Skip to main content

FindInstance (and Solve, ...) abysmally slow on a fully determined system of linear equations and inequalities: why?


I took a quick look for FindInstance and Solve-related questions but came up empty for the aspect that I am curious about. So here is my newbie question:


FindInstance[{

s==9,r==8,d==7,n==6,e==5,y==2,m==1,o==0
},{s,e,n,d,m,o,r,y},Integers]

runs as quickly as one would expect. But


FindInstance[{
s!=e!=n!=d!=m!=o!=r!=y,
s==9,r==8,d==7,n==6,e==5,y==2,m==1,o==0
},{s,e,n,d,m,o,r,y},Integers]

takes ages -- long enough that I ran out of patience before MMA was done.



And now I am curious: Why would Mathematica suddenly display less maths ability than a third-grader?




bill_s suggested something much faster, but it is not equivalent to the original problem. The original inequality required all variable values to be different from all other variable values, such that each value can only be used for one variable. The FindInstance statement in Bill's post only compares x[i] to the ith value, but not to the other n-1 values.


In other news,


FindInstance[{
(*s!=e,s!=n,s!=d,s!=m,s!=o,s!=r,s!=y,*)
(*e!=n,e!=d,e!=m,e!=o,e!=r,e!=y,*)
n!=d,n!=m,n!=o,n!=r,n!=y,
d!=m,d!=o,d!=r,d!=y,
m!=o,m!=r,m!=y,

o!=r,o!=y,
r!=y,
s==9,r==8,d==7,n==6,e==5,y==2,m==1,o==0
},{s,e,n,d,m,o,r,y},Integers]

~1.1 seconds (on my laptop).


FindInstance[{
(*s!=e,s!=n,s!=d,s!=m,s!=o,s!=r,s!=y,*)
e!=n,e!=d,e!=m,e!=o,e!=r,e!=y,
n!=d,n!=m,n!=o,n!=r,n!=y,

d!=m,d!=o,d!=r,d!=y,
m!=o,m!=r,m!=y,
o!=r,o!=y,
r!=y,
s==9,r==8,d==7,n==6,e==5,y==2,m==1,o==0
},{s,e,n,d,m,o,r,y},Integers]

2nd comment uncommentd. ~20 s.


FindInstance[{
s!=e,s!=n,s!=d,s!=m,s!=o,s!=r,s!=y,

e!=n,e!=d,e!=m,e!=o,e!=r,e!=y,
n!=d,n!=m,n!=o,n!=r,n!=y,
d!=m,d!=o,d!=r,d!=y,
m!=o,m!=r,m!=y,
o!=r,o!=y,
r!=y,
s==9,r==8,d==7,n==6,e==5,y==2,m==1,o==0
},{s,e,n,d,m,o,r,y},Integers]

Both comments uncommented. ~1 minute.



The original version (multiple inequalities in one condition):


Timing[FindInstance[{
s!=e!=n!=d!=m!=o!=r!=y,
s==9,r==8,d==7,n==6,e==5,y==2,m==1,o==0},
{s,e,n,d,m,o,r,y},Integers]]

150 seconds!



Answer



No one has upgraded this post in a long time and as Danny promised all the problems the OP posted have been dealt with. In v 11.1 for instance, the last one now runs in a lot less than 150 seconds.


Timing[FindInstance[{

s!=e!=n!=d!=m!=o!=r!=y,
s==9,r==8,d==7,n==6,e==5,y==2,m==1,o==0},
{s,e,n,d,m,o,r,y},Integers]]


{0.01, {{s -> 9, e -> 5, n -> 6, d -> 7, m -> 1, o -> 0, r -> 8, y -> 2}}}

Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...