给定两个数字X和Y。任务是查找[X,Y]范围内(包括两个端点)的元素的数量,这些元素的除数最大。
例子:
Input: X = 2, Y = 9
Output: 2
6, 8 are numbers with the maximum number of divisors.
Input: X = 1, Y = 10
Output: 3
6, 8, 10 are numbers with the maximum number of divisors.
方法1:
- 逐一遍历从X到Y的所有元素。
- 查找每个元素的除数。
- 将除数的数量存储在数组中,并更新除数的最大数量(maxDivisors)。
- 遍历包含除数的数组,并计算等于maxDivisors的元素数。
- 返回计数。
下面是上述方法的实现:
C++
// C++ implementation of above approach
#include
using namespace std;
// Function to count the divisors
int countDivisors(int n)
{
int count = 0;
// Note that this loop runs till square root
for (int i = 1; i <= sqrt(n); i++) {
if (n % i == 0) {
// If divisors are equal, print only one
if (n / i == i)
count++;
else // Otherwise print both
count += 2;
}
}
return count;
}
// Function to count the number with
// maximum divisors
int MaximumDivisors(int X, int Y)
{
int maxDivisors = INT_MIN, result = 0;
// to store number of divisors
int arr[Y - X + 1];
// Traverse from X to Y
for (int i = X; i <= Y; i++) {
// Count the number of divisors of i
int Div = countDivisors(i);
// Store the value of div in an array
arr[i - X] = Div;
// Update the value of maxDivisors
maxDivisors = max(Div, maxDivisors);
}
// Traverse the array
for (int i = 0; i < (Y - X + 1); i++)
// Count the value equals to maxDivisors
if (arr[i] == maxDivisors)
result++;
return result;
}
// Driver Code
int main()
{
int X = 1, Y = 10;
// function call
cout << MaximumDivisors(X, Y) << endl;
return 0;
}
Java
// Java implementation of above approach
class GFG
{
// Function to count the divisors
static int countDivisors(int n)
{
int count = 0;
// Note that this loop
// runs till square root
for (int i = 1; i <= Math.sqrt(n); i++)
{
if (n % i == 0)
{
// If divisors are equal,
// print only one
if (n / i == i)
count++;
else // Otherwise print both
count += 2;
}
}
return count;
}
// Function to count the number
// with maximum divisors
static int MaximumDivisors(int X, int Y)
{
int maxDivisors = 0, result = 0;
// to store number of divisors
int[] arr = new int[Y - X + 1];
// Traverse from X to Y
for (int i = X; i <= Y; i++)
{
// Count the number of divisors of i
int Div = countDivisors(i);
// Store the value of div in an array
arr[i - X] = Div;
// Update the value of maxDivisors
maxDivisors = Math.max(Div, maxDivisors);
}
// Traverse the array
for (int i = 0; i < (Y - X + 1); i++)
// Count the value equals
// to maxDivisors
if (arr[i] == maxDivisors)
result++;
return result;
}
// Driver Code
public static void main(String[] args)
{
int X = 1, Y = 10;
// function call
System.out.println(MaximumDivisors(X, Y));
}
}
// This code is contributed
// by ChitraNayal
Python3
# from math module import everything
from math import *
# Python 3 implementation of above approach
# Function to count the divisors
def countDivisors(n) :
count = 0
# Note that this loop runs till square root
for i in range(1,int(sqrt(n)+1)) :
if n % i == 0 :
# If divisors are equal, print only one
if n / i == i :
count += 1
# Otherwise print both
else :
count += 2
return count
# Function to count the number with
# maximum divisors
def MaximumDivisors(X,Y) :
result = 0
maxDivisors = 0
# create list to store number of divisors
arr = []
# initialize with 0 upto length Y-X+1
for i in range(Y - X + 1) :
arr.append(0)
# Traverse from X to Y
for i in range(X,Y+1) :
# Count the number of divisors of i
Div = countDivisors(i)
# Store the value of div in an array
arr[i - X] = Div
# Update the value of maxDivisors
maxDivisors = max(Div,maxDivisors)
# Traverse the array
for i in range (Y - X + 1) :
# Count the value equals to maxDivisors
if arr[i] == maxDivisors :
result += 1
return result
# Driver code
if __name__ == "__main__" :
X, Y = 1, 10
# function call
print(MaximumDivisors(X,Y))
C#
// C# implementation of above approach
using System;
class GFG
{
// Function to count the divisors
static int countDivisors(int n)
{
int count = 0;
// Note that this loop
// runs till square root
for (int i = 1; i <= Math.Sqrt(n); i++)
{
if (n % i == 0)
{
// If divisors are equal,
// print only one
if (n / i == i)
count++;
else // Otherwise print both
count += 2;
}
}
return count;
}
// Function to count the number
// with maximum divisors
static int MaximumDivisors(int X, int Y)
{
int maxDivisors = 0, result = 0;
// to store number of divisors
int[] arr = new int[Y - X + 1];
// Traverse from X to Y
for (int i = X; i <= Y; i++)
{
// Count the number of divisors of i
int Div = countDivisors(i);
// Store the value of div in an array
arr[i - X] = Div;
// Update the value of maxDivisors
maxDivisors = Math.Max(Div, maxDivisors);
}
// Traverse the array
for (int i = 0; i < (Y - X + 1); i++)
// Count the value equals
// to maxDivisors
if (arr[i] == maxDivisors)
result++;
return result;
}
// Driver Code
public static void Main()
{
int X = 1, Y = 10;
// function call
Console.Write(MaximumDivisors(X, Y));
}
}
// This code is contributed
// by ChitraNayal
PHP
C++
// C++ implementation of above approach
#include
using namespace std;
// Function to count the elements
// with maximum number of divisors
int MaximumDivisors(int X, int Y)
{
// to store number of divisors
int arr[Y - X + 1];
// initialise with zero
memset(arr, 0, sizeof(arr));
// to store the maximum number of divisors
int mx = INT_MIN;
// to store required answer
int cnt = 0;
for (int i = 1; i * i <= Y; i++) {
int sq = i * i;
int first_divisible;
// Find the first divisible number
if ((X / i) * i >= X)
first_divisible = (X / i) * i;
else
first_divisible = (X / i + 1) * i;
// Count number of divisors
for (int j = first_divisible; j <= Y; j += i) {
if (j < sq)
continue;
else if (j == sq)
arr[j - X]++;
else
arr[j - X] += 2;
}
}
// Find number of elements with
// maximum number of divisors
for (int i = X; i <= Y; i++) {
if (arr[i - X] > mx) {
cnt = 1;
mx = arr[i - X];
}
else if (arr[i - X] == mx)
cnt++;
}
return cnt;
}
// Driver code
int main()
{
int X = 1, Y = 10;
cout << MaximumDivisors(X, Y) << endl;
return 0;
}
Java
// Java implementation of above approach
class GFG
{
// Function to count the elements
// with maximum number of divisors
static int MaximumDivisors(int X, int Y)
{
// to store number of divisors
int[] arr = new int[Y - X + 1];
// initialise with zero
for(int i = 0; i < arr.length; i++)
arr[i] = 0;
// to store the maximum
// number of divisors
int mx = 0;
// to store required answer
int cnt = 0;
for (int i = 1; i * i <= Y; i++)
{
int sq = i * i;
int first_divisible;
// Find the first divisible number
if ((X / i) * i >= X)
first_divisible = (X / i) * i;
else
first_divisible = (X / i + 1) * i;
// Count number of divisors
for (int j = first_divisible;
j <= Y; j += i)
{
if (j < sq)
continue;
else if (j == sq)
arr[j - X]++;
else
arr[j - X] += 2;
}
}
// Find number of elements with
// maximum number of divisors
for (int i = X; i <= Y; i++)
{
if (arr[i - X] > mx)
{
cnt = 1;
mx = arr[i - X];
}
else if (arr[i - X] == mx)
cnt++;
}
return cnt;
}
// Driver code
public static void main(String[] args)
{
int X = 1, Y = 10;
System.out.println(MaximumDivisors(X, Y));
}
}
// This code is contributed
// by ChitraNayal
Python 3
# Python 3 implementation of above approach
# Function to count the elements
# with maximum number of divisors
def MaximumDivisors(X, Y):
# to store number of divisors
# initialise with zero
arr = [0] * (Y - X + 1)
# to store the maximum
# number of divisors
mx = 0
# to store required answer
cnt = 0
i = 1
while i * i <= Y :
sq = i * i
# Find the first divisible number
if ((X // i) * i >= X) :
first_divisible = (X // i) * i
else:
first_divisible = (X // i + 1) * i
# Count number of divisors
for j in range(first_divisible, Y + 1, i):
if j < sq :
continue
elif j == sq :
arr[j - X] += 1
else:
arr[j - X] += 2
i += 1
# Find number of elements with
# maximum number of divisors
for i in range(X, Y + 1):
if arr[i - X] > mx :
cnt = 1
mx = arr[i - X]
elif arr[i - X] == mx :
cnt += 1
return cnt
# Driver code
if __name__ == "__main__":
X = 1
Y = 10
print(MaximumDivisors(X, Y))
# This code is contributed
# by ChitraNayal
C#
// C# implementation of above approach
using System;
class GFG
{
// Function to count the elements
// with maximum number of divisors
static int MaximumDivisors(int X, int Y)
{
// to store number of divisors
int[] arr = new int[Y - X + 1];
// initialise with zero
for(int i = 0; i < arr.Length; i++)
arr[i] = 0;
// to store the maximum
// number of divisors
int mx = 0;
// to store required answer
int cnt = 0;
for (int i = 1; i * i <= Y; i++)
{
int sq = i * i;
int first_divisible;
// Find the first divisible number
if ((X / i) * i >= X)
first_divisible = (X / i) * i;
else
first_divisible = (X / i + 1) * i;
// Count number of divisors
for (int j = first_divisible;
j <= Y; j += i)
{
if (j < sq)
continue;
else if (j == sq)
arr[j - X]++;
else
arr[j - X] += 2;
}
}
// Find number of elements with
// maximum number of divisors
for (int i = X; i <= Y; i++)
{
if (arr[i - X] > mx)
{
cnt = 1;
mx = arr[i - X];
}
else if (arr[i - X] == mx)
cnt++;
}
return cnt;
}
// Driver code
public static void Main()
{
int X = 1, Y = 10;
Console.Write(MaximumDivisors(X, Y));
}
}
// This code is contributed
// by ChitraNayal
PHP
= $X)
$first_divisible = ($X / $i) * $i;
else
$first_divisible = ($X / $i + 1) * $i;
// Count number of divisors
for ($j = $first_divisible;
$j < $Y; $j += $i)
{
if ($j < $sq)
continue;
else if ($j == $sq)
$arr[$j - $X]++;
else
$arr[$j - $X] += 2;
}
}
// Find number of elements with
// maximum number of divisors
for ($i = $X; $i <= $Y; $i++)
{
if ($arr[$i - $X] > $mx)
{
$cnt = 1;
$mx = $arr[$i - $X];
}
else if ($arr[$i - $X] == $mx)
$cnt++;
}
return $cnt;
}
// Driver code
$X = 1;
$Y = 10;
echo MaximumDivisors($X, $Y)."\n";
// This code is contributed
// by ChitraNayal
?>
输出:
3
方法2:
- 创建大小为Y-X + 1的数组,以将X的除数存储在arr [0]中,将X + 1的除数存储在arr [1]中,直到Y。
- 要获取从X到Y的所有数字的除数的数量,请运行两个循环(嵌套)。
- 运行从1到sqrt(Y)的外部循环。
- 运行从first_divisible到Y的内部循环。
- First_divisible是一个数字,它是第一个可被I(外循环)整除且大于或等于X的数字。
在这里,first_divisible是使用“查找最接近n且可被m整除的数”来计算的。然后找到该数字的除数。
下面是上述方法的实现:
C++
// C++ implementation of above approach
#include
using namespace std;
// Function to count the elements
// with maximum number of divisors
int MaximumDivisors(int X, int Y)
{
// to store number of divisors
int arr[Y - X + 1];
// initialise with zero
memset(arr, 0, sizeof(arr));
// to store the maximum number of divisors
int mx = INT_MIN;
// to store required answer
int cnt = 0;
for (int i = 1; i * i <= Y; i++) {
int sq = i * i;
int first_divisible;
// Find the first divisible number
if ((X / i) * i >= X)
first_divisible = (X / i) * i;
else
first_divisible = (X / i + 1) * i;
// Count number of divisors
for (int j = first_divisible; j <= Y; j += i) {
if (j < sq)
continue;
else if (j == sq)
arr[j - X]++;
else
arr[j - X] += 2;
}
}
// Find number of elements with
// maximum number of divisors
for (int i = X; i <= Y; i++) {
if (arr[i - X] > mx) {
cnt = 1;
mx = arr[i - X];
}
else if (arr[i - X] == mx)
cnt++;
}
return cnt;
}
// Driver code
int main()
{
int X = 1, Y = 10;
cout << MaximumDivisors(X, Y) << endl;
return 0;
}
Java
// Java implementation of above approach
class GFG
{
// Function to count the elements
// with maximum number of divisors
static int MaximumDivisors(int X, int Y)
{
// to store number of divisors
int[] arr = new int[Y - X + 1];
// initialise with zero
for(int i = 0; i < arr.length; i++)
arr[i] = 0;
// to store the maximum
// number of divisors
int mx = 0;
// to store required answer
int cnt = 0;
for (int i = 1; i * i <= Y; i++)
{
int sq = i * i;
int first_divisible;
// Find the first divisible number
if ((X / i) * i >= X)
first_divisible = (X / i) * i;
else
first_divisible = (X / i + 1) * i;
// Count number of divisors
for (int j = first_divisible;
j <= Y; j += i)
{
if (j < sq)
continue;
else if (j == sq)
arr[j - X]++;
else
arr[j - X] += 2;
}
}
// Find number of elements with
// maximum number of divisors
for (int i = X; i <= Y; i++)
{
if (arr[i - X] > mx)
{
cnt = 1;
mx = arr[i - X];
}
else if (arr[i - X] == mx)
cnt++;
}
return cnt;
}
// Driver code
public static void main(String[] args)
{
int X = 1, Y = 10;
System.out.println(MaximumDivisors(X, Y));
}
}
// This code is contributed
// by ChitraNayal
的Python 3
# Python 3 implementation of above approach
# Function to count the elements
# with maximum number of divisors
def MaximumDivisors(X, Y):
# to store number of divisors
# initialise with zero
arr = [0] * (Y - X + 1)
# to store the maximum
# number of divisors
mx = 0
# to store required answer
cnt = 0
i = 1
while i * i <= Y :
sq = i * i
# Find the first divisible number
if ((X // i) * i >= X) :
first_divisible = (X // i) * i
else:
first_divisible = (X // i + 1) * i
# Count number of divisors
for j in range(first_divisible, Y + 1, i):
if j < sq :
continue
elif j == sq :
arr[j - X] += 1
else:
arr[j - X] += 2
i += 1
# Find number of elements with
# maximum number of divisors
for i in range(X, Y + 1):
if arr[i - X] > mx :
cnt = 1
mx = arr[i - X]
elif arr[i - X] == mx :
cnt += 1
return cnt
# Driver code
if __name__ == "__main__":
X = 1
Y = 10
print(MaximumDivisors(X, Y))
# This code is contributed
# by ChitraNayal
C#
// C# implementation of above approach
using System;
class GFG
{
// Function to count the elements
// with maximum number of divisors
static int MaximumDivisors(int X, int Y)
{
// to store number of divisors
int[] arr = new int[Y - X + 1];
// initialise with zero
for(int i = 0; i < arr.Length; i++)
arr[i] = 0;
// to store the maximum
// number of divisors
int mx = 0;
// to store required answer
int cnt = 0;
for (int i = 1; i * i <= Y; i++)
{
int sq = i * i;
int first_divisible;
// Find the first divisible number
if ((X / i) * i >= X)
first_divisible = (X / i) * i;
else
first_divisible = (X / i + 1) * i;
// Count number of divisors
for (int j = first_divisible;
j <= Y; j += i)
{
if (j < sq)
continue;
else if (j == sq)
arr[j - X]++;
else
arr[j - X] += 2;
}
}
// Find number of elements with
// maximum number of divisors
for (int i = X; i <= Y; i++)
{
if (arr[i - X] > mx)
{
cnt = 1;
mx = arr[i - X];
}
else if (arr[i - X] == mx)
cnt++;
}
return cnt;
}
// Driver code
public static void Main()
{
int X = 1, Y = 10;
Console.Write(MaximumDivisors(X, Y));
}
}
// This code is contributed
// by ChitraNayal
的PHP
= $X)
$first_divisible = ($X / $i) * $i;
else
$first_divisible = ($X / $i + 1) * $i;
// Count number of divisors
for ($j = $first_divisible;
$j < $Y; $j += $i)
{
if ($j < $sq)
continue;
else if ($j == $sq)
$arr[$j - $X]++;
else
$arr[$j - $X] += 2;
}
}
// Find number of elements with
// maximum number of divisors
for ($i = $X; $i <= $Y; $i++)
{
if ($arr[$i - $X] > $mx)
{
$cnt = 1;
$mx = $arr[$i - $X];
}
else if ($arr[$i - $X] == $mx)
$cnt++;
}
return $cnt;
}
// Driver code
$X = 1;
$Y = 10;
echo MaximumDivisors($X, $Y)."\n";
// This code is contributed
// by ChitraNayal
?>
输出:
3