{"version":9,"randomSeed":"8c89771ac84844ef0edf2df46c1a4dba","graph":{"viewport":{"xmin":-15.36867981558892,"ymin":-35.99945424098888,"xmax":37.38989013174311,"ymax":50.37862819941793}},"expressions":{"list":[{"type":"folder","id":"13","title":"setup"},{"type":"text","id":"15","folderId":"13","text":"given set"},{"type":"expression","id":"1","folderId":"13","color":"#c74440","latex":"A=\\left[11,14,19,22,25,27,29,44\\right]"},{"type":"text","id":"17","folderId":"13","text":"hidden subset"},{"type":"expression","id":"2","folderId":"13","color":"#2d70b3","latex":"B=\\left[14,22,44\\right]"},{"type":"text","id":"21","folderId":"13","text":"count number of occurrences of n in Z (magnitude for intersection)"},{"type":"expression","id":"7","folderId":"13","color":"#2d70b3","latex":"m_{i}\\left(n,Z\\right)=\\operatorname{length}\\left(Z\\left[Z=n\\right]\\right)"},{"type":"text","id":"23","folderId":"13","text":"does S contain B?"},{"type":"expression","id":"8","folderId":"13","color":"#388c46","latex":"f\\left(S\\right)=\\left\\{\\operatorname{total}\\left(\\left[\\min\\left(m_{i}\\left(k,B\\right),1\\right)\\operatorname{for}k=S\\left[1...\\right]\\right]\\right)=\\operatorname{length}\\left(B\\right):1,0\\right\\}"},{"type":"text","id":"25","folderId":"13","text":"count usages"},{"type":"expression","id":"11","folderId":"13","color":"#c74440","latex":"c_{u}=8","slider":{"hardMin":true,"hardMax":true,"min":"0","max":"100","step":"1"}},{"type":"text","id":"27","folderId":"13","text":"f(S), wrapped to implement counter"},{"type":"expression","id":"9","folderId":"13","color":"#6042a6","latex":"F\\left(S\\right)=\\left(c_{u}\\to c_{u}+1,R\\to f\\left(S\\right)\\right)"},{"type":"expression","id":"36","folderId":"13","color":"#c74440","latex":"R=-1"},{"type":"folder","id":"29","title":"naive algorithm"},{"type":"text","id":"31","folderId":"29","text":"list of importance booleans"},{"type":"expression","id":"32","folderId":"29","color":"#2d70b3","latex":"A_{Ni}=\\left[0,1,0,1,0,0,0,1\\right]"},{"type":"expression","id":"53","folderId":"29","color":"#c74440","latex":"A_{No}=\\left[14,22,44\\right]"},{"type":"text","id":"47","folderId":"29","text":"begin naive algorithm"},{"type":"expression","id":"48","folderId":"29","color":"#2d70b3","latex":"A_{Nb}=\\left(c_{u}\\to0,A_{Ni}\\to\\left[\\right],A_{No}\\to\\left[\\right]\\right)"},{"type":"text","id":"34","folderId":"29","text":"step of the naive algorithm"},{"type":"expression","id":"40","folderId":"29","color":"#000000","latex":"L_{wi}\\left(L,k\\right)=\\left\\{k=1:L\\left[2...\\right],\\operatorname{join}\\left(L\\left[1...\\left(k-1\\right)\\right],L\\left[\\left(k+1\\right)...\\right]\\right)\\right\\}"},{"type":"expression","id":"35","folderId":"29","color":"#6042a6","latex":"A_{Ns}=\\left(A_{Ni}\\to\\operatorname{join}\\left(A_{Ni},1-f\\left(L_{wi}\\left(A,\\operatorname{length}\\left(A_{Ni}\\right)+1\\right)\\right)\\right),c_{u}\\to c_{u}+1\\right)"},{"type":"text","id":"50","folderId":"29","text":"finish naive algorithm"},{"type":"expression","id":"51","folderId":"29","color":"#6042a6","latex":"A_{Nf}=\\left(A_{No}\\to A\\left[A_{Ni}=1\\right]\\right)"}]}}