Project Euler Problem 47 Distinct primes factors

Distinct primes factors

Problem 47

The first two consecutive numbers to have two distinct prime factors are:

14 = 2 × 7

15 = 3 × 5
The first three consecutive numbers to have three distinct prime factors are:

644 = 2² × 7 × 23

645 = 3 × 5 × 43

646 = 2 × 17 × 19.
Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?

C++(Faster):

#include <iostream>
#include <cstring>
#include <cmath>
#include <vector>

using namespace std;

const int MAXN = 4000;
const int N = 1000000;

int prime[MAXN+2] = {2, 3, 5};

bool isprime(int n)
{
int q=sqrt(n), i=1;

while(prime[i] <= q)
if(n % prime[i] == 0)
return false;
else
i++;

return true;
}

void maketable(int n)
{
int val1 = 1, val5 = 5;

for(int i=3; i<=n;) {
val1 += 6;
if(isprime(val1))
prime[i++] = val1;

val5 += 6;
if(isprime(val5))
prime[i++] = val5;
}
}

int factorcount[N+1];

void setval(int start, int k, int count)
{
for(int i=start; i<=N; i*=k) {
if(i < 0)
break;
factorcount[i] = count;
}
}

int next(int start)
{
for(;;) {
while(factorcount[start])
start++;

if(factorcount[start+1] == 0 && factorcount[start+2] == 0 && factorcount[start+3] == 0)
break;

while(factorcount[start] == 0)
start++;
}

return start;
}

int fact(int n, int fact[])
{
int i=0, j=0;
while(n > 1) {
if(i > MAXN) {
fact[j++] = n;
break;
}
while(n % prime[i] == 0) {
fact[j] = prime[i];
n /= prime[i];
}
if(fact[j])
j++;
i++;
}
return j;
}

int main()
{
vector<int> v;
int factor[64];

maketable(MAXN);

memset(factorcount, 0, sizeof(factorcount));

for(int i=0; i<=MAXN; i++)
setval(prime[i], prime[i], 1);

int i = 2, count;
i = next(i);
for(; i<N-4;) {
memset(factor, 0, sizeof(factor));

count = fact(i, factor);
if(count != 4) {
for(int j=0; j<count; j++)
setval(i, factor[j], count);
i = next(i + 1);
} else {
v.push_back(i++);
if(v.size() >= 4) {
if(v[0]+1 == v[1] && v[1]+1 == v[2] && v[2]+1 == v[3]) {
cout << v[0] << endl;
break;
} else
v.erase(v.begin());
}
}
}

return 0;
}

C++:

#include <iostream>
#include <cstring>
#include <cmath>
#include <vector>

using namespace std;

const int MAXN = 4000;
const int N = 1000000;

int prime[MAXN+2] = {2, 3, 5};

bool isprime(int n)
{
int q=sqrt(n), i=1;

while(prime[i] <= q)
if(n % prime[i] == 0)
return false;
else
i++;

return true;
}

void maketable(int n)
{
int val1 = 1, val5 = 5;

for(int i=3; i<=n;) {
val1 += 6;
if(isprime(val1))
prime[i++] = val1;

val5 += 6;
if(isprime(val5))
prime[i++] = val5;
}
}

int fact(int n)
{
int i=0, j=0;
while(n > 1) {
if(i > MAXN) {
j = 1;
break;
}
if(n % prime[i] == 0) {
j++;
while(n % prime[i] == 0)
n /= prime[i];
}
i++;
}
return j;
}

int main()
{
vector<int> v;

maketable(MAXN);

for(int i=1; i<=N; i++) {
if(fact(i) == 4) {
v.push_back(i);
if(v.size() >= 4) {
if(v[0]+1 == v[1] && v[1]+1 == v[2] && v[2]+1 == v[3]) {
cout << v[0] << endl;
break;
} else
v.erase(v.begin());
}
}
}

return 0;
}