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| from heapq import * | |
| class vert: | |
| def __init__(self, id): | |
| self.id = id | |
| self.adj = [] | |
| self.prev = None | |
| self.dist = 0 | |
| self.dsv = 0 | |
| self.dut = 0 | |
| # self.dsu = 0 | |
| # self.dvt = 0 | |
| self.best = 0 | |
| self.visited = False | |
| def __eq__(self, other): | |
| return not self.id < other.id and not other.id < self.id | |
| def __ne__(self, other): | |
| return self.id < other.id or other.id < self.id | |
| def __gt__(self, other): | |
| return other.id < self.id | |
| def __ge__(self, other): | |
| return not self.id < other.id | |
| def __le__(self, other): | |
| return not other.id < self.id | |
| def __repr__(self): | |
| return "|{} dsv:{} dut:{}|".format(self.id, self.dsv, self.dut) | |
| class edge: | |
| def __init__(self, to_u, from_v, length): | |
| self.length = length | |
| self.to_u = to_u | |
| self.from_v = from_v | |
| def __repr__(self): | |
| return "| from:{} --> To:{} length:{}|".format(self.from_v, self.to_u, self.length) | |
| S = vert('S') | |
| A = vert('A') | |
| B = vert('B') | |
| C = vert('C') | |
| D = vert('D') | |
| E = vert('E') | |
| F = vert('F') | |
| G = vert('G') | |
| H = vert('H') | |
| S.adj = [edge(A, S, 1), edge(C, S, 4)] | |
| A.adj = [edge(S, A, 1), edge(B, A, 3)] | |
| B.adj = [edge(C, B, 5), edge(A, B, 3)] | |
| C.adj = [edge(B, C, 5), edge(S, C, 4)] | |
| potential_edge = [edge(B,S, 4), edge(S, A, 2)] | |
| graph = [S, A, B, C] | |
| ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' | |
| Solution | |
| ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' | |
| def addroad(G, s, t, E): | |
| def setdsv(w): # Assign distances for s to v | |
| w.dsv = w.dist | |
| def setdut(w): # Assign distance for distance u to t | |
| w.dut = w.dist | |
| # Perform dijktras starting at s then starting from t | |
| dijktras(G, s, setdsv) | |
| dijktras(G, t, setdut) | |
| minedge = None | |
| mindist = float('inf') | |
| # Iterate through potential edges | |
| for e in E: | |
| v = e.from_v | |
| u = e.to_u | |
| # Get length of path from s to t for the 2 cases | |
| s_v_u_t = v.dsv + e.length + u.dut | |
| s_u_v_t = u.dsv + e.length + v.dut | |
| # Find minimum | |
| dst = min(s_v_u_t, s_u_v_t) | |
| # Check if a smaller option was found | |
| if mindist > dst: | |
| minedge = e | |
| mindist = dst | |
| return minedge | |
| def dijktras(G, s, setdist): | |
| pq = [] # Create a priority queue | |
| # Initialize distance values and push into the heap | |
| for v in G: | |
| v.dist = 0 if v == s else float('inf') | |
| heappush(pq, (v.dist, v)) | |
| while not pq == []: | |
| _, u = heappop(pq) # Remove an element from queue | |
| for e in u.adj: | |
| v = e.to_u | |
| if v.dist > u.dist + e.length: | |
| v.dist = u.dist + e.length | |
| setdist(v) # This assign distance to either dsu or dvt | |
| v.prev = u | |
| heappush(pq, (v.dist, v)) |
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