Given an integer **N, **the task is to find the product of proper divisors of the number modulo 109 + 7 for Q queries.
Examples:
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_
Approach: The idea is to pre-compute and store product of proper divisors of elements with the help of Sieve of Eratosthenes.
Below is the implementation of the above approach:
- C++
- Python3
// C++ implementation of
// the above approach
#include <bits/stdc++.h>
#define ll long long int
#define mod 1000000007
**using** **namespace** std;
vector<ll> 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;
}
Output:
2, 6, 8, 64, 279936,
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#arrays #mathematical #school programming #array-range-queries #divisors
