+/*
+ * Empire - A multi-player, client/server Internet based war game.
+ * Copyright (C) 1986-2011, Dave Pare, Jeff Bailey, Thomas Ruschak,
+ * Ken Stevens, Steve McClure, Markus Armbruster
+ *
+ * Empire is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program. If not, see <http://www.gnu.org/licenses/>.
+ *
+ * ---
+ *
+ * See files README, COPYING and CREDITS in the root of the source
+ * tree for related information and legal notices. It is expected
+ * that future projects/authors will amend these files as needed.
+ *
+ * ---
+ *
+ * pathfind.c: Find cheapest paths
+ *
+ * Known contributors to this file:
+ * Markus Armbruster, 2011
+ */
+
+#include <config.h>
+
+#include <assert.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include "file.h"
+#include "optlist.h"
+#include "path.h"
+#include "sect.h"
+
+#ifdef PATH_FIND_DEBUG
+#define DPRINTF(fmt, ...) ((void)printf(fmt , ## __VA_ARGS__))
+#else
+#define DPRINTF(fmt, ...) ((void)0)
+#endif
+
+static char *bufrotate(char *buf, size_t bufsz, size_t i);
+
+/*
+ * Dijkstra's algorithm. Refer to your graph algorithm textbook for
+ * how it works. Implementation is specialized to hex maps.
+ */
+
+/*
+ * Array of sector data, indexed by sector uid
+ *
+ * We need to store a few values per sector visited by the path
+ * search. An array is the stupidest data structure that could
+ * possibly work.
+ *
+ * Extra benefit: it works really well for distribution in a
+ * continental game, where we visit most sectors. That's our most
+ * demanding use of path search, and its performance has noticable
+ * impact on the update.
+ *
+ * Island game distribution is much less demanding. The array may not
+ * be the best choice here, but it's plainly good enough. Same for
+ * path searches outside the update.
+ */
+
+struct pf_map {
+ /*
+ * visit < pf_visit : unvisited, remaining members invalid
+ * visit == pf_visit : open, dir & cost tentative, heapi used
+ * visit == pf_visit + 1 : closed, dir & cost final, heapi unused
+ */
+ unsigned short visit;
+ signed char dir; /* cheapest direction to source */
+ int heapi; /* index in heap, valid if open */
+ double cost; /* cost from source */
+};
+
+static unsigned short pf_visit;
+static struct pf_map *pf_map;
+
+/*
+ * Binary heap, cost priority queue of all open sectors
+ *
+ * Again, we use the stupidest data structure that could possibly
+ * work: an array. And we make it so large it can hold *all* sectors.
+ * In practice, we need much less space, but a tighter upper bound is
+ * not obvious to me right now.
+ */
+
+struct pf_heap {
+ int uid; /* sector uid and */
+ coord x, y; /* coordinates, uid == XYOFFSET(x, y) */
+ double cost; /* cost from source */
+};
+
+static int pf_nheap; /* #entries in pf_nheap[] */
+static struct pf_heap *pf_heap;
+
+/*
+ * Source and costs
+ */
+static coord pf_sx, pf_sy;
+static int pf_suid;
+static natid pf_actor;
+static double (*pf_sct_cost)(natid, int);
+
+/* Is sector with uid UID open? */
+static int
+pf_is_open(int uid)
+{
+ return pf_map[uid].visit == pf_visit;
+}
+
+/* Is sector with uid UID closed? */
+static int
+pf_is_closed(int uid)
+{
+ /*
+ * optimization: check > pf_visit instead of == pf_visit + 1
+ * works because pf_map[uid].visit <= pf_visit + 1
+ */
+ return pf_map[uid].visit > pf_visit;
+}
+
+/* Is sector with uid UID unvisited? */
+static int
+pf_is_unvisited(int uid)
+{
+ return pf_map[uid].visit < pf_visit;
+}
+
+#ifdef PATH_FIND_DEBUG
+static void
+pf_check(void)
+{
+ int i, uid, c;
+
+ for (i = 0; i < pf_nheap; i++) {
+ uid = pf_heap[i].uid;
+ assert(0 <= uid && uid < WORLD_SZ());
+ assert(pf_map[uid].heapi == i);
+ assert(pf_map[uid].visit == pf_visit);
+ assert(pf_map[uid].cost <= pf_heap[i].cost);
+ c = 2 * i + 1;
+ assert(c >= pf_nheap || pf_heap[i].cost <= pf_heap[c].cost);
+ c++;
+ assert(c >= pf_nheap || pf_heap[i].cost <= pf_heap[c].cost);
+ }
+
+ for (uid = 0; uid < WORLD_SZ(); uid++) {
+ assert(pf_map[uid].visit <= pf_visit + 1);
+ if (pf_map[uid].visit == pf_visit) {
+ i = pf_map[uid].heapi;
+ assert(0 <= i && i < pf_nheap && pf_heap[i].uid == uid);
+ }
+ }
+}
+#else
+#define pf_check() ((void)0)
+#endif
+
+/* Swap pf_heap's I-th and J-th elements. */
+static void
+pf_heap_swap(int i, int j)
+{
+ struct pf_heap tmp;
+
+ assert(0 <= i && i < pf_nheap);
+ assert(0 <= j && j < pf_nheap);
+ tmp = pf_heap[i];
+ pf_heap[i] = pf_heap[j];
+ pf_heap[j] = tmp;
+ pf_map[pf_heap[i].uid].heapi = i;
+ pf_map[pf_heap[j].uid].heapi = j;
+}
+
+/* Restore heap property after N-th element's cost increased. */
+static void
+pf_sift_down(int n)
+{
+ int r, c;
+
+ assert(0 <= n && n < pf_nheap);
+ for (r = n; (c = 2 * r + 1) < pf_nheap; r = c) {
+ if (c + 1 < pf_nheap && pf_heap[c].cost > pf_heap[c + 1].cost)
+ c++;
+ if (pf_heap[r].cost < pf_heap[c].cost)
+ break;
+ pf_heap_swap(r, c);
+ }
+}
+
+/* Restore heap property after N-th element's cost decreased. */
+static void
+pf_sift_up(int n)
+{
+ int c, p;
+
+ assert(0 <= n && n < pf_nheap);
+ for (c = n; (p = (c - 1) / 2), c > 0; c = p) {
+ if (pf_heap[p].cost < pf_heap[c].cost)
+ break;
+ pf_heap_swap(p, c);
+ }
+}
+
+/*
+ * Open the unvisited sector X,Y.
+ * UID is sector uid, it equals XYOFFSET(X,Y).
+ * Cheapest path from source comes from direction DIR and has cost COST.
+ */
+static void
+pf_open(int uid, coord x, coord y, int dir, double cost)
+{
+ int i;
+
+ if (pf_is_open(uid)) {
+ i = pf_map[uid].heapi;
+ DPRINTF("pf: reopen %d,%d %g %c %d\n", x, y, cost, dirch[dir], i);
+ assert(cost < pf_map[uid].cost);
+ } else {
+ i = pf_nheap++;
+ DPRINTF("pf: open %d,%d %g %c %d\n", x, y, cost, dirch[dir], i);
+ pf_map[uid].heapi = i;
+ pf_map[uid].visit = pf_visit;
+ pf_heap[i].uid = uid;
+ pf_heap[i].x = x;
+ pf_heap[i].y = y;
+ }
+ pf_map[uid].dir = dir;
+ pf_map[uid].cost = cost;
+ pf_heap[i].cost = cost;
+
+ pf_sift_up(i);
+ pf_check();
+}
+
+/*
+ * Close the sector at the top of the heap.
+ */
+static void
+pf_close(void)
+{
+ int uid = pf_heap[0].uid;
+
+ DPRINTF("pf: close %d,%d %d\n", pf_heap[0].x, pf_heap[0].y, pf_nheap);
+ assert(pf_is_open(uid));
+ if (--pf_nheap) {
+ pf_heap[0] = pf_heap[pf_nheap];
+ pf_map[pf_heap[0].uid].heapi = 0;
+ pf_sift_down(0);
+ }
+ pf_map[uid].visit = pf_visit + 1;
+ pf_check();
+}
+
+static coord
+x_in_dir(coord x, int dir)
+{
+ int xx;
+
+ assert(0 <= x && x < WORLD_X);
+ assert(0 <= dir && dir <= DIR_LAST);
+ xx = x + diroff[dir][0];
+ if (xx < 0)
+ return xx + WORLD_X;
+ if (xx >= WORLD_X)
+ return xx - WORLD_X;
+ return xx;
+}
+
+static coord
+y_in_dir(coord y, int dir)
+{
+ int yy;
+
+ assert(0 <= y && y < WORLD_Y);
+ assert(0 <= dir && dir <= DIR_LAST);
+ yy = y + diroff[dir][1];
+ if (yy < 0)
+ return yy + WORLD_Y;
+ if (yy >= WORLD_Y)
+ return yy - WORLD_Y;
+ return yy;
+}
+
+static int
+rev_dir(int dir)
+{
+ assert(DIR_FIRST <= dir && dir <= DIR_LAST);
+ return dir >= DIR_FIRST + 3 ? dir - 3 : dir + 3;
+}
+
+/*
+ * Set the current source and cost function.
+ * SX,SY is the source.
+ * The cost to enter the sector with uid u is COST(ACTOR, u).
+ * Negative value means the sector can't be entered.
+ */
+static void
+pf_set_source(coord sx, coord sy, natid actor, double (*cost)(natid, int))
+{
+ DPRINTF("pf: source %d,%d\n", sx, sy);
+ pf_sx = sx;
+ pf_sy = sy;
+ pf_suid = XYOFFSET(sx, sy);
+ pf_actor = actor;
+ pf_sct_cost = cost;
+
+ if (!pf_map) {
+ pf_map = calloc(WORLD_SZ(), sizeof(*pf_map));
+ pf_heap = malloc(WORLD_SZ() * sizeof(*pf_heap));
+ pf_visit = 1;
+ } else if ((unsigned short)(pf_visit + 3) < pf_visit) {
+ DPRINTF("pf: visit wrap-around\n");
+ memset(pf_map, 0, WORLD_SZ() * sizeof(*pf_map));
+ pf_visit = 1;
+ } else
+ pf_visit += 2;
+
+ pf_nheap = 0;
+
+ pf_open(pf_suid, pf_sx, pf_sy, DIR_STOP, 0.0);
+}
+
+/*
+ * Find cheapest path from current source to DX,DY, return its cost.
+ */
+double
+path_find_to(coord dx, coord dy)
+{
+ int duid;
+ int uid, nuid, i;
+ double cost, c1;
+ coord x, y, nx, ny;
+
+ DPRINTF("pf: dest %d,%d\n", dx, dy);
+ duid = XYOFFSET(dx, dy);
+ if (pf_is_closed(duid)) {
+ DPRINTF("pf: done old %g\n", pf_map[duid].cost);
+ return pf_map[duid].cost;
+ }
+
+ while (pf_nheap > 0 && (uid = pf_heap[0].uid) != duid) {
+ x = pf_heap[0].x;
+ y = pf_heap[0].y;
+ cost = pf_heap[0].cost;
+ pf_close();
+
+ for (i = 0; i < 6; i++) { /* for all neighbors */
+ nx = x_in_dir(x, DIR_FIRST + i);
+ ny = y_in_dir(y, DIR_FIRST + i);
+ nuid = XYOFFSET(nx, ny);
+ c1 = pf_sct_cost(pf_actor, nuid);
+ if (c1 < 0)
+ continue;
+ if (pf_is_unvisited(nuid) || cost + c1 < pf_map[nuid].cost)
+ pf_open(nuid, nx, ny, DIR_FIRST + i, cost + c1);
+ }
+ }
+
+ DPRINTF("pf: done new %g\n", !pf_nheap ? -1.0 : pf_map[duid].cost);
+ if (!pf_nheap)
+ return -1.0;
+ return pf_map[duid].cost;
+}
+
+/*
+ * Write route from SX,SY to DX,DY to BUF[BUFSIZ], return its length.
+ * If the route is longer than BUFSIZ-1 characters, it's truncated.
+ * You must compute path cost first, with path_find_to().
+ * SX,SY must be on a shortest path from the current source to DX,DY.
+ */
+size_t
+path_find_route(char *buf, size_t bufsz,
+ coord sx, coord sy, coord dx, coord dy)
+{
+ coord x, y;
+ size_t i, len;
+ int suid, uid, d;
+
+ suid = XYOFFSET(sx, sy);
+ assert(bufsz > 0 && !pf_is_unvisited(suid));
+
+ i = bufsz;
+ buf[--i] = 0;
+ len = 0;
+
+ x = dx;
+ y = dy;
+ for (;;) {
+ DPRINTF("pf: %d,%d %.*s%.*s\n",
+ x, y,
+ (int)(bufsz - i), buf + i,
+ len >= bufsz ? (int)i : 0, buf);
+ uid = XYOFFSET(x, y);
+ assert(!pf_is_unvisited(uid));
+ d = pf_map[uid].dir;
+ if (d == DIR_STOP || uid == suid)
+ break;
+ if (!i)
+ i = bufsz;
+ buf[--i] = dirch[d];
+ len++;
+ x = x_in_dir(x, rev_dir(d));
+ y = y_in_dir(y, rev_dir(d));
+ }
+
+ assert(x == sx && y == sy);
+ if (len >= bufsz)
+ bufrotate(buf, bufsz, i);
+ else {
+ assert(i + len < bufsz);
+ memmove(buf, buf + i, len + 1);
+ }
+ return len;
+}
+
+/*
+ * Rotate BUF[BUFSZ] to put BUF[I] into BUF[0], and zero-terminate.
+ */
+static char *
+bufrotate(char *buf, size_t bufsz, size_t i)
+{
+ char tmp[64];
+ size_t n;
+
+ while (i) {
+ n = MIN(i, sizeof(tmp));
+ memcpy(tmp, buf, n);
+ memcpy(buf, buf + n, bufsz - n);
+ memcpy(buf + bufsz - n, tmp, n);
+ i -= n;
+ }
+ buf[bufsz - 1] = 0;
+ return buf;
+}
+
+
+/*
+ * Empire interface glue
+ */
+
+static double
+cost_land(natid actor, int uid, int mobtype)
+{
+ struct sctstr *sp = (void *)empfile[EF_SECTOR].cache;
+
+ if (sp[uid].sct_own != actor)
+ return -1.0;
+ return sector_mcost(&sp[uid], mobtype);
+}
+
+static double
+cost_move(natid actor, int uid)
+{
+ return cost_land(actor, uid, MOB_MOVE);
+}
+
+static double
+cost_march(natid actor, int uid)
+{
+ return cost_land(actor, uid, MOB_MARCH);
+}
+
+static double
+cost_rail(natid actor, int uid)
+{
+ return cost_land(actor, uid, MOB_RAIL);
+}
+
+static double (*cost_tab[])(natid, int) = {
+ cost_move, cost_march, cost_rail
+};
+
+/*
+ * Start finding paths from SX,SY.
+ * Use mobility costs for ACTOR and MOBTYPE.
+ */
+void
+path_find_from(coord sx, coord sy, natid actor, int mobtype)
+{
+ pf_set_source(sx, sy, actor, cost_tab[mobtype]);
+}
+
+/*
+ * Find cheapest path from SX,SY to DX,DY, return its mobility cost.
+ * Use mobility costs for ACTOR and MOBTYPE.
+ */
+double
+path_find(coord sx, coord sy, coord dx, coord dy, natid actor, int mobtype)
+{
+ pf_set_source(sx, sy, actor, cost_tab[mobtype]);
+ return path_find_to(dx, dy);
+}
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