But wait, I donâ€™t think in random weighted graph u use Fibonacci heap , because Fibonacci heap is just using 2 queues if u know 0-1 BFS u know we take deque while pushing we check if the cost is 0 then push into front otherwise push into end .

while in fibonaci heap same happens we take 2 queues ( as in graph there is only two types of cost either X or Y ) so we take 2 queues one for push cost X and other for cost Y but fibo heap works when we know there is only K distinct weights but if there are random weights then Dijkistra works fine and implementation is much simpler

@spandan_35