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  1. import java.math.BigInteger;
  2. import java.util.ArrayList;
  3. import java.util.Collections;
  4. import java.util.Comparator;
  5. import java.util.HashSet;
  6. import java.util.List;
  7. import java.util.Set;
  8. import java.util.stream.Collectors;
  9.  
  10. public class Main
  11. {
  12.     public static void main(String[] args)
  13.     {
  14.         System.out.println(LatticeCircle.valueOf(9, 22, 5, 22, new BigInteger("138125"), 242));
  15.         System.out.println(LatticeCircle.valueOf(7, 38, 5, 38, new BigInteger("785817263725"), 722));
  16.         System.out.println(LatticeCircle.valueOf(17, 38, 13, 38, new BigInteger("13603053979519731025"), 722));
  17.         System.out.println(LatticeCircle.valueOf(9, 38, 6, 38, new BigInteger("23959256988683736880737131790625"), 1444));
  18.         System.out.println(LatticeCircle.valueOf(15, 38, 14, 38, new BigInteger("23959256988683736880737131790625"), 1444));
  19.  
  20.         LatticeCircle lc = LatticeCircle.valueOf(12, 38, 7, 38, new BigInteger("23959256988683736880737131790625"), 1444);
  21.         System.out.println(lc);
  22.         System.out.println(lc.points());
  23.     }
  24. }
  25.  
  26. class LatticeCircle
  27. {
  28.     static int MAX_FACTOR = 1024;
  29.     static BigInteger MAX_RADIUS_SQUARE = BigInteger.valueOf(Long.MAX_VALUE).pow(2);
  30.  
  31.     int cx;
  32.     int cy;
  33.     int cd;
  34.     BigInteger rsq;
  35.     List<LongPoint> points;
  36.  
  37.     LatticeCircle(int cx, int cy, int cd, BigInteger rsq, List<LongPoint> points)
  38.     {
  39.         this.cx = cx;
  40.         this.cy = cy;
  41.         this.cd = cd;
  42.         this.rsq = rsq;
  43.         this.points = points;
  44.     }
  45.  
  46.     @Override
  47.     public String toString()
  48.     {
  49.         BigInteger gcd = rsq.gcd(BigInteger.valueOf(cd * cd));
  50.         return String.format("%d/%d %d/%d %d/%d => %d", cx, cd, cy, cd, rsq.divide(gcd), cd * cd / gcd.intValue(), points.size());
  51.     }
  52.  
  53.     public String points()
  54.     {
  55.         return points.stream().map(LongPoint::toString).collect(Collectors.joining(System.lineSeparator()));
  56.     }
  57.  
  58.     static LatticeCircle valueOf(int x, int dx, int y, int dy, BigInteger rsq, int rd)
  59.     {
  60.         int lcm = dx * dy / gcd(dx, dy);
  61.         x *= lcm / dx;
  62.         y *= lcm / dy;
  63.         if (lcm * lcm % rd != 0) throw new IllegalArgumentException();
  64.         return valueOf(x, y, lcm, rsq.multiply(BigInteger.valueOf((long) lcm * lcm / rd)));
  65.     }
  66.  
  67.     static int gcd(int a, int b)
  68.     {
  69.         return b == 0 ? a : gcd(b, a % b);
  70.     }
  71.  
  72.     static LatticeCircle valueOf(int cx, int cy, int cd, BigInteger cr2)
  73.     {
  74.         if (cd <= 0) throw new IllegalArgumentException();
  75.         if (cr2.equals(BigInteger.ZERO))
  76.         {
  77.             ArrayList<LongPoint> points = new ArrayList<>();
  78.             if (cx % cd == 0 && cy % cd == 0)
  79.             {
  80.                 points.add(new LongPoint(cx / cd, cy / cd));
  81.             }
  82.             return new LatticeCircle(cx, cy, cd, cr2, points);
  83.         }
  84.  
  85.         BigInteger r2 = cr2;
  86.         if (r2.compareTo(BigInteger.ZERO) < 0 || r2.compareTo(MAX_RADIUS_SQUARE) > 0) throw new IllegalArgumentException("r2の値が範囲外");
  87.  
  88.         // 素因数=2の処理
  89.         int p2 = 0;
  90.         while (true)
  91.         {
  92.             long l = r2.longValue();
  93.             int ntz = Long.numberOfTrailingZeros(l);
  94.             if (ntz == 0) break;
  95.             r2 = r2.shiftRight(ntz);
  96.             p2 += ntz;
  97.         }
  98.         long p = 1;
  99.         while(p2 >= 2)
  100.         {
  101.             p <<= 1;
  102.             p2 -= 2;
  103.         }
  104.  
  105.         // 因数のピタゴラス素数が入るリスト
  106.         List<Integer> factors = new ArrayList<>();
  107.  
  108.         for (int i = 3; i <= MAX_FACTOR; i += 2)
  109.         {
  110.             if (!isPrime(i)) continue;
  111.             BigInteger div = BigInteger.valueOf(i);
  112.             BigInteger[] dr = r2.divideAndRemainder(div);
  113.  
  114.             int count = 0;
  115.             while (dr[1].equals(BigInteger.ZERO))
  116.             {
  117.                 r2 = dr[0];
  118.                 dr = r2.divideAndRemainder(div);
  119.                 count++;
  120.             }
  121.  
  122.             if (i % 4 == 1)
  123.             {
  124.                 while(count-- > 0) factors.add(i);
  125.             } else
  126.             {
  127.                 // 4n+3の形の素因数が2n個ではない場合空の格子点リストで円を返す 
  128.                 if (count % 2 == 1) return new LatticeCircle(cx, cy, cd, r2, Collections.EMPTY_LIST);
  129.                 while (count >= 2)
  130.                 {
  131.                     p *= i;
  132.                     count -= 2;
  133.                 }
  134.             }
  135.         }
  136.  
  137.         if (!r2.equals(BigInteger.ONE)) throw new IllegalArgumentException();
  138.  
  139.         long x = p;
  140.         long y = p2 == 1 ? x : 0;
  141.  
  142.         Set<LongPoint> set = new HashSet<>();
  143.         set.add(new LongPoint(+x, +y));
  144.         set.add(new LongPoint(+x, -y));
  145.         set.add(new LongPoint(-x, +y));
  146.         set.add(new LongPoint(-x, -y));
  147.         set.add(new LongPoint(+y, +x));
  148.         set.add(new LongPoint(+y, -x));
  149.         set.add(new LongPoint(-y, +x));
  150.         set.add(new LongPoint(-y, -x));
  151.  
  152.         for (int factor : factors)
  153.         {
  154.             int m = 1, n = 0;
  155.             // m*m+n*n = factorのmとnを探す
  156.             while (true)
  157.             {
  158.                 int nn = factor - m * m;
  159.                 n = (int) Math.sqrt(nn);
  160.                 if (n * n == nn) break;
  161.                 m++;
  162.             }
  163.             set = multiply(set, m, n);
  164.         }
  165.  
  166.         List<LongPoint> result = new ArrayList<>();
  167.         for (LongPoint lp : set)
  168.         {
  169.             if (lp.test(cx, cy, cd))
  170.             {
  171.                 result.add(new LongPoint((lp.x + cx) / cd, (lp.y + cy) / cd));
  172.             }
  173.         }
  174.         result.sort(Comparator.naturalOrder());
  175.         return new LatticeCircle(cx, cy, cd, cr2, result);
  176.     }
  177.  
  178.     static boolean isPrime(int n)
  179.     {
  180.         if (n <= 1) return false;
  181.         if ((n & 1) == 0) return n == 2;
  182.         for (int i = 3, j = (int) Math.sqrt(n); i <= j; i += 2)
  183.             if (n % i == 0) return false;
  184.         return true;
  185.     }
  186.  
  187.     static Set<LongPoint> multiply(Set<LongPoint> src, int m, int n)
  188.     {
  189.         HashSet<LongPoint> dst = new HashSet<>();
  190.         for (LongPoint lp : src)
  191.         {
  192.             dst.add(lp.multiply(m, n));
  193.             dst.add(lp.multiply(n, m));
  194.         }
  195.         return dst;
  196.     }
  197. }
  198.  
  199.  
  200. class LongPoint implements Comparable<LongPoint>
  201. {
  202.     final long x, y;
  203.  
  204.     LongPoint(long x, long y)
  205.     {
  206.         this.x = x;
  207.         this.y = y;
  208.     }
  209.  
  210.     LongPoint multiply(int m, int n)
  211.     {
  212.         return new LongPoint(x * m + y * n, x * n - y * m);
  213.     }
  214.  
  215.     @Override
  216.     public int hashCode()
  217.     {
  218.         return Long.hashCode(x * 31 + y);
  219.     }
  220.  
  221.     @Override
  222.     public boolean equals(Object obj)
  223.     {
  224.         if (!(obj instanceof LongPoint)) return false;
  225.         LongPoint p = (LongPoint) obj;
  226.         return x == p.x && y == p.y;
  227.     }
  228.  
  229.     @Override
  230.     public String toString()
  231.     {
  232.         return "(" + x + "," + y + ")";
  233.     }
  234.  
  235.     @Override
  236.     public int compareTo(LongPoint o)
  237.     {
  238.         // {(0,0),(0,1),(1,1),(1,0)} とかはうまく処理できない
  239.         if (x >>> 63 != o.x >>> 63) return Long.compare(x >>> 63, o.x >>> 63);
  240.         return x >= 0 ? Long.compare(y, o.y) : -Long.compare(y, o.y);
  241.     }
  242.  
  243.     boolean test(int cx, int cy, int cd)
  244.     {
  245.         if (cx < 0 || cy < 0 || cd <= 0) throw new IllegalArgumentException();
  246.         return (x + cx) % cd == 0 && (y + cy) % cd == 0;
  247.     }
  248. }
Runtime error #stdin #stdout 0.93s 2317312KB
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stdin
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Standard input is empty
stdout
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9/22 5/22 138125/242 => 7
7/38 5/38 785817263725/722 => 77
17/38 13/38 13603053979519731025/722 => 777
9/38 6/38 23959256988683736880737131790625/1444 => 7777
15/38 14/38 23959256988683736880737131790625/1444 => 7778
12/38 7/38 23959256988683736880737131790625/1444 => 7776
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https://ideone.com/72sNsk
円周上の格子点の数を数える
language:
Java (HotSpot 12)
created:
6 years ago
visibility:
secret

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