// yukicoder: No.160 最短経路のうち辞書順最小 // 2019.7.19 bal4u #include #include #if 1 #define gc() getchar_unlocked() #define pc(c) putchar_unlocked(c) #else #define gc() getchar() #define pc(c) putchar(c) #endif int in() { // 非負整数の入力 int n = 0, c = gc(); do n = 10 * n + (c & 0xf); while ((c = gc()) >= '0'); return n; } void out(int n) { // 非負整数の表示(出力) int i; char b[20]; if (!n) pc('0'); else { i = 0; while (n) b[i++] = n % 10 + '0', n /= 10; while (i--) pc(b[i]); } } //// 優先度付きキュー(ダイクストラ法用) #define MAX 1000000 typedef struct { int t, n, pre; } QUE; QUE que[MAX]; int qsize; #define PARENT(i) ((i)>>1) #define LEFT(i) ((i)<<1) #define RIGHT(i) (((i)<<1)+1) void min_heapify(int i) { int l, r, min; QUE qt; l = LEFT(i), r = RIGHT(i); if (l < qsize && (que[l].t < que[i].t || (que[l].t == que[i].t && que[l].pre < que[i].pre))) min = l; else min = i; if (r < qsize && que[r].t < que[min].t) min = r; if (min != i) { qt = que[i]; que[i] = que[min]; que[min] = qt; min_heapify(min); } } void deq() { que[0] = que[--qsize]; min_heapify(0); } void enq(int n, int t, int pre) { int i, min; QUE qt; i = qsize++; que[i].t = t, que[i].n = n, que[i].pre = pre; while (i > 0 && (que[min = PARENT(i)].t > que[i].t || (que[min].t == que[i].t && que[min].pre > que[i].pre))) { qt = que[i]; que[i] = que[min]; que[min] = qt; i = min; } } //// 本問題関連 #define INF 0x33333333 #define MAXV 202 int N, S, G; int hi[MAXV], to[MAXV][MAXV], tm[MAXV][MAXV]; int vis[MAXV]; int prev[MAXV]; int a[MAXV], sz; int path(int *a, int n, int pre) { int i, w = 0; a[w++] = n, n = pre; while (n >= 0) a[w++] = n, n = prev[n]; a[w] = -1; return w; } void dijkstra() { int i, n, t, pre, mi; int tmp[MAXV], tsz; mi = INF, memset(vis, INF, sizeof(vis)); enq(G, 0, -1); while (qsize) { n = que[0].n, t = que[0].t, pre = que[0].pre, deq(); if (n == S) { if (t > mi) return; if (t < mi) sz = path(a, n, pre), mi = t; else { tsz = path(tmp, n, pre); for (i = 0; a[i] == tmp[i]; i++); if (tmp[i] < a[i]) { for (i = 0; i < tsz; i++) a[i] = tmp[i]; sz = tsz; } } continue; } if (vis[n] < t || (vis[n] == t && prev[n] <= pre)) continue; vis[n] = t, prev[n] = pre; for (i = 0; i < hi[n]; i++) { int nx = to[n][i], nt = t+tm[n][i]; if (vis[nx] < nt || (vis[nx] == nt && prev[nx] <= n)) continue; enq(nx, nt, n); } } } int main() { int i, k, M; N = in(), M = in(), S = in(), G = in(); while (M--) { int a = in(), b = in(), c = in(); k = hi[a]++, to[a][k] = b, tm[a][k] = c; k = hi[b]++, to[b][k] = a, tm[b][k] = c; } dijkstra(); out(a[0]); for (i = 1; i < sz; i++) pc(' '), out(a[i]); pc('\n'); return 0; }