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93 lines
2.5 KiB
C++
93 lines
2.5 KiB
C++
/*
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* C++ Program to Implement Sieve of Atkins
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*/
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#include <iostream>
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#include <cmath>
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#include <vector>
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#define ll long long
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using namespace std;
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/*
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* Sieve of Atkins
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*/
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void sieve_atkins(ll int n)
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{
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vector<bool> is_prime(n + 1);
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is_prime[2] = true;
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is_prime[3] = true;
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for (ll int i = 5; i <= n; i++)
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{
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is_prime[i] = false;
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}
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ll int lim = ceil(sqrt(n));
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for (ll int x = 1; x <= lim; x++)
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{
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for (ll int y = 1; y <= lim; y++)
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{
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ll int num = (4 * x * x + y * y);
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if (num <= n && (num % 12 == 1 || num % 12 == 5))
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{
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is_prime[num] = true;
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}
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num = (3 * x * x + y * y);
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if (num <= n && (num % 12 == 7))
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{
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is_prime[num] = true;
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}
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if (x > y)
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{
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num = (3 * x * x - y * y);
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if (num <= n && (num % 12 == 11))
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{
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is_prime[num] = true;
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}
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}
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}
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}
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for (ll int i = 5; i <= lim; i++)
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{
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if (is_prime[i])
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{
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for (ll int j = i * i; j <= n; j += i)
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{
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is_prime[j] = false;
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}
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}
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}
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for (ll int i = 2; i <= n; i++)
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{
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if (is_prime[i])
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{
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cout<<i<<"\t";
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}
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}
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}
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/*
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* Main
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*/
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int main()
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{
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ll int n;
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n = 300;
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cout<<"Following are the prime numbers below "<<n<<endl;
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sieve_atkins(n);
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cout<<endl;
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return 0;
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}
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/*
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Following are the prime numbers below 300
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2 3 5 7 11 13 17 19 23 29
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31 37 41 43 47 53 59 61 67 71
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73 79 83 89 97 101 103 107 109 113
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127 131 137 139 149 151 157 163 167 173
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179 181 191 193 197 199 211 223 227 229
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233 239 241 251 257 263 269 271 277 281
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283 293
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------------------
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(program exited with code: 1)
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Press return to continue
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