Is there a name for this priority queue data structure?












2












$begingroup$


While watching a sports tournament, I noticed that the tournament tree looks a lot like a heap. I came up with the following data structure: A complete binary tree where the leaves are elements of some set, and each internal node is the $max$ of its two children. I came up with a BuildHeap algorithm that's $O(n)$, a GetMax algorithm that's $O(1)$, an Insert algorithm that's $O(log n)$, and a Delete algorithm that's $O(log n)$. The number of nodes in this "heap" is $2n-1$ where $n$ is the number of elements in the underlying set. The structure is simpler than a binary heap.



Is there a name for this data structure?






data-structures terminology heaps priority-queues







share|cite|improve this question











$endgroup$

















    2












    $begingroup$


    While watching a sports tournament, I noticed that the tournament tree looks a lot like a heap. I came up with the following data structure: A complete binary tree where the leaves are elements of some set, and each internal node is the $max$ of its two children. I came up with a BuildHeap algorithm that's $O(n)$, a GetMax algorithm that's $O(1)$, an Insert algorithm that's $O(log n)$, and a Delete algorithm that's $O(log n)$. The number of nodes in this "heap" is $2n-1$ where $n$ is the number of elements in the underlying set. The structure is simpler than a binary heap.



    Is there a name for this data structure?






    data-structures terminology heaps priority-queues







    share|cite|improve this question











    $endgroup$















      2












      2








      2





      $begingroup$


      While watching a sports tournament, I noticed that the tournament tree looks a lot like a heap. I came up with the following data structure: A complete binary tree where the leaves are elements of some set, and each internal node is the $max$ of its two children. I came up with a BuildHeap algorithm that's $O(n)$, a GetMax algorithm that's $O(1)$, an Insert algorithm that's $O(log n)$, and a Delete algorithm that's $O(log n)$. The number of nodes in this "heap" is $2n-1$ where $n$ is the number of elements in the underlying set. The structure is simpler than a binary heap.



      Is there a name for this data structure?






      data-structures terminology heaps priority-queues







      share|cite|improve this question











      $endgroup$




      While watching a sports tournament, I noticed that the tournament tree looks a lot like a heap. I came up with the following data structure: A complete binary tree where the leaves are elements of some set, and each internal node is the $max$ of its two children. I came up with a BuildHeap algorithm that's $O(n)$, a GetMax algorithm that's $O(1)$, an Insert algorithm that's $O(log n)$, and a Delete algorithm that's $O(log n)$. The number of nodes in this "heap" is $2n-1$ where $n$ is the number of elements in the underlying set. The structure is simpler than a binary heap.



      Is there a name for this data structure?






      data-structures terminology heaps priority-queues




      data-structures terminology heaps priority-queues






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 27 at 3:31









      Apass.Jack

      13.3k1939




      13.3k1939










      asked Jan 26 at 20:50









      man on laptopman on laptop

      34119




      34119






















          2 Answers
          2






          active

          oldest

          votes


















          6












          $begingroup$

          This is essentially a Segment tree which is a data structure that augments an array with a binary tree as you describe such that:




          • You have fast set and get at any index

          • You have fast "aggregate" queries on ranges

          • You can support fast update queries on ranges, for some combinations of updates and queries


          The $j$th node at height $k$ in the tree "summarizes" a subarray $[j*2^k, (j+1)*2^k)$ of the original array. Since each element of the array appears in only logarithmically many such subarrays, we can do updates in $O(log n)$ time.



          The range queries can use any associative operation. In your example the operation is $max$, but other examples include sum, product, even standard deviation (via sum and sum of squares).




          I originally called this a Fenwick Tree (aka Binary Indexed Tree), which is a similar structure but which compresses the tree into only exactly $n$ storage with no overhead(but loses access to the original array).






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            I think you're right and I confuse them all the time
            $endgroup$
            – Curtis F
            Jan 26 at 22:39






          • 3




            $begingroup$
            For clarification: a Segment tree also uses linear storage.
            $endgroup$
            – Jakube
            Jan 26 at 23:12



















          1












          $begingroup$

          You've just reinvented a range-query structure. This is an instance of the more general idea that, if you put all data at only the leaves of a binary tree, you can use internal nodes to represent substructures, and it will work for any kind of structure that can be recursively defined with an $O(1)$ recursive initialization.



          In this case, you can see that the structure is just an unordered set with a maximum, which is obviously $O(1)$ recursively definable. It is also clear that you can support Insert and DeleteMax and $O(1)$ GetMax, but not $O(log n)$ Search. Additionally, if you think a bit you should be able to figure out how to support $O(log n)$ MergeHeap.






          share|cite|improve this answer









          $endgroup$













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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            6












            $begingroup$

            This is essentially a Segment tree which is a data structure that augments an array with a binary tree as you describe such that:




            • You have fast set and get at any index

            • You have fast "aggregate" queries on ranges

            • You can support fast update queries on ranges, for some combinations of updates and queries


            The $j$th node at height $k$ in the tree "summarizes" a subarray $[j*2^k, (j+1)*2^k)$ of the original array. Since each element of the array appears in only logarithmically many such subarrays, we can do updates in $O(log n)$ time.



            The range queries can use any associative operation. In your example the operation is $max$, but other examples include sum, product, even standard deviation (via sum and sum of squares).




            I originally called this a Fenwick Tree (aka Binary Indexed Tree), which is a similar structure but which compresses the tree into only exactly $n$ storage with no overhead(but loses access to the original array).






            share|cite|improve this answer











            $endgroup$













            • $begingroup$
              I think you're right and I confuse them all the time
              $endgroup$
              – Curtis F
              Jan 26 at 22:39






            • 3




              $begingroup$
              For clarification: a Segment tree also uses linear storage.
              $endgroup$
              – Jakube
              Jan 26 at 23:12
















            6












            $begingroup$

            This is essentially a Segment tree which is a data structure that augments an array with a binary tree as you describe such that:




            • You have fast set and get at any index

            • You have fast "aggregate" queries on ranges

            • You can support fast update queries on ranges, for some combinations of updates and queries


            The $j$th node at height $k$ in the tree "summarizes" a subarray $[j*2^k, (j+1)*2^k)$ of the original array. Since each element of the array appears in only logarithmically many such subarrays, we can do updates in $O(log n)$ time.



            The range queries can use any associative operation. In your example the operation is $max$, but other examples include sum, product, even standard deviation (via sum and sum of squares).




            I originally called this a Fenwick Tree (aka Binary Indexed Tree), which is a similar structure but which compresses the tree into only exactly $n$ storage with no overhead(but loses access to the original array).






            share|cite|improve this answer











            $endgroup$













            • $begingroup$
              I think you're right and I confuse them all the time
              $endgroup$
              – Curtis F
              Jan 26 at 22:39






            • 3




              $begingroup$
              For clarification: a Segment tree also uses linear storage.
              $endgroup$
              – Jakube
              Jan 26 at 23:12














            6












            6








            6





            $begingroup$

            This is essentially a Segment tree which is a data structure that augments an array with a binary tree as you describe such that:




            • You have fast set and get at any index

            • You have fast "aggregate" queries on ranges

            • You can support fast update queries on ranges, for some combinations of updates and queries


            The $j$th node at height $k$ in the tree "summarizes" a subarray $[j*2^k, (j+1)*2^k)$ of the original array. Since each element of the array appears in only logarithmically many such subarrays, we can do updates in $O(log n)$ time.



            The range queries can use any associative operation. In your example the operation is $max$, but other examples include sum, product, even standard deviation (via sum and sum of squares).




            I originally called this a Fenwick Tree (aka Binary Indexed Tree), which is a similar structure but which compresses the tree into only exactly $n$ storage with no overhead(but loses access to the original array).






            share|cite|improve this answer











            $endgroup$



            This is essentially a Segment tree which is a data structure that augments an array with a binary tree as you describe such that:




            • You have fast set and get at any index

            • You have fast "aggregate" queries on ranges

            • You can support fast update queries on ranges, for some combinations of updates and queries


            The $j$th node at height $k$ in the tree "summarizes" a subarray $[j*2^k, (j+1)*2^k)$ of the original array. Since each element of the array appears in only logarithmically many such subarrays, we can do updates in $O(log n)$ time.



            The range queries can use any associative operation. In your example the operation is $max$, but other examples include sum, product, even standard deviation (via sum and sum of squares).




            I originally called this a Fenwick Tree (aka Binary Indexed Tree), which is a similar structure but which compresses the tree into only exactly $n$ storage with no overhead(but loses access to the original array).







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited Jan 27 at 17:26

























            answered Jan 26 at 21:16









            Curtis FCurtis F

            450211




            450211












            • $begingroup$
              I think you're right and I confuse them all the time
              $endgroup$
              – Curtis F
              Jan 26 at 22:39






            • 3




              $begingroup$
              For clarification: a Segment tree also uses linear storage.
              $endgroup$
              – Jakube
              Jan 26 at 23:12


















            • $begingroup$
              I think you're right and I confuse them all the time
              $endgroup$
              – Curtis F
              Jan 26 at 22:39






            • 3




              $begingroup$
              For clarification: a Segment tree also uses linear storage.
              $endgroup$
              – Jakube
              Jan 26 at 23:12
















            $begingroup$
            I think you're right and I confuse them all the time
            $endgroup$
            – Curtis F
            Jan 26 at 22:39




            $begingroup$
            I think you're right and I confuse them all the time
            $endgroup$
            – Curtis F
            Jan 26 at 22:39




            3




            3




            $begingroup$
            For clarification: a Segment tree also uses linear storage.
            $endgroup$
            – Jakube
            Jan 26 at 23:12




            $begingroup$
            For clarification: a Segment tree also uses linear storage.
            $endgroup$
            – Jakube
            Jan 26 at 23:12











            1












            $begingroup$

            You've just reinvented a range-query structure. This is an instance of the more general idea that, if you put all data at only the leaves of a binary tree, you can use internal nodes to represent substructures, and it will work for any kind of structure that can be recursively defined with an $O(1)$ recursive initialization.



            In this case, you can see that the structure is just an unordered set with a maximum, which is obviously $O(1)$ recursively definable. It is also clear that you can support Insert and DeleteMax and $O(1)$ GetMax, but not $O(log n)$ Search. Additionally, if you think a bit you should be able to figure out how to support $O(log n)$ MergeHeap.






            share|cite|improve this answer









            $endgroup$


















              1












              $begingroup$

              You've just reinvented a range-query structure. This is an instance of the more general idea that, if you put all data at only the leaves of a binary tree, you can use internal nodes to represent substructures, and it will work for any kind of structure that can be recursively defined with an $O(1)$ recursive initialization.



              In this case, you can see that the structure is just an unordered set with a maximum, which is obviously $O(1)$ recursively definable. It is also clear that you can support Insert and DeleteMax and $O(1)$ GetMax, but not $O(log n)$ Search. Additionally, if you think a bit you should be able to figure out how to support $O(log n)$ MergeHeap.






              share|cite|improve this answer









              $endgroup$
















                1












                1








                1





                $begingroup$

                You've just reinvented a range-query structure. This is an instance of the more general idea that, if you put all data at only the leaves of a binary tree, you can use internal nodes to represent substructures, and it will work for any kind of structure that can be recursively defined with an $O(1)$ recursive initialization.



                In this case, you can see that the structure is just an unordered set with a maximum, which is obviously $O(1)$ recursively definable. It is also clear that you can support Insert and DeleteMax and $O(1)$ GetMax, but not $O(log n)$ Search. Additionally, if you think a bit you should be able to figure out how to support $O(log n)$ MergeHeap.






                share|cite|improve this answer









                $endgroup$



                You've just reinvented a range-query structure. This is an instance of the more general idea that, if you put all data at only the leaves of a binary tree, you can use internal nodes to represent substructures, and it will work for any kind of structure that can be recursively defined with an $O(1)$ recursive initialization.



                In this case, you can see that the structure is just an unordered set with a maximum, which is obviously $O(1)$ recursively definable. It is also clear that you can support Insert and DeleteMax and $O(1)$ GetMax, but not $O(log n)$ Search. Additionally, if you think a bit you should be able to figure out how to support $O(log n)$ MergeHeap.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Jan 27 at 10:05









                user21820user21820

                1304




                1304






























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