algorithm - How to find increasing subsequence of numbers with maximum sum? -

-

how find increasing subsequence of numbers maximum sum. find o(n^2) want know o(n log n).

thanks!

i'm assuming:

  • you don't care subsequence length @ all.
  • subsequences don't need contiguous

this makes world of difference!

solution

let optimal set s of increasing subsequences (is) array a set of iss such each s in a have 1 of:

  • s in in s
  • there s' in s such
    • sum(s') >= sum(s) and
    • largest_element(s') <= largest_element(s)

the optimal set s can ordered both largest element of subsequences , sum - order should same. mean smallest/largest sequence later.

our algorithm must find optimal set of a , return largest sequence. s can calculated by:

s := {[]} //contains empty subsequence each element x in a:    s_less := (largest sequence in s ends in less x)    s := append x s_less    s_more := (smallest sequence in s has sum greater s)     remove subsequences in s between s_less , s_more      (they made obsolete 's')     add s s

the largest subsequence in s largest subsequence in array.

each step can implemented in o(log n) s balanced binary tree. n steps give o(n*log n) total complexity.

caveat: there +- 1 error(s) in pseudo code - finding them left exercize reader :)

i'll try give concrete example. maybe helps make idea clearer. subsequence right best 1 far other ones because in future grow heaviest sequence.

curr array | optimal subsequences []              []  //best can 8 simgleton sequence: [8]             [] [8]  //the heaviest sequence can make ending 12 [8,12] total of 20 //we still keep [8] because couble of 9s , 10s might make better tahn 8+12 [8,12]          [] [8] [8,12]  [8,12,11]       [] [8] [8,11] [8,12] [8,12,11,9]     [] [8] [8,9] [8,11] [8,12]  //[8,9,10] makes [8,11] , [8,12] obsolete (remove those). //it not heavier last number smaller. [8,12,11,9,10]  [] [8] [8,9] [8,9,10]

Comments

Post a Comment

Popular posts from this blog

python - Scipy curvefit RuntimeError:Optimal parameters not found: Number of calls to function has reached maxfev = 1000 -

-
Image
i want make logharitmic fit. keep getting runtime error: optimal parameters not found: number of calls function has reached maxfev = 1000 i use following script. can tell me go wrong? use spyder still beginner. import math import matplotlib mpl scipy.optimize import curve_fit import numpy np #data f1=[735.0,696.0,690.0,683.0,680.0,678.0,679.0,675.0,671.0,669.0,668.0,664.0,664.0] t1=[1,90000.0,178200.0,421200.0,505800.0,592200.0,768600.0,1036800.0,1371600.0,1630800.0,1715400.0,2345400.0,2409012.0] f1n=np.array(f1) t1n=np.array(t1) plt.plot(t1,f1,'ro',label="original data") # curvefit def func(t,a,b): return a+b*np.log(t) t=np.linspace(0,3600*24*28,13) popt, pcov = curve_fit(func, t, f1n, maxfev=1000) plt.plot(t, func(t, *popt), label="fitted curve") plt.legend(loc='upper left') plt.show() your original data t1 , f1 . therefore curve_fit should given t1 second argument, not t . popt, pcov = curve_fit(func,...
Read more

binding - How can you make the color of elements of a WPF DrawingImage dynamic? -

-
we have need make vector graphic images change color of elements within graphic @ runtime. seem setting colors based on either static or dynamic resource values wouldn't work. want have multiple versions of same graphic, each abilty set graphic elements (path, line, etc) different colors don't think dynamic resource approach work. leaves data binding seems right approach. update graphic use data binding expr instead of hard-coded brush color so: <drawingimage x:key="graphic1"> <drawingimage.drawing> <drawinggroup> <drawinggroup.children> <geometrydrawing geometry="f1 m 8.4073,23.9233l"> <geometrydrawing.pen> <pen linejoin="round" brush="{binding line1brush, mode=oneway}"/> </geometrydrawing.pen> </geometrydrawing> <geometrydrawing geometry="f1 m 3.6875,2.56251l"> <geometrydrawing....
Read more

c# - How to add a new treeview at the selected node? -

-
i have treeview 4 levels; parent, child, grandchild, great-grandchild. selectednode @ grandchild level. what i'm trying create new "treeview" @ grandchild - no, dont wnat create new node "selectednode" (grandchild). should somelike this: parent child grandchild (new treeview) parent grandchild great-grandchild child great-grandchild child grandchild grandchild it similar parent table mother , father went off , had new childern different spouse other spouse of there existing children. private sub populaterootlevel() ' query find first round of parent populatenodes(dt, jcatreeview.nodes) end sub private sub populatenodes(byval dt datatable, byval nodes treenodecollection) each dr datarow in dt.rows dim tn new treenode() tn.text = dr("title").tostring()...
Read more