{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":925,"title":"Unique - Very Very Large Numbers","description":"Given a vector column, with some very large numbers, create the ascending sort and unique vector.\r\n\r\n*Input:* A  (column vector)\r\n\r\n*Output:* B (unique and ascending sorted column vector)\r\n\r\n*Examples:* [5;4;3;2;2;1] outputs [1;2;3;4;5]\r\n\r\n[9223372036854775808;9223372036854775806] outputs [9223372036854775806;9223372036854775808] ","description_html":"\u003cp\u003eGiven a vector column, with some very large numbers, create the ascending sort and unique vector.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e A  (column vector)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e B (unique and ascending sorted column vector)\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [5;4;3;2;2;1] outputs [1;2;3;4;5]\u003c/p\u003e\u003cp\u003e[9223372036854775808;9223372036854775806] outputs [9223372036854775806;9223372036854775808]\u003c/p\u003e","function_template":"function y = unique_large(x)\r\n  y = unique(x);\r\nend","test_suite":"%%\r\na=randi(2^32,100,'uint32');\r\nassert(isequal(unique_large(a),unique(a)))\r\n%%\r\nformat long\r\na=[uint64(9223372036854775808);uint64(9223372036854775806)];\r\nout=unique_large(a);\r\nassert(isequal(out,flipud(a)),sprintf('\\nsize(a)= %i %i \\noutput= \\n %14.0f\\n %14.0f \\n',size(out),out))\r\n%%\r\nformat long\r\na=[uint64(18446744073709551615);uint64(18233720368547758060);uint64(9223372036854779806)];\r\n\r\nout=unique_large(a);\r\n\r\nassert(isequal(out,flipud(a)),sprintf('\\nsize(a)= %i %i \\noutput= \\n %16.0f \\n %16.0f \\n %16.0f \\n',size(out),out))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":80,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-08-29T18:59:33.000Z","updated_at":"2026-03-24T06:44:26.000Z","published_at":"2012-08-29T19:55:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector column, with some very large numbers, create the ascending sort and unique vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e A (column vector)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e B (unique and ascending sorted column vector)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [5;4;3;2;2;1] outputs [1;2;3;4;5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[9223372036854775808;9223372036854775806] outputs [9223372036854775806;9223372036854775808]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1651,"title":"Circumcircle Points","description":"Determine the radius of the minimum sized circle that encompasses all the points.\r\n\r\nPer \u003chttp://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf Smallest Sphere Paper\u003e this question was first addressed by Sylvester in 1857, Megiddo in 1982, and optimized by Emo Welzl in 1991.\r\n\r\n*Input:* Points  (eg [0 0;0 1;2 0])  Minimum of 3 points\r\n\r\n*Output:* r  (radius of optimally centered circle)\r\n\r\n*Example:*  [0 0;0 1;2 0]  yields [xc,yc,r] [1 .5 1.118] Output r=1.118\r\n\r\n*Theory:*\r\nBest Circumcircle may occur in two ways:\r\n\r\n1) Center of Line connecting pair with maximum separation, or\r\n\r\n2) A circle utilizing three points from the set\r\n\r\n*Related Challenges:*\r\n\r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/1336-geometry-find-circle-given-3-non-colinear-points/solutions/map Circle from 3 Points\u003e\r\n\r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/554-is-the-point-in-a-circle/solutions/map Are Points in Circle\u003e\r\n\r\n*Warning:* Rounding Errors may cause solution errors. Usage of 10*eps(r) may be appropriate.\r\n\r\n\r\n","description_html":"\u003cp\u003eDetermine the radius of the minimum sized circle that encompasses all the points.\u003c/p\u003e\u003cp\u003ePer \u003ca href = \"http://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf\"\u003eSmallest Sphere Paper\u003c/a\u003e this question was first addressed by Sylvester in 1857, Megiddo in 1982, and optimized by Emo Welzl in 1991.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Points  (eg [0 0;0 1;2 0])  Minimum of 3 points\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e r  (radius of optimally centered circle)\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e  [0 0;0 1;2 0]  yields [xc,yc,r] [1 .5 1.118] Output r=1.118\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e\r\nBest Circumcircle may occur in two ways:\u003c/p\u003e\u003cp\u003e1) Center of Line connecting pair with maximum separation, or\u003c/p\u003e\u003cp\u003e2) A circle utilizing three points from the set\u003c/p\u003e\u003cp\u003e\u003cb\u003eRelated Challenges:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1336-geometry-find-circle-given-3-non-colinear-points/solutions/map\"\u003eCircle from 3 Points\u003c/a\u003e\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/554-is-the-point-in-a-circle/solutions/map\"\u003eAre Points in Circle\u003c/a\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eWarning:\u003c/b\u003e Rounding Errors may cause solution errors. Usage of 10*eps(r) may be appropriate.\u003c/p\u003e","function_template":"function r = Circumcircle_radius(pts)\r\n  r=0;\r\nend","test_suite":"%%\r\npts=[0 0;5 0;1.8 2.4]; % 3 4 5 triangle\r\nr_exp=2.5;\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0 0;6 0;1.8 2.4]; % 3 x 6 triangle\r\nr_exp=3; % Two Point Solver\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0 0;0 1;1 2;3 0]; % r^2=2.5\r\nr_exp=sqrt(2.5);\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0 1; 0 3; 0 4; 2 6; 3 0; 4 5]; % r2 9.2820069 \r\nr_exp=sqrt(9.2820069 );\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0,2;0,6;1,1;3,0;3,3;4,10;5,10;7,2;9,7]; % r2 26.6919 \r\nr_exp=sqrt(26.6919420552286 );\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0,19;1,25;1,30;1,34;3,11;4,30;8,17;9,6;11,44;12,45;15,46;21,0;21,9;21,48;22,42;26,11;31,40;34,27;37,44;39,34;41,8;43,9;43,10;46,16;46,35;48,23]; % r2  exp 608.7807\r\nr_exp=sqrt(608.780718525455);\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\n% Random case to avoid hard coders\r\nxc=rand;\r\nyc=rand;\r\nr=.5+rand;\r\npts=[];\r\n% Equilateral points\r\npts(1,:)=[xc+r,yc];\r\npts(2,:)=[xc+r*cos(2*pi/3),yc+r*sin(2*pi/3)];\r\npts(3,:)=[xc+r*cos(-2*pi/3),yc+r*sin(-2*pi/3)];\r\nfor i=4:10\r\n rnew=rand*r;\r\n theta=randi(360)*pi/180;\r\n pts(i,:)=[xc+rnew*cos(theta),yc+rnew*sin(theta)];\r\nend\r\npts=pts(randperm(size(pts,1)),:);\r\nr_exp=r;\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\n% Random case to avoid hard coders\r\nxc=rand;\r\nyc=rand;\r\nr=.5+rand;\r\npts=[];\r\n% Equilateral points\r\npts(1,:)=[xc+r,yc];\r\npts(2,:)=[xc+r*cos(2*pi/3),yc+r*sin(2*pi/3)];\r\npts(3,:)=[xc+r*cos(-2*pi/3),yc+r*sin(-2*pi/3)];\r\nfor i=4:30\r\n rnew=rand*r;\r\n theta=randi(360)*pi/180;\r\n pts(i,:)=[xc+rnew*cos(theta),yc+rnew*sin(theta)];\r\nend\r\npts=pts(randperm(size(pts,1)),:);\r\nr_exp=r;\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-17T00:11:46.000Z","updated_at":"2013-06-17T00:27:11.000Z","published_at":"2013-06-17T00:27:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the radius of the minimum sized circle that encompasses all the points.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSmallest Sphere Paper\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e this question was first addressed by Sylvester in 1857, Megiddo in 1982, and optimized by Emo Welzl in 1991.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Points (eg [0 0;0 1;2 0]) Minimum of 3 points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e r (radius of optimally centered circle)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [0 0;0 1;2 0] yields [xc,yc,r] [1 .5 1.118] Output r=1.118\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Circumcircle may occur in two ways:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Center of Line connecting pair with maximum separation, or\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) A circle utilizing three points from the set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated Challenges:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1336-geometry-find-circle-given-3-non-colinear-points/solutions/map\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCircle from 3 Points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/554-is-the-point-in-a-circle/solutions/map\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAre Points in Circle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWarning:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Rounding Errors may cause solution errors. Usage of 10*eps(r) may be appropriate.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":925,"title":"Unique - Very Very Large Numbers","description":"Given a vector column, with some very large numbers, create the ascending sort and unique vector.\r\n\r\n*Input:* A  (column vector)\r\n\r\n*Output:* B (unique and ascending sorted column vector)\r\n\r\n*Examples:* [5;4;3;2;2;1] outputs [1;2;3;4;5]\r\n\r\n[9223372036854775808;9223372036854775806] outputs [9223372036854775806;9223372036854775808] ","description_html":"\u003cp\u003eGiven a vector column, with some very large numbers, create the ascending sort and unique vector.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e A  (column vector)\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e B (unique and ascending sorted column vector)\u003c/p\u003e\u003cp\u003e\u003cb\u003eExamples:\u003c/b\u003e [5;4;3;2;2;1] outputs [1;2;3;4;5]\u003c/p\u003e\u003cp\u003e[9223372036854775808;9223372036854775806] outputs [9223372036854775806;9223372036854775808]\u003c/p\u003e","function_template":"function y = unique_large(x)\r\n  y = unique(x);\r\nend","test_suite":"%%\r\na=randi(2^32,100,'uint32');\r\nassert(isequal(unique_large(a),unique(a)))\r\n%%\r\nformat long\r\na=[uint64(9223372036854775808);uint64(9223372036854775806)];\r\nout=unique_large(a);\r\nassert(isequal(out,flipud(a)),sprintf('\\nsize(a)= %i %i \\noutput= \\n %14.0f\\n %14.0f \\n',size(out),out))\r\n%%\r\nformat long\r\na=[uint64(18446744073709551615);uint64(18233720368547758060);uint64(9223372036854779806)];\r\n\r\nout=unique_large(a);\r\n\r\nassert(isequal(out,flipud(a)),sprintf('\\nsize(a)= %i %i \\noutput= \\n %16.0f \\n %16.0f \\n %16.0f \\n',size(out),out))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":80,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-08-29T18:59:33.000Z","updated_at":"2026-03-24T06:44:26.000Z","published_at":"2012-08-29T19:55:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a vector column, with some very large numbers, create the ascending sort and unique vector.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e A (column vector)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e B (unique and ascending sorted column vector)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExamples:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [5;4;3;2;2;1] outputs [1;2;3;4;5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e[9223372036854775808;9223372036854775806] outputs [9223372036854775806;9223372036854775808]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":1651,"title":"Circumcircle Points","description":"Determine the radius of the minimum sized circle that encompasses all the points.\r\n\r\nPer \u003chttp://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf Smallest Sphere Paper\u003e this question was first addressed by Sylvester in 1857, Megiddo in 1982, and optimized by Emo Welzl in 1991.\r\n\r\n*Input:* Points  (eg [0 0;0 1;2 0])  Minimum of 3 points\r\n\r\n*Output:* r  (radius of optimally centered circle)\r\n\r\n*Example:*  [0 0;0 1;2 0]  yields [xc,yc,r] [1 .5 1.118] Output r=1.118\r\n\r\n*Theory:*\r\nBest Circumcircle may occur in two ways:\r\n\r\n1) Center of Line connecting pair with maximum separation, or\r\n\r\n2) A circle utilizing three points from the set\r\n\r\n*Related Challenges:*\r\n\r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/1336-geometry-find-circle-given-3-non-colinear-points/solutions/map Circle from 3 Points\u003e\r\n\r\n\u003chttp://www.mathworks.com/matlabcentral/cody/problems/554-is-the-point-in-a-circle/solutions/map Are Points in Circle\u003e\r\n\r\n*Warning:* Rounding Errors may cause solution errors. Usage of 10*eps(r) may be appropriate.\r\n\r\n\r\n","description_html":"\u003cp\u003eDetermine the radius of the minimum sized circle that encompasses all the points.\u003c/p\u003e\u003cp\u003ePer \u003ca href = \"http://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf\"\u003eSmallest Sphere Paper\u003c/a\u003e this question was first addressed by Sylvester in 1857, Megiddo in 1982, and optimized by Emo Welzl in 1991.\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e Points  (eg [0 0;0 1;2 0])  Minimum of 3 points\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e r  (radius of optimally centered circle)\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e  [0 0;0 1;2 0]  yields [xc,yc,r] [1 .5 1.118] Output r=1.118\u003c/p\u003e\u003cp\u003e\u003cb\u003eTheory:\u003c/b\u003e\r\nBest Circumcircle may occur in two ways:\u003c/p\u003e\u003cp\u003e1) Center of Line connecting pair with maximum separation, or\u003c/p\u003e\u003cp\u003e2) A circle utilizing three points from the set\u003c/p\u003e\u003cp\u003e\u003cb\u003eRelated Challenges:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/1336-geometry-find-circle-given-3-non-colinear-points/solutions/map\"\u003eCircle from 3 Points\u003c/a\u003e\u003c/p\u003e\u003cp\u003e\u003ca href = \"http://www.mathworks.com/matlabcentral/cody/problems/554-is-the-point-in-a-circle/solutions/map\"\u003eAre Points in Circle\u003c/a\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eWarning:\u003c/b\u003e Rounding Errors may cause solution errors. Usage of 10*eps(r) may be appropriate.\u003c/p\u003e","function_template":"function r = Circumcircle_radius(pts)\r\n  r=0;\r\nend","test_suite":"%%\r\npts=[0 0;5 0;1.8 2.4]; % 3 4 5 triangle\r\nr_exp=2.5;\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0 0;6 0;1.8 2.4]; % 3 x 6 triangle\r\nr_exp=3; % Two Point Solver\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0 0;0 1;1 2;3 0]; % r^2=2.5\r\nr_exp=sqrt(2.5);\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0 1; 0 3; 0 4; 2 6; 3 0; 4 5]; % r2 9.2820069 \r\nr_exp=sqrt(9.2820069 );\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0,2;0,6;1,1;3,0;3,3;4,10;5,10;7,2;9,7]; % r2 26.6919 \r\nr_exp=sqrt(26.6919420552286 );\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\npts=[0,19;1,25;1,30;1,34;3,11;4,30;8,17;9,6;11,44;12,45;15,46;21,0;21,9;21,48;22,42;26,11;31,40;34,27;37,44;39,34;41,8;43,9;43,10;46,16;46,35;48,23]; % r2  exp 608.7807\r\nr_exp=sqrt(608.780718525455);\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\n% Random case to avoid hard coders\r\nxc=rand;\r\nyc=rand;\r\nr=.5+rand;\r\npts=[];\r\n% Equilateral points\r\npts(1,:)=[xc+r,yc];\r\npts(2,:)=[xc+r*cos(2*pi/3),yc+r*sin(2*pi/3)];\r\npts(3,:)=[xc+r*cos(-2*pi/3),yc+r*sin(-2*pi/3)];\r\nfor i=4:10\r\n rnew=rand*r;\r\n theta=randi(360)*pi/180;\r\n pts(i,:)=[xc+rnew*cos(theta),yc+rnew*sin(theta)];\r\nend\r\npts=pts(randperm(size(pts,1)),:);\r\nr_exp=r;\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n%%\r\n% Random case to avoid hard coders\r\nxc=rand;\r\nyc=rand;\r\nr=.5+rand;\r\npts=[];\r\n% Equilateral points\r\npts(1,:)=[xc+r,yc];\r\npts(2,:)=[xc+r*cos(2*pi/3),yc+r*sin(2*pi/3)];\r\npts(3,:)=[xc+r*cos(-2*pi/3),yc+r*sin(-2*pi/3)];\r\nfor i=4:30\r\n rnew=rand*r;\r\n theta=randi(360)*pi/180;\r\n pts(i,:)=[xc+rnew*cos(theta),yc+rnew*sin(theta)];\r\nend\r\npts=pts(randperm(size(pts,1)),:);\r\nr_exp=r;\r\nr = Circumcircle_radius(pts);\r\nassert(abs(r-r_exp)\u003c.001)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-17T00:11:46.000Z","updated_at":"2013-06-17T00:27:11.000Z","published_at":"2013-06-17T00:27:11.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eDetermine the radius of the minimum sized circle that encompasses all the points.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePer\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eSmallest Sphere Paper\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e this question was first addressed by Sylvester in 1857, Megiddo in 1982, and optimized by Emo Welzl in 1991.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Points (eg [0 0;0 1;2 0]) Minimum of 3 points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e r (radius of optimally centered circle)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e [0 0;0 1;2 0] yields [xc,yc,r] [1 .5 1.118] Output r=1.118\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTheory:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Best Circumcircle may occur in two ways:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1) Center of Line connecting pair with maximum separation, or\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2) A circle utilizing three points from the set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated Challenges:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/1336-geometry-find-circle-given-3-non-colinear-points/solutions/map\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCircle from 3 Points\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://www.mathworks.com/matlabcentral/cody/problems/554-is-the-point-in-a-circle/solutions/map\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eAre Points in Circle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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