{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-16T00:12:35.000Z","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":"2026-04-16T00:00:00.000Z","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":48970,"title":"Taxi vs Euclides","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 21px; transform-origin: 343px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"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: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate the difference between the Taxicab and Euclidean distance of the vectors. Round the result to the 4th decimal.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = taxiVsEuclides(x)\r\n    y = x;\r\nend","test_suite":"%%\r\nv1=1:10;\r\nv2=11:20;\r\nassert(isequal(taxiVsEuclides(v1,v2),68.3772))\r\n%%\r\nv1=1:4:50;\r\nv2=25:4:75;\r\nassert(isequal(taxiVsEuclides(v1,v2),225.4668))\r\n%%\r\nv1=1:8:50;\r\nv2=25:8:75;\r\nassert(isequal(taxiVsEuclides(v1,v2),104.5020))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":698530,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-22T15:25:35.000Z","updated_at":"2026-03-15T03:35:12.000Z","published_at":"2020-12-31T01:18:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the difference between the Taxicab and Euclidean distance of the vectors. Round the result to the 4th decimal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":264,"title":"Find the \"ordinary\" or Euclidean distance between A and Z","description":"A, B and Z define three points in the 3D _Euclidean_ space of the form:\r\nA = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\r\n\r\nFind the *Euclidean distance* between A and Z where\r\n  \r\n  A = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\n  \r\n  \u003e\u003e euclidean(A,B,Z)\r\n  \r\n  ans = 5.830951894845301\r\n\r\nYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors\r\nfor all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are.\r\nSo 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function\r\ninput vectors.\r\n\r\nHINT: use the Pythagorean formula.","description_html":"\u003cp\u003eA, B and Z define three points in the 3D \u003ci\u003eEuclidean\u003c/i\u003e space of the form:\r\nA = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\u003c/p\u003e\u003cp\u003eFind the \u003cb\u003eEuclidean distance\u003c/b\u003e between A and Z where\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eA = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e\u003e\u003e euclidean(A,B,Z)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 5.830951894845301\r\n\u003c/pre\u003e\u003cp\u003eYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors\r\nfor all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are.\r\nSo 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function\r\ninput vectors.\u003c/p\u003e\u003cp\u003eHINT: use the Pythagorean formula.\u003c/p\u003e","function_template":"function y = euclidean(A,B,Z)\r\n  y = findEuclid(A,B,Z);\r\nend","test_suite":"%%\r\nA = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [1;0;0]; B = [5;3;0]; Z=[5;3;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0,0,0]; B = [4,3,0]; Z=[4,3,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;0;0]; B = [4;3;0]; Z=[4;3;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0,3,0]; B = [4,0,0]; Z=[4,0,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;3;0]; B = [4;0;0]; Z=[4;0;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;3;0]; B = [4;0;0]; Z=[4;0;12];\r\ny_correct = 13;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":177,"test_suite_updated_at":"2012-02-12T03:40:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-05T23:24:30.000Z","updated_at":"2026-02-11T14:15:21.000Z","published_at":"2012-02-12T03:52:07.000Z","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\u003eA, B and Z define three points in the 3D\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEuclidean\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e space of the form: A = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\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\u003eFind the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEuclidean distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between A and Z where\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[A = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\\n\\n\u003e\u003e euclidean(A,B,Z)\\n\\nans = 5.830951894845301]]\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:t\u003eYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors for all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are. So 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function input vectors.\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\u003eHINT: use the Pythagorean formula.\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":43007,"title":"Euclidean inter-point distance matrix","description":"The Euclidean distance between two points in a p-dimensional space is a really common thing to compute in the field of computational geometry. In fact, it is pretty easy to do. norm(u-v) would seem to do the trick, for vectors u and v.\r\n\r\nBut what if you have a large number of points between which you want to compute ALL of those distances between every pair of points? In this problem, given an n by p array A, where each row of the matrix will be viewed as containing the coordinates of one p-dimensional point, you need to compute the n by n inter-point distance matrix.\r\n\r\nThus, D(i,J) will be the Euclidean distance between the i'th and j'th rows of A. Of course, D will be a symmetric matrix, with zeros on the diagonal.\r\n\r\nSo you can test your code, here is an example:\r\n\r\n  A = [1 1\r\n       5 2\r\n       2 2\r\n       4 5]\r\n\r\n  format short g\r\n  D = interDist(A)\r\n  D =\r\n         0       4.1231       1.4142            5\r\n    4.1231            0            3       3.1623\r\n    1.4142            3            0       3.6056\r\n         5       3.1623       3.6056            0\r\n\r\nThus, thinking of the points [1 1] and [5 2] as the coordinates of two points in the (x,y) plane, the Euclidean distance between them in that plane is 4.1231...\r\n\r\nAs you can see, the matrix is symmetric, with zeros on the main diagonal. That must always happen, since the distance between any point and itself must be zero.","description_html":"\u003cp\u003eThe Euclidean distance between two points in a p-dimensional space is a really common thing to compute in the field of computational geometry. In fact, it is pretty easy to do. norm(u-v) would seem to do the trick, for vectors u and v.\u003c/p\u003e\u003cp\u003eBut what if you have a large number of points between which you want to compute ALL of those distances between every pair of points? In this problem, given an n by p array A, where each row of the matrix will be viewed as containing the coordinates of one p-dimensional point, you need to compute the n by n inter-point distance matrix.\u003c/p\u003e\u003cp\u003eThus, D(i,J) will be the Euclidean distance between the i'th and j'th rows of A. Of course, D will be a symmetric matrix, with zeros on the diagonal.\u003c/p\u003e\u003cp\u003eSo you can test your code, here is an example:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eA = [1 1\r\n     5 2\r\n     2 2\r\n     4 5]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eformat short g\r\nD = interDist(A)\r\nD =\r\n       0       4.1231       1.4142            5\r\n  4.1231            0            3       3.1623\r\n  1.4142            3            0       3.6056\r\n       5       3.1623       3.6056            0\r\n\u003c/pre\u003e\u003cp\u003eThus, thinking of the points [1 1] and [5 2] as the coordinates of two points in the (x,y) plane, the Euclidean distance between them in that plane is 4.1231...\u003c/p\u003e\u003cp\u003eAs you can see, the matrix is symmetric, with zeros on the main diagonal. That must always happen, since the distance between any point and itself must be zero.\u003c/p\u003e","function_template":"function D = interDist(A)\r\n  % compute the interpoint distance matrix between rows of A\r\n  D = A;\r\nend\r\n\r\n","test_suite":"%%\r\nA = eye(3);\r\ny_correct = (1-A)*sqrt(2);\r\ntol = 10*eps;\r\nassert(norm(interDist(A)-y_correct) \u003c tol)\r\n\r\n%%\r\nA = (1:4)';\r\ny_correct = [     0     1     2     3;...\r\n     1     0     1     2;...\r\n     2     1     0     1;...\r\n     3     2     1     0];\r\ntol = 10*eps;\r\nassert(norm(interDist(A)-y_correct) \u003c tol)\r\n\r\n\r\n\r\n\r\n%%\r\nA = magic(3);\r\ny_correct = [0       6.48074069840786 9.79795897113271; ...\r\n  6.48074069840786                0 6.48074069840786; ...\r\n  9.79795897113271 6.48074069840786                0];\r\ntol = 1000*eps;\r\nassert(norm(interDist(A)-y_correct) \u003c tol)\r\n\r\n%%\r\nA = reshape((1:20).^2,4,5);\r\ntol = 1e-12;\r\ny_correct = [0 49.4469412603045 102.761860629321 160.015624237135; ...\r\n   49.4469412603045 0 53.3385414123783 110.634533487515; ...\r\n   102.761860629321 53.3385414123783 0 57.3149195236284; ...\r\n   160.015624237135 110.634533487515 57.3149195236284 0];\r\nassert(norm(interDist(A)-y_correct) \u003c tol)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2016-10-02T16:43:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-02T13:56:26.000Z","updated_at":"2026-04-02T13:14:06.000Z","published_at":"2016-10-02T16:43:44.000Z","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\u003eThe Euclidean distance between two points in a p-dimensional space is a really common thing to compute in the field of computational geometry. In fact, it is pretty easy to do. norm(u-v) would seem to do the trick, for vectors u and v.\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\u003eBut what if you have a large number of points between which you want to compute ALL of those distances between every pair of points? In this problem, given an n by p array A, where each row of the matrix will be viewed as containing the coordinates of one p-dimensional point, you need to compute the n by n inter-point distance matrix.\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\u003eThus, D(i,J) will be the Euclidean distance between the i'th and j'th rows of A. Of course, D will be a symmetric matrix, with zeros on the diagonal.\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\u003eSo you can test your code, here is an example:\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[A = [1 1\\n     5 2\\n     2 2\\n     4 5]\\n\\nformat short g\\nD = interDist(A)\\nD =\\n       0       4.1231       1.4142            5\\n  4.1231            0            3       3.1623\\n  1.4142            3            0       3.6056\\n       5       3.1623       3.6056            0]]\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:t\u003eThus, thinking of the points [1 1] and [5 2] as the coordinates of two points in the (x,y) plane, the Euclidean distance between them in that plane is 4.1231...\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\u003eAs you can see, the matrix is symmetric, with zeros on the main diagonal. That must always happen, since the distance between any point and itself must be zero.\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":48970,"title":"Taxi vs Euclides","description":null,"description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; 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: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 42px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 343px 21px; transform-origin: 343px 21px; vertical-align: baseline; \"\u003e\u003cdiv style=\"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: 320px 21px; text-align: left; transform-origin: 320px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan 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: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eCalculate the difference between the Taxicab and Euclidean distance of the vectors. Round the result to the 4th decimal.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = taxiVsEuclides(x)\r\n    y = x;\r\nend","test_suite":"%%\r\nv1=1:10;\r\nv2=11:20;\r\nassert(isequal(taxiVsEuclides(v1,v2),68.3772))\r\n%%\r\nv1=1:4:50;\r\nv2=25:4:75;\r\nassert(isequal(taxiVsEuclides(v1,v2),225.4668))\r\n%%\r\nv1=1:8:50;\r\nv2=25:8:75;\r\nassert(isequal(taxiVsEuclides(v1,v2),104.5020))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":1,"created_by":698530,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":31,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2020-12-22T15:25:35.000Z","updated_at":"2026-03-15T03:35:12.000Z","published_at":"2020-12-31T01:18:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\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\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the difference between the Taxicab and Euclidean distance of the vectors. Round the result to the 4th decimal.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":264,"title":"Find the \"ordinary\" or Euclidean distance between A and Z","description":"A, B and Z define three points in the 3D _Euclidean_ space of the form:\r\nA = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\r\n\r\nFind the *Euclidean distance* between A and Z where\r\n  \r\n  A = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\n  \r\n  \u003e\u003e euclidean(A,B,Z)\r\n  \r\n  ans = 5.830951894845301\r\n\r\nYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors\r\nfor all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are.\r\nSo 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function\r\ninput vectors.\r\n\r\nHINT: use the Pythagorean formula.","description_html":"\u003cp\u003eA, B and Z define three points in the 3D \u003ci\u003eEuclidean\u003c/i\u003e space of the form:\r\nA = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\u003c/p\u003e\u003cp\u003eFind the \u003cb\u003eEuclidean distance\u003c/b\u003e between A and Z where\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eA = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003e\u003e\u003e euclidean(A,B,Z)\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eans = 5.830951894845301\r\n\u003c/pre\u003e\u003cp\u003eYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors\r\nfor all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are.\r\nSo 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function\r\ninput vectors.\u003c/p\u003e\u003cp\u003eHINT: use the Pythagorean formula.\u003c/p\u003e","function_template":"function y = euclidean(A,B,Z)\r\n  y = findEuclid(A,B,Z);\r\nend","test_suite":"%%\r\nA = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [1;0;0]; B = [5;3;0]; Z=[5;3;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0,0,0]; B = [4,3,0]; Z=[4,3,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;0;0]; B = [4;3;0]; Z=[4;3;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0,3,0]; B = [4,0,0]; Z=[4,0,3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;3;0]; B = [4;0;0]; Z=[4;0;3];\r\ny_correct = 5.830951894845301;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n%%\r\nA = [0;3;0]; B = [4;0;0]; Z=[4;0;12];\r\ny_correct = 13;\r\nassert(isequal(euclidean(A,B,Z),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":6,"created_by":1103,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":177,"test_suite_updated_at":"2012-02-12T03:40:41.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-02-05T23:24:30.000Z","updated_at":"2026-02-11T14:15:21.000Z","published_at":"2012-02-12T03:52:07.000Z","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\u003eA, B and Z define three points in the 3D\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEuclidean\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e space of the form: A = [x1;y1;0]; B = [x2;y2;0]; Z = [x2;y2;z];\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\u003eFind the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEuclidean distance\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e between A and Z where\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[A = [1,0,0]; B = [5,3,0]; Z=[5,3,3];\\n\\n\u003e\u003e euclidean(A,B,Z)\\n\\nans = 5.830951894845301]]\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:t\u003eYour function should be able to handle 1 x 3 vectors or 3 x 1 vectors for all input parameters: A,B and Z. Z need not be 1 x 3 if A and B are. So 1x3,1x3,3x1 inputs, corresponding A, B and Z, are possible function input vectors.\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\u003eHINT: use the Pythagorean formula.\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":43007,"title":"Euclidean inter-point distance matrix","description":"The Euclidean distance between two points in a p-dimensional space is a really common thing to compute in the field of computational geometry. In fact, it is pretty easy to do. norm(u-v) would seem to do the trick, for vectors u and v.\r\n\r\nBut what if you have a large number of points between which you want to compute ALL of those distances between every pair of points? In this problem, given an n by p array A, where each row of the matrix will be viewed as containing the coordinates of one p-dimensional point, you need to compute the n by n inter-point distance matrix.\r\n\r\nThus, D(i,J) will be the Euclidean distance between the i'th and j'th rows of A. Of course, D will be a symmetric matrix, with zeros on the diagonal.\r\n\r\nSo you can test your code, here is an example:\r\n\r\n  A = [1 1\r\n       5 2\r\n       2 2\r\n       4 5]\r\n\r\n  format short g\r\n  D = interDist(A)\r\n  D =\r\n         0       4.1231       1.4142            5\r\n    4.1231            0            3       3.1623\r\n    1.4142            3            0       3.6056\r\n         5       3.1623       3.6056            0\r\n\r\nThus, thinking of the points [1 1] and [5 2] as the coordinates of two points in the (x,y) plane, the Euclidean distance between them in that plane is 4.1231...\r\n\r\nAs you can see, the matrix is symmetric, with zeros on the main diagonal. That must always happen, since the distance between any point and itself must be zero.","description_html":"\u003cp\u003eThe Euclidean distance between two points in a p-dimensional space is a really common thing to compute in the field of computational geometry. In fact, it is pretty easy to do. norm(u-v) would seem to do the trick, for vectors u and v.\u003c/p\u003e\u003cp\u003eBut what if you have a large number of points between which you want to compute ALL of those distances between every pair of points? In this problem, given an n by p array A, where each row of the matrix will be viewed as containing the coordinates of one p-dimensional point, you need to compute the n by n inter-point distance matrix.\u003c/p\u003e\u003cp\u003eThus, D(i,J) will be the Euclidean distance between the i'th and j'th rows of A. Of course, D will be a symmetric matrix, with zeros on the diagonal.\u003c/p\u003e\u003cp\u003eSo you can test your code, here is an example:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eA = [1 1\r\n     5 2\r\n     2 2\r\n     4 5]\r\n\u003c/pre\u003e\u003cpre class=\"language-matlab\"\u003eformat short g\r\nD = interDist(A)\r\nD =\r\n       0       4.1231       1.4142            5\r\n  4.1231            0            3       3.1623\r\n  1.4142            3            0       3.6056\r\n       5       3.1623       3.6056            0\r\n\u003c/pre\u003e\u003cp\u003eThus, thinking of the points [1 1] and [5 2] as the coordinates of two points in the (x,y) plane, the Euclidean distance between them in that plane is 4.1231...\u003c/p\u003e\u003cp\u003eAs you can see, the matrix is symmetric, with zeros on the main diagonal. That must always happen, since the distance between any point and itself must be zero.\u003c/p\u003e","function_template":"function D = interDist(A)\r\n  % compute the interpoint distance matrix between rows of A\r\n  D = A;\r\nend\r\n\r\n","test_suite":"%%\r\nA = eye(3);\r\ny_correct = (1-A)*sqrt(2);\r\ntol = 10*eps;\r\nassert(norm(interDist(A)-y_correct) \u003c tol)\r\n\r\n%%\r\nA = (1:4)';\r\ny_correct = [     0     1     2     3;...\r\n     1     0     1     2;...\r\n     2     1     0     1;...\r\n     3     2     1     0];\r\ntol = 10*eps;\r\nassert(norm(interDist(A)-y_correct) \u003c tol)\r\n\r\n\r\n\r\n\r\n%%\r\nA = magic(3);\r\ny_correct = [0       6.48074069840786 9.79795897113271; ...\r\n  6.48074069840786                0 6.48074069840786; ...\r\n  9.79795897113271 6.48074069840786                0];\r\ntol = 1000*eps;\r\nassert(norm(interDist(A)-y_correct) \u003c tol)\r\n\r\n%%\r\nA = reshape((1:20).^2,4,5);\r\ntol = 1e-12;\r\ny_correct = [0 49.4469412603045 102.761860629321 160.015624237135; ...\r\n   49.4469412603045 0 53.3385414123783 110.634533487515; ...\r\n   102.761860629321 53.3385414123783 0 57.3149195236284; ...\r\n   160.015624237135 110.634533487515 57.3149195236284 0];\r\nassert(norm(interDist(A)-y_correct) \u003c tol)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":28,"test_suite_updated_at":"2016-10-02T16:43:44.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-02T13:56:26.000Z","updated_at":"2026-04-02T13:14:06.000Z","published_at":"2016-10-02T16:43:44.000Z","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\u003eThe Euclidean distance between two points in a p-dimensional space is a really common thing to compute in the field of computational geometry. In fact, it is pretty easy to do. norm(u-v) would seem to do the trick, for vectors u and v.\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\u003eBut what if you have a large number of points between which you want to compute ALL of those distances between every pair of points? In this problem, given an n by p array A, where each row of the matrix will be viewed as containing the coordinates of one p-dimensional point, you need to compute the n by n inter-point distance matrix.\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\u003eThus, D(i,J) will be the Euclidean distance between the i'th and j'th rows of A. Of course, D will be a symmetric matrix, with zeros on the diagonal.\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\u003eSo you can test your code, here is an example:\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[A = [1 1\\n     5 2\\n     2 2\\n     4 5]\\n\\nformat short g\\nD = interDist(A)\\nD =\\n       0       4.1231       1.4142            5\\n  4.1231            0            3       3.1623\\n  1.4142            3            0       3.6056\\n       5       3.1623       3.6056            0]]\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:t\u003eThus, thinking of the points [1 1] and [5 2] as the coordinates of two points in the (x,y) plane, the Euclidean distance between them in that plane is 4.1231...\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\u003eAs you can see, the matrix is symmetric, with zeros on the main diagonal. 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