{"version":9,"randomSeed":"9cc157d7b0e19c86004c2182a2650adb","graph":{"viewport":{"xmin":-10.000000000000002,"ymin":-7.989919268165225,"xmax":9.999999999999998,"ymax":7.989919268165225}},"expressions":{"list":[{"type":"text","id":"33","text":"weights (normalised frequencies) of symbols"},{"type":"expression","id":"73","color":"#388c46","latex":"W_{wpe}=\\left[0.1,0.15,0.3,0.16,0.29\\right]"},{"type":"text","id":"77","text":"ETAOINSR(other)"},{"type":"expression","id":"74","color":"#6042a6","latex":"W_{mnl}=\\left[0.125,0.093,0.08,0.076,0.076,0.072,0.065,0.063,0.35\\right]"},{"type":"expression","id":"1","color":"#c74440","latex":"W=\\left[0.125,0.093,0.08,0.076,0.076,0.072,0.065,0.063,0.35\\right]"},{"type":"text","id":"35","text":"tree nodes (pairs of child nodes)"},{"type":"expression","id":"2","color":"#2d70b3","latex":"T=\\left[\\left(8,7\\right),\\left(6,4\\right),\\left(5,3\\right),\\left(2,1\\right),\\left(10,11\\right),\\left(12,13\\right),\\left(14,9\\right),\\left(15,16\\right)\\right]","hidden":true,"labelSize":"medium"},{"type":"folder","id":"12","title":"recursive weight summation","hidden":true,"collapsed":true},{"type":"expression","id":"3","folderId":"12","color":"#388c46","latex":"w_{0}\\left(k\\right)=\\left\\{k\\le\\operatorname{length}\\left(W\\right):W\\left[k\\right],W\\left[T\\left[k-\\operatorname{length}\\left(W\\right)\\right].x\\right]+W\\left[T\\left[k-\\operatorname{length}\\left(W\\right)\\right].y\\right]\\right\\}"},{"type":"expression","id":"4","folderId":"12","color":"#6042a6","latex":"w_{1}\\left(k\\right)=\\left\\{k\\le\\operatorname{length}\\left(W\\right):W\\left[k\\right],w_{0}\\left(T\\left[k-\\operatorname{length}\\left(W\\right)\\right].x\\right)+w_{0}\\left(T\\left[k-\\operatorname{length}\\left(W\\right)\\right].y\\right)\\right\\}"},{"type":"expression","id":"5","folderId":"12","color":"#000000","latex":"w_{2}\\left(k\\right)=\\left\\{k\\le\\operatorname{length}\\left(W\\right):W\\left[k\\right],w_{1}\\left(T\\left[k-\\operatorname{length}\\left(W\\right)\\right].x\\right)+w_{1}\\left(T\\left[k-\\operatorname{length}\\left(W\\right)\\right].y\\right)\\right\\}"},{"type":"expression","id":"6","folderId":"12","color":"#c74440","latex":"w_{3}\\left(k\\right)=\\left\\{k\\le\\operatorname{length}\\left(W\\right):W\\left[k\\right],w_{2}\\left(T\\left[k-\\operatorname{length}\\left(W\\right)\\right].x\\right)+w_{2}\\left(T\\left[k-\\operatorname{length}\\left(W\\right)\\right].y\\right)\\right\\}"},{"type":"expression","id":"9","folderId":"12","color":"#6042a6","latex":"w_{4}\\left(k\\right)=\\left\\{k\\le\\operatorname{length}\\left(W\\right):W\\left[k\\right],w_{3}\\left(T\\left[k-\\operatorname{length}\\left(W\\right)\\right].x\\right)+w_{3}\\left(T\\left[k-\\operatorname{length}\\left(W\\right)\\right].y\\right)\\right\\}"},{"type":"expression","id":"10","color":"#000000","latex":"w\\left(k\\right)=w_{4}\\left(\\operatorname{floor}\\left(k\\right)\\right)","hidden":true},{"type":"text","id":"38","text":"is node k not in a tree?"},{"type":"expression","id":"22","color":"#000000","latex":"C\\left(k\\right)=\\prod_{s=1}^{\\operatorname{length}\\left(T\\right)}\\left\\{T\\left[s\\right].x=k:0,1\\right\\}\\left\\{T\\left[s\\right].y=k:0,1\\right\\}","hidden":true,"labelSize":"medium"},{"type":"expression","id":"24","color":"#2d70b3","latex":"J_{0}=\\left[1...\\left(\\operatorname{length}\\left(W\\right)+\\operatorname{length}\\left(T\\right)\\right)\\right]"},{"type":"text","id":"41","text":"nodes not in the tree"},{"type":"expression","id":"25","color":"#388c46","latex":"J=J_{0}\\left[C\\left(J_{0}\\right)=1\\right]"},{"type":"text","id":"43","text":"... sorted by frequency"},{"type":"expression","id":"13","color":"#2d70b3","latex":"L=\\operatorname{sort}\\left(J,\\left[w\\left(j\\right)\\operatorname{for}j=J\\right]\\right)"},{"type":"text","id":"45","text":"add the two lowest to a new node"},{"type":"expression","id":"15","color":"#6042a6","latex":"S_{T}=\\left(T\\to\\operatorname{join}\\left(T,\\left(L\\left[1\\right],L\\left[2\\right]\\right)\\right)\\right)","labelSize":"medium"},{"type":"text","id":"47","text":"prepend bit b to ternary-binary string s"},{"type":"expression","id":"26","color":"#6042a6","latex":"K\\left(s,b\\right)=\\left(b+1\\right)+3s","labelSize":"medium"},{"type":"text","id":"49","text":"binary expansion (list) of ternary-binary string"},{"type":"expression","id":"28","color":"#c74440","latex":"X\\left(s\\right)=\\left[\\operatorname{mod}\\left(\\operatorname{floor}\\left(\\frac{s}{3^{j}}\\right),3\\right)-1\\operatorname{for}j=\\left[0...\\operatorname{floor}\\left(\\log_{3}s\\right)\\right]\\right]"},{"type":"text","id":"52","text":"codewords"},{"type":"expression","id":"53","color":"#2d70b3","latex":"E=\\left[25,16,22,77,13,50,68,41,8\\right]"},{"type":"folder","id":"65","title":"recursively find path from root node to other node","collapsed":true},{"type":"expression","id":"58","folderId":"65","color":"#000000","latex":"P_{0}\\left(k,m\\right)=\\left\\{T\\left[m\\right].x=k:1,T\\left[m\\right].y=k:2,0\\right\\}","labelSize":"medium"},{"type":"expression","id":"61","folderId":"65","color":"#388c46","latex":"P_{1}\\left(k,m\\right)=\\left\\{T\\left[m\\right].x=k:1,T\\left[m\\right].y=k:2,P_{0}\\left(k,T\\left[m\\right].x-\\operatorname{length}\\left(W\\right)\\right)>0:K\\left(P_{0}\\left(k,T\\left[m\\right].x-\\operatorname{length}\\left(W\\right)\\right),0\\right),P_{0}\\left(k,T\\left[m\\right].y-\\operatorname{length}\\left(W\\right)\\right)>0:K\\left(P_{0}\\left(k,T\\left[m\\right].y-\\operatorname{length}\\left(W\\right)\\right),1\\right),0\\right\\}"},{"type":"expression","id":"62","folderId":"65","color":"#6042a6","latex":"P_{2}\\left(k,m\\right)=\\left\\{T\\left[m\\right].x=k:1,T\\left[m\\right].y=k:2,P_{1}\\left(k,T\\left[m\\right].x-\\operatorname{length}\\left(W\\right)\\right)>0:K\\left(P_{1}\\left(k,T\\left[m\\right].x-\\operatorname{length}\\left(W\\right)\\right),0\\right),P_{1}\\left(k,T\\left[m\\right].y-\\operatorname{length}\\left(W\\right)\\right)>0:K\\left(P_{1}\\left(k,T\\left[m\\right].y-\\operatorname{length}\\left(W\\right)\\right),1\\right),0\\right\\}"},{"type":"expression","id":"63","folderId":"65","color":"#000000","latex":"P_{3}\\left(k,m\\right)=\\left\\{T\\left[m\\right].x=k:1,T\\left[m\\right].y=k:2,P_{2}\\left(k,T\\left[m\\right].x-\\operatorname{length}\\left(W\\right)\\right)>0:K\\left(P_{2}\\left(k,T\\left[m\\right].x-\\operatorname{length}\\left(W\\right)\\right),0\\right),P_{2}\\left(k,T\\left[m\\right].y-\\operatorname{length}\\left(W\\right)\\right)>0:K\\left(P_{2}\\left(k,T\\left[m\\right].y-\\operatorname{length}\\left(W\\right)\\right),1\\right),0\\right\\}"},{"type":"expression","id":"66","folderId":"65","color":"#2d70b3","latex":"P_{4}\\left(k,m\\right)=\\left\\{T\\left[m\\right].x=k:1,T\\left[m\\right].y=k:2,P_{3}\\left(k,T\\left[m\\right].x-\\operatorname{length}\\left(W\\right)\\right)>0:K\\left(P_{3}\\left(k,T\\left[m\\right].x-\\operatorname{length}\\left(W\\right)\\right),0\\right),P_{3}\\left(k,T\\left[m\\right].y-\\operatorname{length}\\left(W\\right)\\right)>0:K\\left(P_{3}\\left(k,T\\left[m\\right].y-\\operatorname{length}\\left(W\\right)\\right),1\\right),0\\right\\}"},{"type":"expression","id":"67","color":"#388c46","latex":"P\\left(k\\right)=P_{4}\\left(\\operatorname{floor}\\left(k\\right),\\operatorname{length}\\left(T\\right)\\right)"},{"type":"expression","id":"69","color":"#000000","latex":"E\\to\\left[P\\left(j\\right)\\operatorname{for}j=\\left[1...\\operatorname{length}\\left(W\\right)\\right]\\right]"},{"type":"text","id":"71","text":"string in alphabet to encode"},{"type":"expression","id":"72","color":"#2d70b3","latex":"I=\\left[\\right]"}]}}