Problem 47838. Count the ways pairs of parentheses can be matched correctly

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Several problems in Cody deal with the practical problem of checking whether parentheses are correctly matched (e.g., </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/80\"><w:r><w:t>80</w:t></w:r></w:hyperlink><w:r><w:t>, </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/465\"><w:r><w:t>465</w:t></w:r></w:hyperlink><w:r><w:t>, </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/1303\"><w:r><w:t>1303</w:t></w:r></w:hyperlink><w:r><w:t>, </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/2653-beauty-of-parentheses\"><w:r><w:t>2653</w:t></w:r></w:hyperlink><w:r><w:t>). In this problem you are asked to count the ways a given number of pairs of parentheses can be matched correctly in an expression. For example, three pairs can be matched in five ways: </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[()()(), (())(), (()()), ((())), ()(())]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function that takes the number of pairs and determines the number of ways the parentheses can be matched correctly. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 145.433px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 72.7167px; transform-origin: 407px 72.7167px; vertical-align: baseline; "><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 370.317px 7.91667px; transform-origin: 370.317px 7.91667px; unicode-bidi: normal; "><span style="">Several problems in Cody deal with the practical problem of checking whether parentheses are correctly matched (e.g., </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/80"><span style=""><span style="">80</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; "><span style="">, </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/465"><span style=""><span style="perspective-origin: 11.675px 7.91667px; transform-origin: 11.675px 7.91667px; ">465</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; "><span style="">, </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/1303"><span style=""><span style="">1303</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; "><span style="">, </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/2653-beauty-of-parentheses"><span style=""><span style="">2653</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 331.392px 7.91667px; transform-origin: 331.392px 7.91667px; unicode-bidi: normal; "><span style="">). In this problem you are asked to count the ways a given number of pairs of parentheses can be matched correctly in an expression. For example, three pairs can be matched in five ways: </span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 0.833333px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 0.833333px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 0.833333px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 0.833333px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 146.3px 7.91667px; transform-origin: 146.3px 7.91667px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; ">()()(), (())(), (()()), ((())), ()(())</span></span></div></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 361.992px 7.91667px; transform-origin: 361.992px 7.91667px; unicode-bidi: normal; "><span style="">Write a function that takes the number of pairs and determines the number of ways the parentheses can be matched correctly. </span></span></div></div></div>

Solve

Solution Stats

10 Solutions
4 Solvers

Last Solution submitted on Apr 06, 2021

Last 200 Solutions

Problem Recent Solvers4

Problem Tags

combinatorics parentheses special numbers

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 47838. Count the ways pairs of parentheses can be matched correctly

Solution Stats

Last 200 Solutions

Problem Recent Solvers4

Suggested Problems

More from this Author88

Problem Tags

Community Treasure Hunt

Problem 47838. Count the ways pairs of parentheses can be matched correctly

Solution Stats

Last 200 Solutions

Problem Recent Solvers4

Suggested Problems

More from this Author88

Problem Tags

Community Treasure Hunt

Players