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| 1 | +import sys, heapq |
| 2 | + |
| 3 | +n, m = map(int, input().split()) |
| 4 | +INF = 1000000000 |
| 5 | +d = [[INF]*(n+1) for _ in range(n+1)] |
| 6 | +result = 0 |
| 7 | + |
| 8 | +for i in range(m): |
| 9 | + a, b, dist = map(int, input().split()) |
| 10 | + d[a][b] = dist |
| 11 | + d[b][a] = dist |
| 12 | + |
| 13 | +for i in range(n): |
| 14 | + d[i+1][i+1] = 0 |
| 15 | + |
| 16 | +def dijkstra1(start, dest): # 달빛여우 |
| 17 | + q = [] |
| 18 | + distance = [INF] * (n+1) |
| 19 | + distance[start] = 0 |
| 20 | + heapq.heappush(q, [0, start]) |
| 21 | + |
| 22 | + while(q): |
| 23 | + cur_distance, cur = heapq.heappop(q) |
| 24 | + |
| 25 | + for i in range(1, n+1): |
| 26 | + if 0 < d[cur][i] < INF: |
| 27 | + if d[cur][i] + cur_distance < distance[i]: |
| 28 | + distance[i] = d[cur][i] + cur_distance |
| 29 | + heapq.heappush(q, [distance[i], i]) |
| 30 | + |
| 31 | + return distance[dest] |
| 32 | + |
| 33 | +def dijkstra2(start, dest): #달빛늑대 |
| 34 | + q = [] |
| 35 | + distance = [[INF] * (n + 1) for _ in range(2)] # distance[0] 빠른도착 , distance[1] 느린 도착 |
| 36 | + distance[start][start] = 0 |
| 37 | + heapq.heappush(q, [0, start, 1]) # 3번째 인자를 추가, 1 = 두배의 속력, -1 = 절반의 속력 |
| 38 | + result_distance = [INF] * (n+1) |
| 39 | + |
| 40 | + while(q): |
| 41 | + cur_distance, cur, condition = heapq.heappop(q) |
| 42 | + |
| 43 | + for i in range(1, n+1): |
| 44 | + if 0 < d[cur][i] < INF: |
| 45 | + if condition == 1: |
| 46 | + if (d[cur][i]/2) + cur_distance < distance[0][i]: |
| 47 | + distance[0][i] = (d[cur][i] / 2) + cur_distance |
| 48 | + heapq.heappush(q, [distance[0][i], i, -1]) |
| 49 | + |
| 50 | + elif condition == -1: |
| 51 | + if (d[cur][i] * 2) + cur_distance < distance[1][i]: |
| 52 | + distance[1][i] = (d[cur][i] * 2) + cur_distance |
| 53 | + heapq.heappush(q, [distance[1][i], i, 1]) |
| 54 | + |
| 55 | + for i in range(1, n+1): |
| 56 | + result_distance[i] = min(distance[0][i], distance[1][i]) |
| 57 | + |
| 58 | + return result_distance[dest] |
| 59 | + |
| 60 | + |
| 61 | +for i in range(2, n+1): |
| 62 | + if dijkstra1(1, i) < dijkstra2(1, i): |
| 63 | + result += 1 |
| 64 | + |
| 65 | +print(result) |
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