Mixing
Compare two algorithms with each other
I am fairly new algorithms and the math behind it.
I am very sorry if this is the wrong place to ask if so please let me know and I can delete this question.
I would need help with the following algorithms.
The task is to choose α so that B is asymptotically faster than A.
A: $ T_a$(n) = 7$T_a$($frac{n}{2}$)+n²
B: $ T_b$(n) = α$T_b$($frac{n}{4}$)+n²
I have tried to figure out what the asymptotically upper bound would be and I have come up with this formula for A:
A: T(n) = n² + $sum_{k=1}^k 7^{k-1} frac{(n^2)}{2^k}+7^kT(frac{n}{2^k})$
k is for n < 2 = ld(n)
But I do not understand how to go on from here.
Any help would be very apricated.
sequences-and-series algorithms asymptotics
edited Nov 21 '18 at 20:23
Scientifica
6,37641335
asked Nov 21 '18 at 20:01
MarkMark
111
add a comment |
I am fairly new algorithms and the math behind it.
I am very sorry if this is the wrong place to ask if so please let me know and I can delete this question.
I would need help with the following algorithms.
The task is to choose α so that B is asymptotically faster than A.
A: $ T_a$(n) = 7$T_a$($frac{n}{2}$)+n²
B: $ T_b$(n) = α$T_b$($frac{n}{4}$)+n²
I have tried to figure out what the asymptotically upper bound would be and I have come up with this formula for A:
A: T(n) = n² + $sum_{k=1}^k 7^{k-1} frac{(n^2)}{2^k}+7^kT(frac{n}{2^k})$
k is for n < 2 = ld(n)
But I do not understand how to go on from here.
Any help would be very apricated.
sequences-and-series algorithms asymptotics
edited Nov 21 '18 at 20:23
Scientifica
6,37641335
asked Nov 21 '18 at 20:01
MarkMark
111
add a comment |
I am fairly new algorithms and the math behind it.
I am very sorry if this is the wrong place to ask if so please let me know and I can delete this question.
I would need help with the following algorithms.
The task is to choose α so that B is asymptotically faster than A.
A: $ T_a$(n) = 7$T_a$($frac{n}{2}$)+n²
B: $ T_b$(n) = α$T_b$($frac{n}{4}$)+n²
I have tried to figure out what the asymptotically upper bound would be and I have come up with this formula for A:
A: T(n) = n² + $sum_{k=1}^k 7^{k-1} frac{(n^2)}{2^k}+7^kT(frac{n}{2^k})$
k is for n < 2 = ld(n)
But I do not understand how to go on from here.
Any help would be very apricated.
sequences-and-series algorithms asymptotics
edited Nov 21 '18 at 20:23
Scientifica
6,37641335
asked Nov 21 '18 at 20:01
MarkMark
111
I am fairly new algorithms and the math behind it.
I am very sorry if this is the wrong place to ask if so please let me know and I can delete this question.
I would need help with the following algorithms.
The task is to choose α so that B is asymptotically faster than A.
A: $ T_a$(n) = 7$T_a$($frac{n}{2}$)+n²
B: $ T_b$(n) = α$T_b$($frac{n}{4}$)+n²
I have tried to figure out what the asymptotically upper bound would be and I have come up with this formula for A:
A: T(n) = n² + $sum_{k=1}^k 7^{k-1} frac{(n^2)}{2^k}+7^kT(frac{n}{2^k})$
k is for n < 2 = ld(n)
But I do not understand how to go on from here.
Any help would be very apricated.
sequences-and-series algorithms asymptotics
sequences-and-series algorithms asymptotics
edited Nov 21 '18 at 20:23
Scientifica
6,37641335
asked Nov 21 '18 at 20:01
MarkMark
111
edited Nov 21 '18 at 20:23
Scientifica
6,37641335
asked Nov 21 '18 at 20:01
MarkMark
111
edited Nov 21 '18 at 20:23
Scientifica
6,37641335
edited Nov 21 '18 at 20:23
Scientifica
6,37641335
edited Nov 21 '18 at 20:23
Scientifica
6,37641335
6,37641335
asked Nov 21 '18 at 20:01
MarkMark
111
asked Nov 21 '18 at 20:01
MarkMark
111
asked Nov 21 '18 at 20:01
MarkMark
111
111
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
If you are familiar with Master theorem, you can solve it easily. From the master theorem as $c_{crit} = log_27 sim 2.81$ we know that $A = O(n^{2.81}) = Theta(n^{log_27})$. Hence, if $a = 4^2 = 16$, from master thorem $B = Theta(n^2log(n))$ and asymptotically faster than $A$. Also, for all $a < 16$ this would be true.
answered Nov 22 '18 at 11:10
OmGOmG
2,212620
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: "69"
};
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: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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
},
noCode: 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%2fmath.stackexchange.com%2fquestions%2f3008266%2fcompare-two-algorithms-with-each-other%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
If you are familiar with Master theorem, you can solve it easily. From the master theorem as $c_{crit} = log_27 sim 2.81$ we know that $A = O(n^{2.81}) = Theta(n^{log_27})$. Hence, if $a = 4^2 = 16$, from master thorem $B = Theta(n^2log(n))$ and asymptotically faster than $A$. Also, for all $a < 16$ this would be true.
answered Nov 22 '18 at 11:10
OmGOmG
2,212620
add a comment |
If you are familiar with Master theorem, you can solve it easily. From the master theorem as $c_{crit} = log_27 sim 2.81$ we know that $A = O(n^{2.81}) = Theta(n^{log_27})$. Hence, if $a = 4^2 = 16$, from master thorem $B = Theta(n^2log(n))$ and asymptotically faster than $A$. Also, for all $a < 16$ this would be true.
answered Nov 22 '18 at 11:10
OmGOmG
2,212620
add a comment |
If you are familiar with Master theorem, you can solve it easily. From the master theorem as $c_{crit} = log_27 sim 2.81$ we know that $A = O(n^{2.81}) = Theta(n^{log_27})$. Hence, if $a = 4^2 = 16$, from master thorem $B = Theta(n^2log(n))$ and asymptotically faster than $A$. Also, for all $a < 16$ this would be true.
answered Nov 22 '18 at 11:10
OmGOmG
2,212620
If you are familiar with Master theorem, you can solve it easily. From the master theorem as $c_{crit} = log_27 sim 2.81$ we know that $A = O(n^{2.81}) = Theta(n^{log_27})$. Hence, if $a = 4^2 = 16$, from master thorem $B = Theta(n^2log(n))$ and asymptotically faster than $A$. Also, for all $a < 16$ this would be true.
answered Nov 22 '18 at 11:10
OmGOmG
2,212620
answered Nov 22 '18 at 11:10
OmGOmG
2,212620
answered Nov 22 '18 at 11:10
OmGOmG
2,212620
answered Nov 22 '18 at 11:10
OmGOmG
2,212620
2,212620
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics 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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2fmath.stackexchange.com%2fquestions%2f3008266%2fcompare-two-algorithms-with-each-other%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
