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| 1 | +package example; |
| 2 | + |
| 3 | +// Java program to print print all primes smaller than |
| 4 | +// n using segmented sieve |
| 5 | + |
| 6 | +import java.util.Vector; |
| 7 | +import static java.lang.Math.sqrt; |
| 8 | +import static java.lang.Math.floor; |
| 9 | + |
| 10 | +class Main |
| 11 | +{ |
| 12 | + // This methid finds all primes smaller than 'limit' |
| 13 | + // using simple sieve of eratosthenes. It also stores |
| 14 | + // found primes in vector prime[] |
| 15 | + static void simpleSieve(int limit, Vector<Integer> prime) |
| 16 | + { |
| 17 | + // Create a boolean array "mark[0..n-1]" and initialize |
| 18 | + // all entries of it as true. A value in mark[p] will |
| 19 | + // finally be false if 'p' is Not a prime, else true. |
| 20 | + boolean mark[] = new boolean[limit+1]; |
| 21 | + |
| 22 | + for (int i = 0; i < mark.length; i++) |
| 23 | + mark[i] = true; |
| 24 | + |
| 25 | + for (int p=2; p*p<limit; p++) |
| 26 | + { |
| 27 | + // If p is not changed, then it is a prime |
| 28 | + if (mark[p] == true) |
| 29 | + { |
| 30 | + // Update all multiples of p |
| 31 | + for (int i=p*p; i<limit; i+=p) |
| 32 | + mark[i] = false; |
| 33 | + } |
| 34 | + } |
| 35 | + |
| 36 | + // Print all prime numbers and store them in prime |
| 37 | + for (int p=2; p<limit; p++) |
| 38 | + { |
| 39 | + if (mark[p] == true) |
| 40 | + { |
| 41 | + prime.add(p); |
| 42 | + System.out.print(p + " "); |
| 43 | + } |
| 44 | + } |
| 45 | + } |
| 46 | + |
| 47 | + // Prints all prime numbers smaller than 'n' |
| 48 | + static void segmentedSieve(int n) |
| 49 | + { |
| 50 | + // Compute all primes smaller than or equal |
| 51 | + // to square root of n using simple sieve |
| 52 | + int limit = (int) (floor(sqrt(n))+1); |
| 53 | + Vector<Integer> prime = new Vector<>(); |
| 54 | + simpleSieve(limit, prime); |
| 55 | + |
| 56 | + // Divide the range [0..n-1] in different segments |
| 57 | + // We have chosen segment size as sqrt(n). |
| 58 | + int low = limit; |
| 59 | + int high = 2*limit; |
| 60 | + |
| 61 | + // While all segments of range [0..n-1] are not processed, |
| 62 | + // process one segment at a time |
| 63 | + while (low < n) |
| 64 | + { |
| 65 | + if (high >= n) |
| 66 | + high = n; |
| 67 | + |
| 68 | + // To mark primes in current range. A value in mark[i] |
| 69 | + // will finally be false if 'i-low' is Not a prime, |
| 70 | + // else true. |
| 71 | + boolean mark[] = new boolean[limit+1]; |
| 72 | + |
| 73 | + for (int i = 0; i < mark.length; i++) |
| 74 | + mark[i] = true; |
| 75 | + |
| 76 | + // Use the found primes by simpleSieve() to find |
| 77 | + // primes in current range |
| 78 | + for (int i = 0; i < prime.size(); i++) |
| 79 | + { |
| 80 | + // Find the minimum number in [low..high] that is |
| 81 | + // a multiple of prime.get(i) (divisible by prime.get(i)) |
| 82 | + // For example, if low is 31 and prime.get(i) is 3, |
| 83 | + // we start with 33. |
| 84 | + int loLim = (int) (floor(low/prime.get(i)) * prime.get(i)); |
| 85 | + if (loLim < low) |
| 86 | + loLim += prime.get(i); |
| 87 | + |
| 88 | + /* Mark multiples of prime.get(i) in [low..high]: |
| 89 | + We are marking j - low for j, i.e. each number |
| 90 | + in range [low, high] is mapped to [0, high-low] |
| 91 | + so if range is [50, 100] marking 50 corresponds |
| 92 | + to marking 0, marking 51 corresponds to 1 and |
| 93 | + so on. In this way we need to allocate space only |
| 94 | + for range */ |
| 95 | + for (int j=loLim; j<high; j+=prime.get(i)) |
| 96 | + mark[j-low] = false; |
| 97 | + } |
| 98 | + |
| 99 | + // Numbers which are not marked as false are prime |
| 100 | + for (int i = low; i<high; i++) |
| 101 | + if (mark[i - low] == true) |
| 102 | + System.out.print(i + " "); |
| 103 | + |
| 104 | + // Update low and high for next segment |
| 105 | + low = low + limit; |
| 106 | + high = high + limit; |
| 107 | + } |
| 108 | + } |
| 109 | + |
| 110 | + // Driver method |
| 111 | + public static void main(String args[]) |
| 112 | + { |
| 113 | + int n = 100; |
| 114 | + System.out.println("Primes smaller than " + n + ":"); |
| 115 | + segmentedSieve(n); |
| 116 | + } |
| 117 | +} |
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