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    <p>Well, as Darren already said, <a href="http://www.cplusplus.com/reference/stl/priority_queue/" rel="noreferrer"><code>std::priority_queue</code></a> doesn't have means for decreasing the priority of an element and neither the removal of an element other than the current min. But the default <code>std::priority_queue</code> is nothing more than a simple container adaptor around a <code>std::vector</code> that uses the std heap functions from <code>&lt;algorithm&gt;</code> (<a href="http://www.cplusplus.com/reference/algorithm/push_heap/" rel="noreferrer"><code>std::push_heap</code></a>, <a href="http://www.cplusplus.com/reference/algorithm/pop_heap/" rel="noreferrer"><code>std::pop_heap</code></a> and <a href="http://www.cplusplus.com/reference/algorithm/make_heap/" rel="noreferrer"><code>std::make_heap</code></a>). So for Dijkstra (where you need priority update) I usually just do this myself and use a simple <code>std::vector</code>.</p> <p>A push is then just the O(log N) operation</p> <pre><code>vec.push_back(item); std::push_heap(vec.begin(), vec.end()); </code></pre> <p>Of course for constructing a queue anew from N elements, we don't push them all using this O(log N) operation (making the whole thing O(Nlog N)) but just put them all into the vector followed by a simple O(N)</p> <pre><code>std::make_heap(vec.begin(), vec.end()); </code></pre> <p>The min element is a simple O(1)</p> <pre><code>vec.front(); </code></pre> <p>A pop is the simple O(log N) sequence</p> <pre><code>std::pop_heap(vec.begin(), vec.end()); vec.pop_back(); </code></pre> <p>So far this is just what <code>std::priority_queue</code> usually does under the hood. Now to change an item's priority we just need to change it (however it may be incorporated in the item's type) and make the sequence a valid heap again</p> <pre><code>std::make_heap(vec.begin(), vec.end()); </code></pre> <p>I know this is an O(N) operation, but on the other hand this removes any need for keeping track of an item's position in the heap with an additional data structure or (even worse) an augmentation of the items' type. And the performance penalty over a logarithmic priority update is in practice not that signficant, considering the ease of use, compact and linear memory useage of <code>std::vector</code> (which impacts runtime, too), and the fact that I often work with graphs that have rather few edges (linear in the vertex count) anyway.</p> <p>It may not in all cases be the fastest way, but certainly the easiest.</p> <p><strong>EDIT:</strong> Oh, and since the standard library uses max-heaps, you need to use an equivalent to <code>&gt;</code> for comparing priorities (however you get them from the items), instead of the default <code>&lt;</code> operator.</p>
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    1. POEasiest way of using min priority queue with key update in C++
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    1. USChristian Rau
    1. USChristian Rau
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    1. COWhen you say *to change an item's priority we just need to change it* - do you mean that an `O(N)` search is done to find the item within the heap, the item is updated and then the full heap is re-built (at `O(N)` again)?
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      1. USDarren Engwirda
    2. CO@DarrenEngwirda No, I usually have the priority connected to the item anyway (either by being determined from the item directly or by an ID->value array or something the like), which makes updating the priority O(1). If I knew the item's position in the heap (which I don't want to keep track of), then could just use the O(log N) `std::push_heap` over `std::make_heap`. The priority is part of the item and not of the heap (of course this requires a non-trivial comparison predicate). By just using `std::make_heap` the heap doesn't need to know which item's priority changed and we can just do it.
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