt;
}
// Driver code
public static void Main(String[] args)
{
int l = 2, r = 8, p = 2;
Console.WriteLine(getCount(l, r, p));
}
}
// This code is contributed by PrinciRaj1992
Java脚本
输出:
7
如果您希望与行业专家一起参加现场课程,请参阅《 Geeks现场课程》和《 Geeks现场课程美国》。