A prime is a positive integer X that has exactly two distinct divisors: 1 and X. The first few prime integers are 2, 3, 5, 7, 11 and 13.
A prime D is called a prime divisor of a positive integer P if there exists a positive integer K such that D * K = P. For example, 2 and 5 are prime divisors of 20.
You are given two positive integers N and M. The goal is to check whether the sets of prime divisors of integers N and M are exactly the same.
For example, given:
- N = 15 and M = 75, the prime divisors are the same: {3, 5};
- N = 10 and M = 30, the prime divisors aren't the same: {2, 5} is not equal to {2, 3, 5};
- N = 9 and M = 5, the prime divisors aren't the same: {3} is not equal to {5}.
Write a function:
class Solution { public int solution(int[] A, int[] B); }
that, given two non-empty arrays A and B of Z integers, returns the number of positions K for which the prime divisors of A[K] and B[K] are exactly the same.
For example, given:
A[0] = 15 B[0] = 75 A[1] = 10 B[1] = 30 A[2] = 3 B[2] = 5the function should return 1, because only one pair (15, 75) has the same set of prime divisors.
Write an efficient algorithm for the following assumptions:
- Z is an integer within the range [1..6,000];
- each element of arrays A and B is an integer within the range [1..2,147,483,647].
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A, int[] B) {
int result = 0;
for (int i = 0; i < A.length; i++) {
if (A[i] == B[i]) {
result +=1;
continue;
}
int gcd = gcdBinary(A[i], B[i], 1);
int a = A[i] / gcd;
int b = B[i] / gcd;
if (gcd % a == 0 && gcd % b == 0) result += 1;
else if (A[i] > B[i] && A[i] % b == 0) result += 1;
else if (A[i] < B[i] && B[i] % a == 0) result += 1;
}
return result;
}
private int gcdBinary(int a, int b, int res) {
if (a == b) return res * a;
else if (a % 2 == 0 && b % 2 == 0) return gcdBinary(a >> 1, b >> 1, 2 * res);
else if (a % 2 == 0) return gcdBinary(a >> 1, b, res);
else if (b % 2 == 0) return gcdBinary(a, b >> 1, res);
else if (a > b) return gcdBinary(a - b, b, res);
else return gcdBinary(a, b - a, res);
}
}
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A, int[] B) {
int result = 0;
for (int i = 0; i < A.length; i++) {
if (A[i] == B[i]) {
result +=1;
continue;
}
if (compute(A[i], B[i]) && compute(B[i], A[i])) result += 1;
}
return result;
}
private boolean compute(int a, int b) {
if (b%a == 0) return true;
int gcd = gcdBinary(a, b, 1);
if (gcd == 1) return false;
return compute(a/gcd, b);
}
private int gcdBinary(int a, int b, int res) {
if (a == b) return res * a;
else if (a % 2 == 0 && b % 2 == 0) return gcdBinary(a >> 1, b >> 1, 2 * res);
else if (a % 2 == 0) return gcdBinary(a >> 1, b, res);
else if (b % 2 == 0) return gcdBinary(a, b >> 1, res);
else if (a > b) return gcdBinary(a - b, b, res);
else return gcdBinary(a, b - a, res);
}
}
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A, int[] B) {
int result = 0;
for (int i = 0; i < A.length; i++) {
if (A[i] == B[i]) {
result +=1;
continue;
}
if (compute(A[i], B[i]) && compute(B[i], A[i])) result += 1;
}
return result;
}
private boolean compute(int a, int b) {
if (b%a == 0) return true;
int gcd = gcdBinary(a, b, 1);
if (gcd == 1) return false;
return compute(a/gcd, b);
}
private int gcdBinary(int a, int b, int res) {
if (a == b) return res * a;
else if (a % 2 == 0 && b % 2 == 0) return gcdBinary(a >> 1, b >> 1, 2 * res);
else if (a % 2 == 0) return gcdBinary(a >> 1, b, res);
else if (b % 2 == 0) return gcdBinary(a, b >> 1, res);
else if (a > b) return gcdBinary(a - b, b, res);
else return gcdBinary(a, b - a, res);
}
}
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] A, int[] B) {
int result = 0;
for (int i = 0; i < A.length; i++) {
if (A[i] == B[i]) {
result +=1;
continue;
}
if (compute(A[i], B[i]) && compute(B[i], A[i])) result += 1;
}
return result;
}
private boolean compute(int a, int b) {
if (b%a == 0) return true;
int gcd = gcdBinary(a, b, 1);
if (gcd == 1) return false;
return compute(a/gcd, b);
}
private int gcdBinary(int a, int b, int res) {
if (a == b) return res * a;
else if (a % 2 == 0 && b % 2 == 0) return gcdBinary(a >> 1, b >> 1, 2 * res);
else if (a % 2 == 0) return gcdBinary(a >> 1, b, res);
else if (b % 2 == 0) return gcdBinary(a, b >> 1, res);
else if (a > b) return gcdBinary(a - b, b, res);
else return gcdBinary(a, b - a, res);
}
}
The solution obtained perfect score.