// yukicoder: No.160 最短経路のうち辞書順最小 // 2019.7.20 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; } 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) 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 i, min; QUE qt; i = qsize++; que[i].t = t, que[i].n = n; while (i > 0 && que[min = PARENT(i)].t > que[i].t) { qt = que[i]; que[i] = que[min]; que[min] = qt; i = min; } } //// 本問題関連 #define INF 0x33333333 #define MIN(a,b) ((a)<=(b)?(a):(b)) #define MAXV 202 int N; int hi[MAXV], to[MAXV][MAXV], tm[MAXV][MAXV]; int vis[MAXV], prev[MAXV]; void dijkstra(int start, int goal) { int i, n, t; memset(vis, INF, sizeof(vis)); memset(prev, INF, sizeof(prev)); enq(start, 0); while (qsize) { n = que[0].n, t = que[0].t, deq(); if (n == goal) break; 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, enq(nx, nt); else if (vis[nx] == nt) prev[nx] = MIN(prev[nx], n); } } } int main() { int i, k, M, S, G; 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(G, S); out(S); while (S != G) S = prev[S], pc(' '), out(S); pc('\n'); return 0; }