18/03: Problem D

18-03-24/d.py

@@ -0,0 +1,54 @@
+def main():
+    n, m, k = map(int, input().split())
+    a = [int(i) for i in input().split()]
+    # roads = [list(map(int, input().split())) for _ in range(m)]
+
+    voisins = {i:set() for i in range(1, n+1)}
+
+    A = set(a) # pour les test d'appartenance
+    special = False
+    for _ in range(m):
+        x, y = map(int, input().split())
+        voisins[x].add(y)
+        voisins[y].add(x)
+        if not special and (x in A and y in A):
+            special = True
+
+
+    def distance(source, dist):
+        """calculer la distance d'un sommet à tous les autres"""
+        non_vus = set((i+1 for i in range(n) if i+1 != source))
+        queue = [source]
+        dist[source] = 0
+        while queue != []:
+            nextQ = []
+            while queue != []:
+                s = queue.pop()
+                for v in voisins[s]:
+                    if v in non_vus:
+                        non_vus.remove(v)
+                        nextQ.append(v)
+                        dist[v] = dist[s]+1
+            queue = nextQ
+    
+    dist_n = [0 for _ in range(n+1)]
+    dist_1 = [0 for _ in range(n+1)]
+    distance(n, dist_n)
+    distance(1, dist_1)
+
+    if special:
+        return dist_n[1] # On ne rajoute rien
+
+    # On regarde lequel ajouter
+    a.sort(key=lambda x: dist_1[x]-dist_n[x])
+    sp_count = len(a)
+    b = [dist_n[a[-1]] for i in range(sp_count)]
+    for sp in range(1, sp_count):
+        b[sp_count-1-sp] = max(b[sp_count-sp], dist_n[a[sp_count-sp]])
+
+    return min(
+        dist_1[n],
+        max((dist_1[a[i]]+b[i] for i in range(0, len(a)-1)))+1
+    )
+
+print(main())