/*  POTM ENTRY:  knight.c                       		*/
/*  Your Name:   Staffan Ulfberg				*/
/*  Your email:  staffanu@nada.kth.se                      	*/

#define __USE_FIXED_PROTOTYPES__

#include 
#include 
#include 
#include 
#include 

int getrusage(int, struct rusage *);

void kruskal(void);
void twoopt(void);
void lin_kernighan(void);
void random_path(void);

#define SIZE 100
#define EXTRA 6
#define MAX_TIME 580

#define abs(a) ((a)<0?-(a):(a))
#define swap(a, b) (a ^= b, b ^= a, a ^= b)
#define wrap(a) ((a)<0?(a)+n:(a)>=n?(a)-n:a)

short dx[8] = { -1, -2, -2, -1, 1, 2, 2, 1};
short dy[8] = { -2, -1, 1, 2, 2, 1, -1, -2};

extern unsigned char disttohome[SIZE+EXTRA][SIZE+EXTRA];
short visited[SIZE+EXTRA][SIZE+EXTRA];

short dist[101][101]; 
short n, x[101], y[101], path[101], saved_path[101];

double u[97];
int uni_i, uni_j;

void inituni(int seed) {
  int i;

  srand(seed);
  for (i = 0; i < 97; i++)
    u[i] = (rand() % 1000) / 1000.0;
  uni_i = 0, uni_j = 97-33;
}

double uni(void) {
  double r;

  u[uni_i] = (r = u[uni_i]-u[uni_j],  r += r < 0);
  uni_i = (uni_i + 1) % 97;
  uni_j = (uni_j + 1) % 97;
  return r;
}


short distance(short x1, short y1, short x2, short y2) {
  if (abs(x1-x2) == 1 && abs(y1-y2) == 1)
    return !x1 && !y1 || !x2 && !y2 ? 4 : 2;
  else
    return disttohome[abs(x1-x2)][abs(y1-y2)];
}

void strokepath(short x1, short y1, short x2, short y2, int print,
		short *steps, short *uhit) {
  short force, k, v, d;

  if (x1 == x2 && y1 == y2) return;

  d = uni() > .5;

  for (force = 0; force <= 1; force++)
    for (k = d ? 7 : 0; k >= 0 && k <= 7; d ? k-- : k++)
      if (x1+dx[k]>=0 && y1+dy[k]>=0
	  && x1+dx[k]=0 && j+dy[k]>=0
	      && i+dx[k] 1+disttohome[i][j])
	    changed = disttohome[i+dx[k]][j+dy[k]] = 1+disttohome[i][j];
      }
  } while (changed); 

  for (i = 0; i < 106; i++) {
    for (j = 0; j < 106; j++)
      printf("%c", 32+disttohome[i][j]);
    printf("\n");
  }*/

  for (i = 0; i < n; i++)
    for (j = 0; j < n; j++)
      dist[i][j] = distance(x[i], y[i], x[j], y[j]);

  kruskal(); twoopt(); lin_kernighan();  
  save_path(); beststeps = path_len(); j = 0;

  while (getrusage(RUSAGE_SELF, &rusage),
	 rusage.ru_utime.tv_sec + rusage.ru_stime.tv_sec < MAX_TIME
	 && j < 10) {

    random_path(); lin_kernighan();

    if ((steps = path_len()) < beststeps)
      save_path(), beststeps = steps, j = 0;
    if (steps == beststeps)
      j++;
  }
  restore_path();

  for (beststeps = 10000, bestuhit = i = 0, ibest = 0;
       i < 6 || i < 100 && bestuhit-beststeps; i++) {
    inituni(i);
    printpath(0, &steps, &uhit);
    if (steps < beststeps || steps == beststeps && uhit >= bestuhit)
      ibest = i, beststeps = steps, bestuhit = uhit;
  }
  inituni(ibest);
  printpath(1, &steps, &uhit);
}


short sets[101][101];
short flag[101];

#define clearflag() memset(flag, 0, sizeof(*flag) * n);

void initsets(void) {
  int i, j;

  for (i = 0; i < n; i++)  
    for (j = 0; j < 101; j++)
      sets[i][j] = -1;
}

int _isconnected(int a, int b) {
  int i;

  if (flag[a]) return 0;
  if (a == b) return 1;
  flag[a] = 1;

  for (i = 0; sets[a][i] >= 0; i++)
    if (_isconnected(sets[a][i], b))
      return 1;
  return 0;
}

int isconnected(int a, int b) {
  clearflag();
  return _isconnected(a, b);
}

void unionsets(int a, int b) {
  int i;

  for (i = 0; sets[a][i] >= 0; i++);
  sets[a][i] = b;
  for (i = 0; sets[b][i] >= 0; i++);
  sets[b][i] = a;
}

int c = 0;

void _visitall(int a) {
  int i;

  if (flag[a]) return;
  flag[a] = 1;

  path[c++] = a;

  for (i = 0; sets[a][i] >= 0; i++)
    _visitall(sets[a][i]);
}

struct edge {
  short a, b, w;
} edges[101*101];

int comp(struct edge *x, struct edge *y) {
  return x->w - y->w;
}

void kruskal(void) {
  int i, j, k = 0;

  for (i = 0; i < n; i++)
    for (j = 0; j < n; j++)
      edges[k].a = i, edges[k].b = j, edges[k++].w = dist[i][j];
  
  qsort(edges, k, sizeof(struct edge), (int (*)()) comp);

  initsets();

  for (i = 0; i < k; i++)
    if (!isconnected(edges[i].a, edges[i].b)) 
      unionsets(edges[i].a, edges[i].b);

  c = 0;
  clearflag();
  _visitall(0);
}

void swappath(int i, int j) {
  int k, l, a, b;

  l = wrap(j-i+1) / 2;
  for (k = 0; k < l; k++)
    a = wrap(i+k), b = wrap(j-k), swap(path[a], path[b]);
}

void twoopt(void) {
  int i, j, i2, j2, change;

  do {
    change = 0;
    for (i = 0; i < n; i++)
      for (j = i + 2; j < n; j++) {
	i2 = wrap(i + 1), j2 = wrap(j + 1);
	if (dist[path[i]][path[i2]]+dist[path[j]][path[j2]]
	    > dist[path[i]][path[j]]+dist[path[i2]][path[j2]])
	  swappath(i + 1, j), change = 1;
      }
  } while (change);
}

int best;

void _lin_kernighan(int home, int remote, int sum) {
  int thisbest = 0, u, v = 0, this, min = 100000, i, oldbest, wr, wr2;
  int uu, vv, ruv;

  flag[home] = flag[remote] = 1;
  wr = wrap(remote+1); wr2 = wrap(remote-1);
  for (i = 0; i < n; i++)
    if (!flag[i] && i != wr && i != wr2	&& dist[path[i]][path[remote]] < min)
      min = dist[path[i]][path[remote]], v = i;
  if (min == 100000)
    return;
  flag[v] = 1;

  u = wrap(v + home - remote);

  sum -= dist[path[remote]][path[v]];
  this = sum + dist[path[u]][path[v]] - dist[path[u]][path[home]];

  if (this > best)
    thisbest = 1, best = this;
  oldbest = best;

  if (thisbest || sum > best) {
    
    uu = u, vv = v;
    if (uu < remote) uu += n;
    if (vv < remote) vv += n;
    ruv = uu < vv;

    if (ruv) swappath(remote, u); else swappath(u, remote);

    _lin_kernighan(home, remote, sum + dist[path[v]][path[remote]]);

    if (!thisbest && oldbest == best)
      if (ruv) swappath(remote, u); else swappath(u, remote);
  }
}

void lin_kernighan(void) {
  int i, j, changed;
  
  do {
    changed = 0;
    for (i = 0; i < n; i++)
      for (j = -1; j <= 1; j+= 2) {
	best = 0;
	clearflag();
	_lin_kernighan(i, wrap(i+j), dist[path[i]][path[wrap(i+j)]]);
	if (best) changed = 1;
      }
  } while (changed);
}

void random_path(void) {
  int i, j;

  for (i = 0; i < n; i++)
    path[i] = i;

  for (i = n - 1; i > 1; i--)
    j = i * uni(), swap(path[i], path[j]);
}


unsigned char disttohome[106][106] = {
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"\"!$#\"#$%$%&'&'()()*+*+,-,-././01012323454567678989:;:;<=<=>?>?@A@ABCBCDEDEFGFGHIHIJKJKLMLMNONOPQPQRSRSTUTU",
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"\"#\"#$#$%$%&'&'()()*+*+,-,-././01012323454567678989:;:;<=<=>?>?@A@ABCBCDEDEFGFGHIHIJKJKLMLMNONOPQPQRSRSTUTU",
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"$#$#$%$%&%&'&'()()*+*+,-,-././01012323454567678989:;:;<=<=>?>?@A@ABCBCDEDEFGFGHIHIJKJKLMLMNONOPQPQRSRSTUTU",  
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"GFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGHGHIHIJIJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\",
"FGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGFGHGHIHIJIJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]",
"GHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHIHIJIJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^",
"HGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHGHIHIJIJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]",
"IHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIJIJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^",
"HIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIHIJIJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_",
"IJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^",
"JIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJIJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_",
"KJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`",
"JKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKJKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_",
"KLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`",
"LKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLKLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a",
"MLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`",
"LMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMLMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`a",
"MNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ab",
"NMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNMNONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`aba",
"ONONONONONONONONONONONONONONONONONONONONONONONONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`abab",
"NONONONONONONONONONONONONONONONONONONONONONONONOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababc",
"OPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcb",
"POPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPOPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbc",
"QPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcd",
"PQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQPQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdc",
"QRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdcd",
"RQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRQRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdcde",
"SRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdcded",
"RSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSRSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdcdede",
"STSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdcdedef",
"TSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTSTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdcdedefe",
"UTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdcdedefef",
"TUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUTUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdcdedefefg",
"UVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVUVWVWXWXYXYZYZ[Z[\\[\\]\\]^]^_^_`_`a`ababcbcdcdedefefgf"
};












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