奥运五环中的数字 --- 编程小题

FreddyMusic

奥运五环中的数字 --- 编程小题

Pandigital Olympic Circles





提示：

1. 共八解
2. 思考如何提高算法效率和降低运行时间。

答案：Mathematica online demonstration and Code
http://demonstrations.wolfram.com/PandigitalOlympicCirclesPuzzle/

游客，如果您要查看本帖隐藏内容请回复

[ 本帖最后由 FreddyMusic 于 2008-4-27 16:26 编辑 ]

shunfly

。。。
纯回复贴

wyxajg

ok!ok!

changqing

向FreddyMusic学习！

pcqsl

en, en,

1. fontsize = 25;
   
2. c1[n1_, n2_] :=
   
3.   Graphics[{Blue, Thick, Circle[{-2.2, 1}],
   
4.     Text[Style[n1, Black, fontsize], {-2.2, 1.3}],
   
5.     Text[Style[n2, Black, fontsize], {-1.1 - .55, .6}]}];
   
6. c2[n3_, n4_, n5_] :=
   
7.   Graphics[{Black, Thick, Circle[{0, 1}],
   
8.     Text[Style[n3, Black, fontsize], {-.55, .6}],
   
9.     Text[Style[n4, Black, fontsize], {0, 1.3}],
   
10.     Text[Style[n5, Black, fontsize], {.55, .6}]}];
    
11. c3[n6_, n7_] :=
    
12.   Graphics[{Red, Thick, Circle[{2.2, 1}],
    
13.     Text[Style[n6, Black, fontsize], {2.2 - .55, .6}],
    
14.     Text[Style[n7, Black, fontsize], {2.2, 1.3}]}];
    
15. c4[n2_, n8_, n3_] :=
    
16.   Graphics[{Yellow, Thick, Circle[{-1.1, 0.3}],
    
17.     Text[Style[n8, Black, fontsize], {-1.1, -0.3}]}];
    
18. c5[n5_, n9_, n6_] :=
    
19.   Graphics[{Green, Thick, Circle[{1.1, 0.3}],
    
20.     Text[Style[n9, Black, fontsize], {1.1, -0.3}]}];
    
21. graph[r_] :=
    
22. Show[c1[r[[1]], r[[2]]], c2[r[[3]], r[[4]], r[[5]]],
    
23.   c3[r[[6]], r[[7]]], c4[r[[2]], r[[8]], r[[3]]],
    
24.   c5[r[[5]], r[[9]], r[[6]]], PlotRange -> 3.5, AspectRatio -> 1]
    
25. 
    
26. rsum = 13;
    
27. c = Permutations[Range[9], {4}];
    
28. csum = Total[c, {2}];
    
29. v = rsum*5 - 45;
    
30. p = Flatten[Position[csum, v]];
    
31. l = {};
    
32. Do[{
    
33.    cc = c[[p[[i]]]];
    
34.    r = {rsum - cc[[1]], cc[[1]], cc[[2]], rsum - cc[[2]] - cc[[3]],
    
35.      cc[[3]], cc[[4]], rsum - cc[[4]], rsum - cc[[1]] - cc[[2]],
    
36.      rsum - cc[[3]] - cc[[4]]};
    
37.    r1 = Union[r];
    
38.    If[ Min[r1] == 1 && Max[r1] == 9 &&
    
39.      Length[r1] == 9, {l = Append[l, r]}];}, {i, Length[p]}];
    
40. Length[l];
    
41. y = Table[graph[l[[i]]], {i, Length[l]}]

复制代码

[ 本帖最后由 pcqsl 于 2008-4-23 06:35 编辑 ]

FreddyMusic

pcqsl,

Speed good,
Algorithm smart.

luozhenyan0303

什么东西也要顶一下

FreddyMusic

pcqsl,

游客，本帖隐藏的内容需要积分高于 5 才可浏览，您当前积分为 0

[ 本帖最后由 FreddyMusic 于 2008-4-24 15:27 编辑 ]

FreddyMusic

We have two possiblity:

1. To make dynamic list with more digitals and one pcs shorter rings.
Eg. digital 1-11 or 1-13,  / Rings 6 or 7 pcs   ( One digital in one ring space )
then check the middle data same as our demo ?

2. To make with more digitals and two digital in one rings.   
Eg. digital 1-19  / Rings 5 pcs ( two digital in one ring space ) ( three digital in one ring space)
then check the middle data same as our demo ?

What's your opinion ? I perfer the 2nd.

[ 本帖最后由 FreddyMusic 于 2008-4-24 15:24 编辑 ]

pcqsl

原帖由 FreddyMusic 于 2008-4-24 15:17 发表
We have two possiblity:

1. To make dynamic list with more digitals and one pcs shorter rings.
Eg. digital 1-11 or 1-13,  / Rings 6 or 7 pcs   ( One digital in one ring space )
then check the mid ...

According to my understanding, we were just asked for dynamic controls, the sliders.  It is simple.  I don't think they are asking for more complicated problems and algorithms.  By slightly modifying your code, I come up with

1. rsum = 11;
   
2. Print["Control the identical target sum of each circle by " Slider[
   
3.    Dynamic[rsum], {3, 24, 1}]]
   
4. Print["Current target sum is " Style[Dynamic[rsum], Large, Bold, Purple]]
   
5. Dynamic[{
   
6.   numberintwo = Permutations[Range[1, 9], {4}];
   
7.   csum = Total[numberintwo, {2}];
   
8.   v = rsum*5 - 45;
   
9.   p = Flatten[Position[csum, v]];
   
10.   
    
11.   (* Search pandigital list *)
    
12.   Sol = {};
    
13.   Do[{cc = numberintwo[[p[]]];
    
14.        r = { rsum - cc[[1]], cc[[1]],  rsum  - cc[[1]] - cc[[2]],
    
15.       cc[[2]],  rsum  - cc[[2]] - cc[[3]], cc[[3]],
    
16.       rsum - cc[[3]] - cc[[4]], cc[[4]], rsum - cc[[4]]};
    
17.        r1 = Union[r];
    
18.        If[
    
19.      Min[r1] == 1 && Max[r1] == 9 &&
    
20.       Length[r1] == 9, {Sol = Append[Sol, r]}];}, {i, Length[p]}];
    
21.   
    
22.   (* Plot digital and rings *)
    
23.   If[Sol == {},
    
24.    Graphics[{Text[
    
25.       Style["No solution.", Large, Bold, Purple], {0, 0},
    
26.       Automatic]}, ImageSize -> {575, 300}],
    
27.    GraphicsGrid[Table[
    
28.      Graphics[{Thickness[0.01],
    
29.        (* Plot Olympic five rings *)
    
30.        RGBColor[0, .5, .76], Circle[{0, 0}, 2],
    
31.        RGBColor[34/256, 30/256, 29/256], Circle[{4.5, 0}, 2],
    
32.        RGBColor[235/256, 29/256, 42/256], Circle[{9, 0}, 2],
    
33.        RGBColor[251/256, 178/256, 49/256], Circle[{2.25, -2.25}, 2],
    
34.        RGBColor[1/256, 156/256, 88/256], Circle[{6.75, -2.25}, 2],
    
35.        (* Replot Olympic five rings to make it connect *)
    
36.        RGBColor[0, .5, .76], Circle[{0, 0}, 2, {-Pi/3, 0}],
    
37.        RGBColor[34/256, 30/256, 29/256],
    
38.        Circle[{4.5, 0}, 2, {-Pi/3, 0}],
    
39.        RGBColor[34/256, 30/256, 29/256],
    
40.        Circle[{4.5, 0}, 2, {Pi*1.3, Pi*1.5}],
    
41.        RGBColor[235/256, 29/256, 42/256],
    
42.        Circle[{9, 0}, 2, {Pi*1.3, Pi*1.5}],
    
43.        (* Plot Numbers in rings *)
    
44.        Text[Style[Sol[[2 i + j]][[1]], 20, Purple], {0, 0}],
    
45.        Text[
    
46.         Style[Sol[[2 i + j]][[2]], 20, Purple], {2.25/2, -2.25/2}],
    
47.        Text[Style[Sol[[2 i + j]][[3]], 20, Purple], {2.25, -2.25}],
    
48.        Text[
    
49.         Style[Sol[[2 i + j]][[4]], 20,
    
50.          Purple], {(2.25 + 4.5)/2, -2.25/2}],
    
51.        Text[Style[Sol[[2 i + j]][[5]], 20, Purple], {4.5, 0}],
    
52.        Text[
    
53.         Style[Sol[[2 i + j]][[6]], 20,
    
54.          Purple], {(4.5 + 6.75)/2, -2.25/2}],
    
55.        Text[Style[Sol[[2 i + j]][[7]], 20, Purple], {6.75, -2.25}],
    
56.        Text[
    
57.         Style[Sol[[2 i + j]][[8]], 20,
    
58.          Purple], {(6.75 + 9)/2, -2.25/2}],
    
59.        Text[Style[Sol[[2 i + j]][[9]], 20, Purple], {9, 0}]
    
60.        }], {i, 0, Length[Sol]/2 - 1}, {j, 1, 2}],
    
61.     ImageSize -> {575, 300}]]}]

复制代码

You see the range of sum is from 3 to 24.  The basic reason is that there are at least two or at most three numbers in any circle, so  the sum can not be less than 1+2 or greater than 9+8+7. Definitely, this is a necessary condition.

And I remove "found" because we have checked fully.  "No solution" is the fact.

[ 本帖最后由 pcqsl 于 2008-4-25 04:31 编辑 ]

FreddyMusic

pcqsl，

OK, I send attahced Demo to editor, we wait what they say.

See attachment.

FreddyMusic

pcqsl,

They go back to the previous demonstration design.
but they want to have mutiply dynamic sliders in future.
Good News, they published this demonstration.
http://demonstrations.wolfram.com/PandigitalOlympicCirclesPuzzle/

Cheers !

============================================

Editor's comments

I think we'll stick with the original version. You simply changed thesetter to a slider. That's not the point. Discrete controls are fine aslong as there is a good reason for them. Your concept works better witha discrete control. The point is that was the only control. Its best totry to come up with multiple controls so that more than one thing ischanging and its obvious this isn't just a collection of static slides.This is more obvious with multiple controls or sliders. Just, in the future, remember to try to make these more dynamic.

cgy123000

好的，见识一下！

wangyubzd

厉害厉害！

xiongqingqing

hao jianshiyixia

causalgia

nbnbnbnbnb

盐淮剑客

顶起来 。。。。。。。。。。。。。

盐淮剑客

非常不错

sincos

tdddddd:handshake

yyh1255

先顶后看
好东西我会分享的