SOLVING RECURRENCE RELATION BY BACK SUBSTITUTION

NIHAR MUKHIYA asked Jul 2, 2017 • retagged Jul 6, 2022 by Lakshman Bhaiya

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aka 53 asked Nov 21, 2017

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Algo Recurrence Relation using Bck Substitution

T(n) = 4T(n/2) + C ......where C ConstantT(n) = 16T(n/4) + 5CCant figure out how to generalize and compare with base condition T(n) = 1 from above step.

aka 53 asked Nov 21, 2017

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Himanshu Goyal asked Oct 12, 2016

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What will be the time complexity of recurrence relation T(n)=c+T(n-1) using substitution method?

What will be the solution of the recurrence relation $T(n)=c+T(n-1)$ using substitution method?c is a constant here.

Himanshu Goyal asked Oct 12, 2016

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piyushkr asked Dec 23, 2015

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What will be the time complexity of recurrence relation T(n)=2T(n-1)+c using substitution method?

Where c is constant.

piyushkr asked Dec 23, 2015

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PEKKA asked Dec 6, 2016

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Solve the recurrence using back substitution method

Solve the following Recurrence Equation using back substitution method T(n)= 2T(n/2)+log n

PEKKA asked Dec 6, 2016

	Total		PHP			MySQL			Other		RAM
	Time (ms)	%	Time (ms)	%	File count	Time (ms)	%	Query count	Time (ms)	%	Amount	%
Setup	4.0	5%	2.5	3%	72	1.5	2%	2	0.0	0%	569k	48%
Control	12.7	18%	1.4	2%	5	11.5	17%	12	0.0	0%	233k	19%
View	1.6	2%	1.6	2%	12	0.0	0%	0	0.0	0%	87k	7%
Theme	42.4	62%	4.7	7%	15	37.7	55%	3	0.0	0%	281k	23%
Stats	6.9	10%	0.1	0%	0	6.8	10%	1	0.0	0%	0k	0%
Total	67.6	100%	10.3	15%	104	57.6	85%	18	0.0	0%	1172k	100%

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('goclasses_wq15','goclasses_wq','goclasses2024-dm-1','goclasses2024-programming-1','goclasses2024-dm-2','goclasses2024-programming-2','goclasses2024-dm-3','goclasses2024-programming-3','goclasses2024-dm-4','goclasses2024-ds-1','goclasses2024-dm-5','goclasses2024-dm-05','goclasses2024-ds-2','goclasses_wq11','goclasses2024-dl-1','goclasses2024-ds-3','goclasses2024-dl-2','goclasses2024-ds-4','goclasses2024-dl-3','go2024-quantitative-aptitude-1','go2024-verbal-aptitude-1','go2024-spatial-and-analytical-aptitude-1','go2024-digital-logic-1','go2024-programming-1','go2024-algorithms-1','go2024-probability-1','go2024-linear-algebra-1','go2024-calculus-1','go2024-dbms-1','go2024-toc-1','go2024-cd-1','go2024-os-1','go2024-os-2','go2024-cn-1','go2024-coa-1','go2024-ds-1','go2024-dm-1','go2024-dm-2','go2024-dm-3','go2024-dm-4','go2024-mix-1','go2024-mix-2','go2024-algorithms-2','go2024-mix-3','go2024-mix-4','go2024-mockgate-1','go2024-mockgate-2','go2024-mockgate-3','go2024-mockgate-4','go2024-mockgate-5','go2024-mockgate-6','goclasses2024-ds-5','goclasses2024-toc-1','goclasses2024-algo-1','goclasses2024-algo-2','goclasses2024-toc-2','goclasses2024-algo-3','goclasses2024-toc-3','goclasses_wq14','goclasses2024-toc-4','goclasses2024-toc-5','goclasses2024-la','goclasses2024-coa-1','goclasses2024-algo-4','goclasses_wq16','goclasses2024-probability','goclasses2024-calculus','goclasses2024-coa-2','goclasses2024-coa-3','goclasses2024-dbms-1','goclasses2024-dbms-2','goclasses2024-mix-1','goclasses2024-os-1','goclasses2024-os-2','goclasses2024-os-3','goclasses2024-dbms-3','goclasses2024-os-4','goclasses2024-dbms-4','goclasses2024-dbms-5','goclasses2024-mix-2','goclasses2024-cd-1','goclasses2024-cd-3','goclasses2024-cd-2','goclasses2024-coa-4','goclasses2024-mockgate-1','goclasses2024-mockgate-2','goclasses2024-mockgate-3','goclasses2024-cn-2','go2024-topictest-1','goclasses2024-mockgate-4','goclasses2024-cn-1','goclasses2024-cn-3','go2024-topictest-2','goclasses2024-mix-3','goclasses2024-mockgate-5','goclasses2024-mix-4','goclasses2024-mockgate-6','goclasses2024-mockgate-7','goclasses2024-mockgate-8','goclasses2024-cn-4','goclasses2024-mockgate-9','goclasses2024-iiith-mock-3','dm_test_2','dm_test_2_new','goclasses2024_wq9','goclasses2024-probability-1','goclasses2024_wq10','testsbyankitg-dm-3','goclasses2024-la-1','goclasses2023-iiith-mock-4','goclasses2024_wq11','testsbyankitg-dm-4','testsbyankitg_dm-4','testsbyankitg_dm_4','testsbyankitg-dm_4','dm-test-4','dm-logic-test-4','dm_logic_test_4','testsbyankitg-dm-logic-4','logic_dm_test_4','logic-test-4','testsbyankitg-logic-dm-4','goclasses2023-iiith-mock-5','goclasses2024_wq12','goclasses2024_wq13','goclasses2024_wq14','goclasses2024_wq15','goclasses2023-nielit-mock-1','goclasses2024_wq16','goclasses2023-nielit-mock-2','goclasses2024_wq17','goclasses2024_wq18','','goclasses2023-nielit-mock-3','goclasses2024_wq19','goclasses2023-nielit-mock-4','goclasses2024_wq20','goclasses2024-toc-4-weekly-quiz','goclasses2023-nielit-mock-5','goclasses2024-dm-6','goclasses2024-toc-6','goclasses2024-ds-4-weekly-quiz','goclasses2024_wq21','goclasses2023-nielit-mock-6','goclasses2024_wq22','goclasses2024-mix-1-weekly-quiz','goclasses2024-dl-1-weekly-quiz','goclasses2024_wq23','goclasses2024_wq24','goclasses2023-scholarship-test','goclasses2024_wq25','goclasses2023-nielit-mock-7','goclasses2024_wq26','goclasses2024_wq27','goclasses2024_wq28','goclasses2024-toc-7','goclasses2024_wq29','goclasses2024_wq30','goclasses2023-nielit-mock-8','goclasses2024_wq31','goclasses2024-ds-5-weekly-quiz','goclasses2023-nielit-mock-9','goclasses2024_wq32','goclasses2024_wq33','goclasses2023-nielit-mock-10','goclasses2024_wq34','goclasses2024-mockgate-10','goclasses2024-mockgate-da-1','goclasses2024-mockgate-da-2','goclasses2023-iiith-mock-2','goclasses2023-iiith-mock-3','goclasses2025_wq1','goclasses2025_wq2','goclasses2025_wq3','goclasses2025_wq4','goclasses2024-iiith-mock-2','goclasses2025_wq5','test123','testq','goclasses_wq41'))

) JOIN qa_posts AS parents ON qa_posts.parentid=parents.postid WHERE parents.parentid=135714 AND LEFT(parents.type, 1)='A'

1.76 ms - 5 rows - 44 columns

SELECT qa_posts.postid, qa_posts.categoryid, qa_posts.type, LEFT(qa_posts.type, 1) AS `basetype`, INSTR(qa_posts.type, '_HIDDEN')>0 AS `hidden`, INSTR(qa_posts.type, '_QUEUED')>0 AS `queued`, qa_posts.acount, qa_posts.amaxvote, qa_posts.selchildid, qa_posts.closedbyid, qa_posts.upvotes, qa_posts.downvotes, qa_posts.netvotes, qa_posts.views, qa_posts.hotness, qa_posts.flagcount, qa_posts.title, qa_posts.tags, UNIX_TIMESTAMP(qa_posts.created) AS `created`, qa_posts.name, qa_categories.title AS `categoryname`, qa_categories.backpath AS `categorybackpath`, CONCAT_WS(',', qa_posts.catidpath1, qa_posts.catidpath2, qa_posts.catidpath3, qa_posts.categoryid) AS `categoryids`, qa_posts.userid, qa_posts.cookieid, qa_posts.createip AS `createip`, qa_userpoints.points, qa_users.flags, qa_users.level, qa_users.email AS `email`, qa_users.handle AS `handle`, BINARY qa_users.avatarblobid AS `avatarblobid`, qa_users.avatarwidth, qa_users.avatarheight FROM qa_posts LEFT JOIN qa_categories ON qa_categories.categoryid=qa_posts.categoryid LEFT JOIN qa_users ON qa_posts.userid=qa_users.userid LEFT JOIN qa_userpoints ON qa_posts.userid=qa_userpoints.userid join qa_posts ef on qa_posts.postid = ef.postid and ef.postid not in(select postid  from qa_posttags pt where pt.wordid  in (select wordid from qa_words wd where wd.word in ('goclasses_wq15','goclasses_wq','goclasses2024-dm-1','goclasses2024-programming-1','goclasses2024-dm-2','goclasses2024-programming-2','goclasses2024-dm-3','goclasses2024-programming-3','goclasses2024-dm-4','goclasses2024-ds-1','goclasses2024-dm-5','goclasses2024-dm-05','goclasses2024-ds-2','goclasses_wq11','goclasses2024-dl-1','goclasses2024-ds-3','goclasses2024-dl-2','goclasses2024-ds-4','goclasses2024-dl-3','go2024-quantitative-aptitude-1','go2024-verbal-aptitude-1','go2024-spatial-and-analytical-aptitude-1','go2024-digital-logic-1','go2024-programming-1','go2024-algorithms-1','go2024-probability-1','go2024-linear-algebra-1','go2024-calculus-1','go2024-dbms-1','go2024-toc-1','go2024-cd-1','go2024-os-1','go2024-os-2','go2024-cn-1','go2024-coa-1','go2024-ds-1','go2024-dm-1','go2024-dm-2','go2024-dm-3','go2024-dm-4','go2024-mix-1','go2024-mix-2','go2024-algorithms-2','go2024-mix-3','go2024-mix-4','go2024-mockgate-1','go2024-mockgate-2','go2024-mockgate-3','go2024-mockgate-4','go2024-mockgate-5','go2024-mockgate-6','goclasses2024-ds-5','goclasses2024-toc-1','goclasses2024-algo-1','goclasses2024-algo-2','goclasses2024-toc-2','goclasses2024-algo-3','goclasses2024-toc-3','goclasses_wq14','goclasses2024-toc-4','goclasses2024-toc-5','goclasses2024-la','goclasses2024-coa-1','goclasses2024-algo-4','goclasses_wq16','goclasses2024-probability','goclasses2024-calculus','goclasses2024-coa-2','goclasses2024-coa-3','goclasses2024-dbms-1','goclasses2024-dbms-2','goclasses2024-mix-1','goclasses2024-os-1','goclasses2024-os-2','goclasses2024-os-3','goclasses2024-dbms-3','goclasses2024-os-4','goclasses2024-dbms-4','goclasses2024-dbms-5','goclasses2024-mix-2','goclasses2024-cd-1','goclasses2024-cd-3','goclasses2024-cd-2','goclasses2024-coa-4','goclasses2024-mockgate-1','goclasses2024-mockgate-2','goclasses2024-mockgate-3','goclasses2024-cn-2','go2024-topictest-1','goclasses2024-mockgate-4','goclasses2024-cn-1','goclasses2024-cn-3','go2024-topictest-2','goclasses2024-mix-3','goclasses2024-mockgate-5','goclasses2024-mix-4','goclasses2024-mockgate-6','goclasses2024-mockgate-7','goclasses2024-mockgate-8','goclasses2024-cn-4','goclasses2024-mockgate-9','goclasses2024-iiith-mock-3','dm_test_2','dm_test_2_new','goclasses2024_wq9','goclasses2024-probability-1','goclasses2024_wq10','testsbyankitg-dm-3','goclasses2024-la-1','goclasses2023-iiith-mock-4','goclasses2024_wq11','testsbyankitg-dm-4','testsbyankitg_dm-4','testsbyankitg_dm_4','testsbyankitg-dm_4','dm-test-4','dm-logic-test-4','dm_logic_test_4','testsbyankitg-dm-logic-4','logic_dm_test_4','logic-test-4','testsbyankitg-logic-dm-4','goclasses2023-iiith-mock-5','goclasses2024_wq12','goclasses2024_wq13','goclasses2024_wq14','goclasses2024_wq15','goclasses2023-nielit-mock-1','goclasses2024_wq16','goclasses2023-nielit-mock-2','goclasses2024_wq17','goclasses2024_wq18','','goclasses2023-nielit-mock-3','goclasses2024_wq19','goclasses2023-nielit-mock-4','goclasses2024_wq20','goclasses2024-toc-4-weekly-quiz','goclasses2023-nielit-mock-5','goclasses2024-dm-6','goclasses2024-toc-6','goclasses2024-ds-4-weekly-quiz','goclasses2024_wq21','goclasses2023-nielit-mock-6','goclasses2024_wq22','goclasses2024-mix-1-weekly-quiz','goclasses2024-dl-1-weekly-quiz','goclasses2024_wq23','goclasses2024_wq24','goclasses2023-scholarship-test','goclasses2024_wq25','goclasses2023-nielit-mock-7','goclasses2024_wq26','goclasses2024_wq27','goclasses2024_wq28','goclasses2024-toc-7','goclasses2024_wq29','goclasses2024_wq30','goclasses2023-nielit-mock-8','goclasses2024_wq31','goclasses2024-ds-5-weekly-quiz','goclasses2023-nielit-mock-9','goclasses2024_wq32','goclasses2024_wq33','goclasses2023-nielit-mock-10','goclasses2024_wq34','goclasses2024-mockgate-10','goclasses2024-mockgate-da-1','goclasses2024-mockgate-da-2','goclasses2023-iiith-mock-2','goclasses2023-iiith-mock-3','goclasses2025_wq1','goclasses2025_wq2','goclasses2025_wq3','goclasses2025_wq4','goclasses2024-iiith-mock-2','goclasses2025_wq5','test123','testq','goclasses_wq41'))

) WHERE qa_posts.postid=(SELECT IF(LEFT(parent.type, 1)='A', parent.parentid, parent.postid) FROM qa_posts AS child LEFT JOIN qa_posts AS parent ON parent.postid=child.parentid WHERE child.postid=135714 AND parent.type IN('Q','A'))

1.51 ms - 0 rows - 34 columns

SELECT qa_posts.postid, qa_posts.categoryid, qa_posts.type, LEFT(qa_posts.type, 1) AS `basetype`, INSTR(qa_posts.type, '_HIDDEN')>0 AS `hidden`, INSTR(qa_posts.type, '_QUEUED')>0 AS `queued`, qa_posts.acount, qa_posts.amaxvote, qa_posts.selchildid, qa_posts.closedbyid, qa_posts.upvotes, qa_posts.downvotes, qa_posts.netvotes, qa_posts.views, qa_posts.hotness, qa_posts.flagcount, qa_posts.title, qa_posts.tags, UNIX_TIMESTAMP(qa_posts.created) AS `created`, qa_posts.name, qa_categories.title AS `categoryname`, qa_categories.backpath AS `categorybackpath`, CONCAT_WS(',', qa_posts.catidpath1, qa_posts.catidpath2, qa_posts.catidpath3, qa_posts.categoryid) AS `categoryids`, qa_posts.content AS `content`, qa_posts.notify AS `notify`, UNIX_TIMESTAMP(qa_posts.updated) AS `updated`, qa_posts.updatetype AS `updatetype`, qa_posts.format, qa_posts.lastuserid, qa_posts.lastip AS `lastip`, qa_posts.parentid, qa_posts.lastviewip AS `lastviewip`, qa_posts.userid, qa_posts.cookieid, qa_posts.createip AS `createip`, qa_userpoints.points, qa_users.flags, qa_users.level, qa_users.email AS `email`, qa_users.handle AS `handle`, BINARY qa_users.avatarblobid AS `avatarblobid`, qa_users.avatarwidth, qa_users.avatarheight, lastusers.handle AS `lasthandle` FROM qa_posts LEFT JOIN qa_categories ON qa_categories.categoryid=qa_posts.categoryid LEFT JOIN qa_users ON qa_posts.userid=qa_users.userid LEFT JOIN qa_users AS lastusers ON qa_posts.lastuserid=lastusers.userid LEFT JOIN qa_userpoints ON qa_posts.userid=qa_userpoints.userid join qa_posts ef on qa_posts.postid = ef.postid and ef.postid not in(select postid  from qa_posttags pt where pt.wordid  in (select wordid from qa_words wd where wd.word in ('goclasses_wq15','goclasses_wq','goclasses2024-dm-1','goclasses2024-programming-1','goclasses2024-dm-2','goclasses2024-programming-2','goclasses2024-dm-3','goclasses2024-programming-3','goclasses2024-dm-4','goclasses2024-ds-1','goclasses2024-dm-5','goclasses2024-dm-05','goclasses2024-ds-2','goclasses_wq11','goclasses2024-dl-1','goclasses2024-ds-3','goclasses2024-dl-2','goclasses2024-ds-4','goclasses2024-dl-3','go2024-quantitative-aptitude-1','go2024-verbal-aptitude-1','go2024-spatial-and-analytical-aptitude-1','go2024-digital-logic-1','go2024-programming-1','go2024-algorithms-1','go2024-probability-1','go2024-linear-algebra-1','go2024-calculus-1','go2024-dbms-1','go2024-toc-1','go2024-cd-1','go2024-os-1','go2024-os-2','go2024-cn-1','go2024-coa-1','go2024-ds-1','go2024-dm-1','go2024-dm-2','go2024-dm-3','go2024-dm-4','go2024-mix-1','go2024-mix-2','go2024-algorithms-2','go2024-mix-3','go2024-mix-4','go2024-mockgate-1','go2024-mockgate-2','go2024-mockgate-3','go2024-mockgate-4','go2024-mockgate-5','go2024-mockgate-6','goclasses2024-ds-5','goclasses2024-toc-1','goclasses2024-algo-1','goclasses2024-algo-2','goclasses2024-toc-2','goclasses2024-algo-3','goclasses2024-toc-3','goclasses_wq14','goclasses2024-toc-4','goclasses2024-toc-5','goclasses2024-la','goclasses2024-coa-1','goclasses2024-algo-4','goclasses_wq16','goclasses2024-probability','goclasses2024-calculus','goclasses2024-coa-2','goclasses2024-coa-3','goclasses2024-dbms-1','goclasses2024-dbms-2','goclasses2024-mix-1','goclasses2024-os-1','goclasses2024-os-2','goclasses2024-os-3','goclasses2024-dbms-3','goclasses2024-os-4','goclasses2024-dbms-4','goclasses2024-dbms-5','goclasses2024-mix-2','goclasses2024-cd-1','goclasses2024-cd-3','goclasses2024-cd-2','goclasses2024-coa-4','goclasses2024-mockgate-1','goclasses2024-mockgate-2','goclasses2024-mockgate-3','goclasses2024-cn-2','go2024-topictest-1','goclasses2024-mockgate-4','goclasses2024-cn-1','goclasses2024-cn-3','go2024-topictest-2','goclasses2024-mix-3','goclasses2024-mockgate-5','goclasses2024-mix-4','goclasses2024-mockgate-6','goclasses2024-mockgate-7','goclasses2024-mockgate-8','goclasses2024-cn-4','goclasses2024-mockgate-9','goclasses2024-iiith-mock-3','dm_test_2','dm_test_2_new','goclasses2024_wq9','goclasses2024-probability-1','goclasses2024_wq10','testsbyankitg-dm-3','goclasses2024-la-1','goclasses2023-iiith-mock-4','goclasses2024_wq11','testsbyankitg-dm-4','testsbyankitg_dm-4','testsbyankitg_dm_4','testsbyankitg-dm_4','dm-test-4','dm-logic-test-4','dm_logic_test_4','testsbyankitg-dm-logic-4','logic_dm_test_4','logic-test-4','testsbyankitg-logic-dm-4','goclasses2023-iiith-mock-5','goclasses2024_wq12','goclasses2024_wq13','goclasses2024_wq14','goclasses2024_wq15','goclasses2023-nielit-mock-1','goclasses2024_wq16','goclasses2023-nielit-mock-2','goclasses2024_wq17','goclasses2024_wq18','','goclasses2023-nielit-mock-3','goclasses2024_wq19','goclasses2023-nielit-mock-4','goclasses2024_wq20','goclasses2024-toc-4-weekly-quiz','goclasses2023-nielit-mock-5','goclasses2024-dm-6','goclasses2024-toc-6','goclasses2024-ds-4-weekly-quiz','goclasses2024_wq21','goclasses2023-nielit-mock-6','goclasses2024_wq22','goclasses2024-mix-1-weekly-quiz','goclasses2024-dl-1-weekly-quiz','goclasses2024_wq23','goclasses2024_wq24','goclasses2023-scholarship-test','goclasses2024_wq25','goclasses2023-nielit-mock-7','goclasses2024_wq26','goclasses2024_wq27','goclasses2024_wq28','goclasses2024-toc-7','goclasses2024_wq29','goclasses2024_wq30','goclasses2023-nielit-mock-8','goclasses2024_wq31','goclasses2024-ds-5-weekly-quiz','goclasses2023-nielit-mock-9','goclasses2024_wq32','goclasses2024_wq33','goclasses2023-nielit-mock-10','goclasses2024_wq34','goclasses2024-mockgate-10','goclasses2024-mockgate-da-1','goclasses2024-mockgate-da-2','goclasses2023-iiith-mock-2','goclasses2023-iiith-mock-3','goclasses2025_wq1','goclasses2025_wq2','goclasses2025_wq3','goclasses2025_wq4','goclasses2024-iiith-mock-2','goclasses2025_wq5','test123','testq','goclasses_wq41'))

) WHERE qa_posts.postid=(SELECT closedbyid FROM qa_posts WHERE postid=135714)

1.50 ms - 0 rows - 44 columns

SELECT qa_posts.postid, qa_posts.categoryid, qa_posts.type, LEFT(qa_posts.type, 1) AS `basetype`, INSTR(qa_posts.type, '_HIDDEN')>0 AS `hidden`, INSTR(qa_posts.type, '_QUEUED')>0 AS `queued`, qa_posts.acount, qa_posts.amaxvote, qa_posts.selchildid, qa_posts.closedbyid, qa_posts.upvotes, qa_posts.downvotes, qa_posts.netvotes, qa_posts.views, qa_posts.hotness, qa_posts.flagcount, qa_posts.title, qa_posts.tags, UNIX_TIMESTAMP(qa_posts.created) AS `created`, qa_posts.name, qa_categories.title AS `categoryname`, qa_categories.backpath AS `categorybackpath`, CONCAT_WS(',', qa_posts.catidpath1, qa_posts.catidpath2, qa_posts.catidpath3, qa_posts.categoryid) AS `categoryids`, qa_posts.content AS `content`, qa_posts.notify AS `notify`, UNIX_TIMESTAMP(qa_posts.updated) AS `updated`, qa_posts.updatetype AS `updatetype`, qa_posts.format, qa_posts.lastuserid, qa_posts.lastip AS `lastip`, qa_posts.parentid, qa_posts.lastviewip AS `lastviewip`, qa_posts.userid, qa_posts.cookieid, qa_posts.createip AS `createip`, qa_userpoints.points, qa_users.flags, qa_users.level, qa_users.email AS `email`, qa_users.handle AS `handle`, BINARY qa_users.avatarblobid AS `avatarblobid`, qa_users.avatarwidth, qa_users.avatarheight, lastusers.handle AS `lasthandle` FROM qa_posts LEFT JOIN qa_categories ON qa_categories.categoryid=qa_posts.categoryid LEFT JOIN qa_users ON qa_posts.userid=qa_users.userid LEFT JOIN qa_users AS lastusers ON qa_posts.lastuserid=lastusers.userid LEFT JOIN qa_userpoints ON qa_posts.userid=qa_userpoints.userid join qa_posts ef on qa_posts.postid = ef.postid and ef.postid not in(select postid  from qa_posttags pt where pt.wordid  in (select wordid from qa_words wd where wd.word in 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) WHERE qa_posts.closedbyid=135714

1.57 ms - 0 rows - 44 columns

SELECT title, content FROM qa_postmetas WHERE postid=135714 AND title='qa_q_extra'

0.16 ms - 0 rows - 2 columns

SELECT qa_categories.categoryid, MAX(qa_categories.parentid) AS `parentid`, MAX(qa_categories.title) AS `title`, MAX(qa_categories.tags) AS `tags`, MAX(qa_categories.qcount) AS `qcount`, MAX(qa_categories.position) AS `position`, COUNT(child.categoryid) AS `childcount`, MAX(qa_categories.content) AS `content`, MAX(qa_categories.backpath) AS `backpath` FROM qa_categories JOIN (SELECT NULL AS parentkey UNION SELECT grandparent.parentid FROM qa_categories JOIN qa_categories AS parent ON qa_categories.parentid=parent.categoryid JOIN qa_categories AS grandparent ON parent.parentid=grandparent.categoryid WHERE qa_categories.categoryid=(SELECT categoryid FROM qa_posts WHERE postid=135714) UNION SELECT parent.parentid FROM qa_categories JOIN qa_categories AS parent ON qa_categories.parentid=parent.categoryid WHERE qa_categories.categoryid=(SELECT categoryid FROM qa_posts WHERE postid=135714) UNION SELECT parentid FROM qa_categories WHERE categoryid=(SELECT categoryid FROM qa_posts WHERE postid=135714) UNION SELECT categoryid FROM qa_categories WHERE categoryid=(SELECT categoryid FROM qa_posts WHERE postid=135714)) y ON qa_categories.parentid<=>parentkey LEFT JOIN qa_categories AS child ON child.parentid=qa_categories.categoryid GROUP BY qa_categories.categoryid ORDER BY qa_categories.position

0.72 ms - 22 rows - 9 columns

SELECT action, period, count FROM qa_iplimits WHERE ip=UNHEX('ac46b2da')

0.14 ms - 0 rows - 3 columns

SELECT pageid, title, flags, permit+0 AS `permit`, nav, tags, position, heading FROM qa_pages WHERE nav IN ('B','M','O','F') ORDER BY position

0.20 ms - 42 rows - 8 columns

SELECT widgetid, place, position, tags, title FROM qa_widgets ORDER BY position

0.12 ms - 25 rows - 5 columns

SELECT entityid, entitytype, level FROM qa_userlevels WHERE userid=NULL

0.08 ms - 0 rows - 3 columns

SELECT answer_str from qa_ec_answers where postid=135714

0.11 ms - 0 rows - 1 column

SELECT qa_posts.postid, qa_posts.categoryid, qa_posts.type, LEFT(qa_posts.type, 1) AS `basetype`, INSTR(qa_posts.type, '_HIDDEN')>0 AS `hidden`, INSTR(qa_posts.type, '_QUEUED')>0 AS `queued`, qa_posts.acount, qa_posts.amaxvote, qa_posts.selchildid, qa_posts.closedbyid, qa_posts.upvotes, qa_posts.downvotes, qa_posts.netvotes, qa_posts.views, qa_posts.hotness, qa_posts.flagcount, qa_posts.title, qa_posts.tags, UNIX_TIMESTAMP(qa_posts.created) AS `created`, qa_posts.name, qa_categories.title AS `categoryname`, qa_categories.backpath AS `categorybackpath`, CONCAT_WS(',', qa_posts.catidpath1, qa_posts.catidpath2, qa_posts.catidpath3, qa_posts.categoryid) AS `categoryids`, qa_posts.userid, qa_posts.cookieid, qa_posts.createip AS `createip`, qa_userpoints.points, qa_users.flags, qa_users.level, qa_users.email AS `email`, qa_users.handle AS `handle`, BINARY qa_users.avatarblobid AS `avatarblobid`, qa_users.avatarwidth, qa_users.avatarheight, score FROM qa_posts LEFT JOIN qa_categories ON qa_categories.categoryid=qa_posts.categoryid LEFT JOIN qa_users ON qa_posts.userid=qa_users.userid LEFT JOIN qa_userpoints ON qa_posts.userid=qa_userpoints.userid join qa_posts ef on qa_posts.postid = ef.postid and ef.postid not in(select postid  from qa_posttags pt where pt.wordid  in (select wordid from qa_words wd where wd.word in 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) JOIN (SELECT postid, SUM(score)+LOG(postid)/1000000 AS score FROM ((SELECT qa_titlewords.postid, LOG(10000/titlecount) AS score FROM qa_titlewords JOIN qa_words ON qa_titlewords.wordid=qa_words.wordid JOIN qa_titlewords AS source ON qa_titlewords.wordid=source.wordid WHERE source.postid=135714 AND titlecount<10000) UNION ALL (SELECT qa_posttags.postid, 2*LOG(10000/tagcount) AS score FROM qa_posttags JOIN qa_words ON qa_posttags.wordid=qa_words.wordid JOIN qa_posttags AS source ON qa_posttags.wordid=source.wordid WHERE source.postid=135714 AND tagcount<10000) UNION ALL (SELECT qa_posts.postid, LOG(10000/qa_categories.qcount) FROM qa_posts JOIN qa_categories ON qa_posts.categoryid=qa_categories.categoryid AND qa_posts.type='Q' WHERE qa_categories.categoryid=(SELECT categoryid FROM qa_posts WHERE postid=135714) AND qa_categories.qcount<10000)) x WHERE postid!=135714 GROUP BY postid ORDER BY score DESC LIMIT 4) y ON qa_posts.postid=y.postid

37.32 ms - 4 rows - 35 columns

SELECT postid, content, format FROM qa_posts WHERE postid IN (172774,73700,32159,90258)

0.28 ms - 4 rows - 3 columns

UPDATE qa_posts SET views=views+1, lastviewip=UNHEX('ac46b2da') WHERE postid=135714 AND (lastviewip IS NULL OR lastviewip!=UNHEX('ac46b2da'))

6.84 ms