Mixing
Is there a name for this priority queue data structure?
$begingroup$
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
edited Jan 27 at 3:31
Apass.Jack
13.3k1939
asked Jan 26 at 20:50
man on laptopman on laptop
34119
$endgroup$
add a comment |
$begingroup$
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
edited Jan 27 at 3:31
Apass.Jack
13.3k1939
asked Jan 26 at 20:50
man on laptopman on laptop
34119
$endgroup$
add a comment |
$begingroup$
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
edited Jan 27 at 3:31
Apass.Jack
13.3k1939
asked Jan 26 at 20:50
man on laptopman on laptop
34119
$endgroup$
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
edited Jan 27 at 3:31
Apass.Jack
13.3k1939
asked Jan 26 at 20:50
man on laptopman on laptop
34119
edited Jan 27 at 3:31
Apass.Jack
13.3k1939
asked Jan 26 at 20:50
man on laptopman on laptop
34119
edited Jan 27 at 3:31
Apass.Jack
13.3k1939
edited Jan 27 at 3:31
Apass.Jack
13.3k1939
edited Jan 27 at 3:31
Apass.Jack
13.3k1939
13.3k1939
asked Jan 26 at 20:50
man on laptopman on laptop
34119
asked Jan 26 at 20:50
man on laptopman on laptop
34119
asked Jan 26 at 20:50
man on laptopman on laptop
34119
34119
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
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).
answered Jan 26 at 21:16
Curtis FCurtis F
450211
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
answered Jan 27 at 10:05
user21820user21820
1304
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "419"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcs.stackexchange.com%2fquestions%2f103444%2fis-there-a-name-for-this-priority-queue-data-structure%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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).
answered Jan 26 at 21:16
Curtis FCurtis F
450211
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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).
answered Jan 26 at 21:16
Curtis FCurtis F
450211
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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).
answered Jan 26 at 21:16
Curtis FCurtis F
450211
$endgroup$
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).
answered Jan 26 at 21:16
Curtis FCurtis F
450211
edited Jan 27 at 17:26
answered Jan 26 at 21:16
Curtis FCurtis F
450211
answered Jan 26 at 21:16
Curtis FCurtis F
450211
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
add a comment |
$begingroup$
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
add a comment |
$begingroup$
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.
answered Jan 27 at 10:05
user21820user21820
1304
$endgroup$
add a comment |
$begingroup$
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.
answered Jan 27 at 10:05
user21820user21820
1304
$endgroup$
add a comment |
$begingroup$
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.
answered Jan 27 at 10:05
user21820user21820
1304
$endgroup$
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.
answered Jan 27 at 10:05
user21820user21820
1304
answered Jan 27 at 10:05
user21820user21820
1304
answered Jan 27 at 10:05
user21820user21820
1304
answered Jan 27 at 10:05
user21820user21820
1304
1304
add a comment |
add a comment |
Thanks for contributing an answer to Computer Science Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcs.stackexchange.com%2fquestions%2f103444%2fis-there-a-name-for-this-priority-queue-data-structure%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
