{"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":1684,"title":"Identify Reachable Points ","description":"Given a vector of 2-D Points and a vector of 2-D Deltas create an array of all Locations that can be reached from the points using the Deltas. The provided Deltas are only positive but the points that can be reached may use Negative Deltas or Y-deltas for X moves, like moves of a Knight dxy [1 2].\r\n\r\n*Input:* [Pts, dxy]\r\n\r\n\r\n*Output:* Mxy\r\n\r\n*Example:* \r\n\r\n  Pts [5 5; 7 9]\r\n\r\n  dxy [0 1]  % Multiple dxy are possible\r\n  \r\n  Mxy =[4 5;5 4;5 6;6 5;6 9;7 8;7 10;8 9]\r\n\r\n*Related Challenges:*\r\n\r\n1) Minimum Sized Circle for N integer points with all unique distances ","description_html":"\u003cp\u003eGiven a vector of 2-D Points and a vector of 2-D Deltas create an array of all Locations that can be reached from the points using the Deltas. The provided Deltas are only positive but the points that can be reached may use Negative Deltas or Y-deltas for X moves, like moves of a Knight dxy [1 2].\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [Pts, dxy]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Mxy\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ePts [5 5; 7 9]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edxy [0 1]  % Multiple dxy are possible\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eMxy =[4 5;5 4;5 6;6 5;6 9;7 8;7 10;8 9]\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eRelated Challenges:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e1) Minimum Sized Circle for N integer points with all unique distances\u003c/p\u003e","function_template":"function Mxy=Knights(Pts,dxy)\r\n  Mxy=Pts;\r\nend","test_suite":"%%\r\nPts=[5 5; 7 9];\r\ndxy=[0 1];\r\nMxy=unique(Knights(Pts,dxy),'rows');\r\n\r\nMxy_exp =[4 5;5 4;5 6;6 5;6 9;7 8;7 10;8 9];\r\nassert(isequal(Mxy,Mxy_exp))\r\n%%\r\nPts=[5 5];\r\ndxy=[0 1;1 2];\r\nMxy=unique(Knights(Pts,dxy),'rows');\r\n\r\nMxy_exp =[3 4;3 6;4 3;4 5;4 7;5 4;5 6;6 3;6 5;6 7;7 4;7 6];\r\nassert(isequal(Mxy,Mxy_exp))\r\n%%\r\npts=randi(20,6,2);\r\ndxy=randi(6,4,2);\r\nMxy=unique(Knights(pts,dxy),'rows');\r\n\r\n nP=size(pts,1);\r\n ndxy=size(dxy,1);\r\n \r\n mxy=[];\r\n for i=1:nP\r\n  mxy=[mxy;\r\n      dxy(:,1)+pts(i,1) dxy(:,2)+pts(i,2);\r\n      -dxy(:,1)+pts(i,1) dxy(:,2)+pts(i,2);\r\n      dxy(:,1)+pts(i,1) -dxy(:,2)+pts(i,2);\r\n      -dxy(:,1)+pts(i,1) -dxy(:,2)+pts(i,2);\r\n       dxy(:,2)+pts(i,1) dxy(:,1)+pts(i,2);\r\n      -dxy(:,2)+pts(i,1) dxy(:,1)+pts(i,2);\r\n      dxy(:,2)+pts(i,1) -dxy(:,1)+pts(i,2);\r\n      -dxy(:,2)+pts(i,1) -dxy(:,1)+pts(i,2)];\r\n end\r\n\r\n Mxy_exp=unique(mxy,'rows');\r\n\r\nassert(isequal(Mxy,Mxy_exp))\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":48,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-28T03:22:54.000Z","updated_at":"2026-02-15T07:15:08.000Z","published_at":"2013-06-28T03:58:36.000Z","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 of 2-D Points and a vector of 2-D Deltas create an array of all Locations that can be reached from the points using the Deltas. The provided Deltas are only positive but the points that can be reached may use Negative Deltas or Y-deltas for X moves, like moves of a Knight dxy [1 2].\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 [Pts, dxy]\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 Mxy\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\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Pts [5 5; 7 9]\\n\\ndxy [0 1]  % Multiple dxy are possible\\n\\nMxy =[4 5;5 4;5 6;6 5;6 9;7 8;7 10;8 9]]]\u003e\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:r\u003e\u003cw:t\u003e1) Minimum Sized Circle for N integer points with all unique distances\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":1684,"title":"Identify Reachable Points ","description":"Given a vector of 2-D Points and a vector of 2-D Deltas create an array of all Locations that can be reached from the points using the Deltas. The provided Deltas are only positive but the points that can be reached may use Negative Deltas or Y-deltas for X moves, like moves of a Knight dxy [1 2].\r\n\r\n*Input:* [Pts, dxy]\r\n\r\n\r\n*Output:* Mxy\r\n\r\n*Example:* \r\n\r\n  Pts [5 5; 7 9]\r\n\r\n  dxy [0 1]  % Multiple dxy are possible\r\n  \r\n  Mxy =[4 5;5 4;5 6;6 5;6 9;7 8;7 10;8 9]\r\n\r\n*Related Challenges:*\r\n\r\n1) Minimum Sized Circle for N integer points with all unique distances ","description_html":"\u003cp\u003eGiven a vector of 2-D Points and a vector of 2-D Deltas create an array of all Locations that can be reached from the points using the Deltas. The provided Deltas are only positive but the points that can be reached may use Negative Deltas or Y-deltas for X moves, like moves of a Knight dxy [1 2].\u003c/p\u003e\u003cp\u003e\u003cb\u003eInput:\u003c/b\u003e [Pts, dxy]\u003c/p\u003e\u003cp\u003e\u003cb\u003eOutput:\u003c/b\u003e Mxy\u003c/p\u003e\u003cp\u003e\u003cb\u003eExample:\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003ePts [5 5; 7 9]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003edxy [0 1]  % Multiple dxy are possible\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eMxy =[4 5;5 4;5 6;6 5;6 9;7 8;7 10;8 9]\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eRelated Challenges:\u003c/b\u003e\u003c/p\u003e\u003cp\u003e1) Minimum Sized Circle for N integer points with all unique distances\u003c/p\u003e","function_template":"function Mxy=Knights(Pts,dxy)\r\n  Mxy=Pts;\r\nend","test_suite":"%%\r\nPts=[5 5; 7 9];\r\ndxy=[0 1];\r\nMxy=unique(Knights(Pts,dxy),'rows');\r\n\r\nMxy_exp =[4 5;5 4;5 6;6 5;6 9;7 8;7 10;8 9];\r\nassert(isequal(Mxy,Mxy_exp))\r\n%%\r\nPts=[5 5];\r\ndxy=[0 1;1 2];\r\nMxy=unique(Knights(Pts,dxy),'rows');\r\n\r\nMxy_exp =[3 4;3 6;4 3;4 5;4 7;5 4;5 6;6 3;6 5;6 7;7 4;7 6];\r\nassert(isequal(Mxy,Mxy_exp))\r\n%%\r\npts=randi(20,6,2);\r\ndxy=randi(6,4,2);\r\nMxy=unique(Knights(pts,dxy),'rows');\r\n\r\n nP=size(pts,1);\r\n ndxy=size(dxy,1);\r\n \r\n mxy=[];\r\n for i=1:nP\r\n  mxy=[mxy;\r\n      dxy(:,1)+pts(i,1) dxy(:,2)+pts(i,2);\r\n      -dxy(:,1)+pts(i,1) dxy(:,2)+pts(i,2);\r\n      dxy(:,1)+pts(i,1) -dxy(:,2)+pts(i,2);\r\n      -dxy(:,1)+pts(i,1) -dxy(:,2)+pts(i,2);\r\n       dxy(:,2)+pts(i,1) dxy(:,1)+pts(i,2);\r\n      -dxy(:,2)+pts(i,1) dxy(:,1)+pts(i,2);\r\n      dxy(:,2)+pts(i,1) -dxy(:,1)+pts(i,2);\r\n      -dxy(:,2)+pts(i,1) -dxy(:,1)+pts(i,2)];\r\n end\r\n\r\n Mxy_exp=unique(mxy,'rows');\r\n\r\nassert(isequal(Mxy,Mxy_exp))\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":48,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2013-06-28T03:22:54.000Z","updated_at":"2026-02-15T07:15:08.000Z","published_at":"2013-06-28T03:58:36.000Z","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 of 2-D Points and a vector of 2-D Deltas create an array of all Locations that can be reached from the points using the Deltas. The provided Deltas are only positive but the points that can be reached may use Negative Deltas or Y-deltas for X moves, like moves of a Knight dxy [1 2].\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 [Pts, dxy]\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 Mxy\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\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Pts [5 5; 7 9]\\n\\ndxy [0 1]  % Multiple dxy are possible\\n\\nMxy =[4 5;5 4;5 6;6 5;6 9;7 8;7 10;8 9]]]\u003e\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:r\u003e\u003cw:t\u003e1) Minimum Sized Circle for N integer points with all unique distances\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 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