给定一个整数N,任务是为Q查询找到模数为10 9 + 7的适当除数的乘积。
例子:
Input: Q = 4, arr[] = { 4, 6, 8, 16 };
Output: 2 6 8 64
Explanation:
4 => 1, 2 = 1 * 2 = 2
6 => 1, 2, 3 = 1 * 2 * 3 = 6
8 => 1, 2, 4 = 1 * 2 * 4 = 8
16 => 1, 2, 4, 8 = 1 * 2 * 4 * 8 = 64
Input: arr[] = { 3, 6, 9, 12 }
Output: 1 6 3 144
方法:这个想法是在Eratosthenes的Sieve的帮助下预先计算和存储元素的适当除数的乘积。
下面是上述方法的实现:
C++
// C++ implementation of
// the above approach
#include
#define ll long long int
#define mod 1000000007
using namespace std;
vector ans(100002, 1);
// Function to precompute the product
// of proper divisors of a number at
// it's corresponding index
void preCompute()
{
for (int i = 2; i <= 100000 / 2; i++) {
for (int j = 2 * i; j <= 100000; j += i) {
ans[j] = (ans[j] * i) % mod;
}
}
}
int productOfProperDivi(int num)
{
// Returning the pre-computed
// values
return ans[num];
}
// Driver code
int main()
{
preCompute();
int queries = 5;
int a[queries] = { 4, 6, 8, 16, 36 };
for (int i = 0; i < queries; i++) {
cout << productOfProperDivi(a[i])
<< ", ";
}
return 0;
}
Java
// Java implementation of
// the above approach
import java.util.*;
class GFG
{
static final int mod = 1000000007;
static long[] ans = new long[100002];
// Function to precompute the product
// of proper divisors of a number at
// it's corresponding index
static void preCompute()
{
for (int i = 2; i <= 100000 / 2; i++)
{
for (int j = 2 * i; j <= 100000; j += i)
{
ans[j] = (ans[j] * i) % mod;
}
}
}
static long productOfProperDivi(int num)
{
// Returning the pre-computed
// values
return ans[num];
}
// Driver code
public static void main(String[] args)
{
Arrays.fill(ans, 1);
preCompute();
int queries = 5;
int[] a = { 4, 6, 8, 16, 36 };
for (int i = 0; i < queries; i++)
{
System.out.print(productOfProperDivi(a[i]) + ", ");
}
}
}
// This code is contributed by Rajput-Ji
Python3
# Python3 implementation of
# the above approach
mod = 1000000007
ans = [1] * (100002)
# Function to precompute the product
# of proper divisors of a number at
# it's corresponding index
def preCompute():
for i in range(2, 100000 // 2 + 1):
for j in range(2 * i, 100001, i):
ans[j] = (ans[j] * i) % mod
def productOfProperDivi(num):
# Returning the pre-computed
# values
return ans[num]
# Driver code
if __name__ == "__main__":
preCompute()
queries = 5
a = [ 4, 6, 8, 16, 36 ]
for i in range(queries):
print(productOfProperDivi(a[i]), end = ", ")
# This code is contributed by chitranayal
C#
// C# implementation of
// the above approach
using System;
class GFG{
static readonly int mod = 1000000007;
static long[] ans = new long[100002];
// Function to precompute the product
// of proper divisors of a number at
// it's corresponding index
static void preCompute()
{
for(int i = 2; i <= 100000 / 2; i++)
{
for(int j = 2 * i; j <= 100000; j += i)
{
ans[j] = (ans[j] * i) % mod;
}
}
}
static long productOfProperDivi(int num)
{
// Returning the pre-computed
// values
return ans[num];
}
// Driver code
public static void Main(String[] args)
{
for(int i = 0 ; i < 100002; i++)
ans[i] = 1;
preCompute();
int queries = 5;
int[] a = { 4, 6, 8, 16, 36 };
for(int i = 0; i < queries; i++)
{
Console.Write(productOfProperDivi(a[i]) + ", ");
}
}
}
// This code is contributed by Princi Singh
输出:
2, 6, 8, 64, 279936,