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Prove Dijkstra's O(E + VlogV) complexity
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[QUOTE="fresh_42, post: 6426178, member: 572553"] I would reason this way: You have to visit each edge and each vertex at least once, for otherwise you might lose the minimum. This gets you ##O(|E|\cdot T_1 +|V|\cdot T_2)## where ##T_i## is the time you use at each edge: ##T_1=T(\text{decrease key})## and the time at each vertex: ##T_2=T(\text{extract minimum})##. To extract minimum we use Fibonacci Heaps which run in ##O(\log n)##. So all you have to do is to show that ##T_1=O(1)## and ##T_2 > O(\log |V|)##. So you have to show the lower boundary for the sort operation via Fibonacci heap (sufficiency) and that any sort algorithm needs at least ##O(\log n)## (necessity). [/QUOTE]
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Prove Dijkstra's O(E + VlogV) complexity
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