A4正方形

mathe · 发表于 2021-1-1 13:05:50

58    {Va: n=7, w=8, a1=3,b1=1, a2=2, b2=1, t=0.340709}    0.144263(0.853539)
59    {Va: n=7, w=8, a1=4,b1=1, a2=1, b2=1, t=0.340709}    0.144263(0.868255)
78    {Va: n=8, w=9, a1=2,b1=2, a2=2, b2=1, t=0.318780}    0.126417(0.881430)
118    {Va: n=10, w=10, a1=5,b1=1, a2=2, b2=3, t=0.372023}    0.103312(0.890567)
122    {Va: n=10, w=9, a1=5,b1=2, a2=3, b2=3, t=0.317272}    0.101907(0.895885)
122    {Va: n=10, w=9, a1=6,b1=2, a2=2, b2=3, t=0.317272}    0.101907(0.895885)
123    {Va: n=10, w=9, a1=3,b1=3, a2=2, b2=3, t=0.306633}    0.101674(0.899095)
127    {Va: n=10, w=11, a1=6,b1=1, a2=3, b2=2, t=0.235304}    0.100426(0.905694)
127    {Va: n=10, w=11, a1=7,b1=1, a2=2, b2=2, t=0.235304}    0.100426(0.905694)
153    {Va: n=11, w=14, a1=2,b1=2, a2=1, b2=1, t=0.254620}    0.091766(0.911055)
154    {Va: n=11, w=13, a1=6,b1=1, a2=5, b2=1, t=0.247089}    0.091655(0.914780)
154    {Va: n=11, w=13, a1=7,b1=1, a2=4, b2=1, t=0.247089}    0.091655(0.914780)
154    {Va: n=11, w=13, a1=8,b1=1, a2=3, b2=1, t=0.247089}    0.091655(0.914780)
154    {Va: n=11, w=13, a1=9,b1=1, a2=2, b2=1, t=0.247089}    0.091655(0.914780)
154    {Va: n=11, w=13, a1=10,b1=1, a2=1, b2=1, t=0.247089} 0.091655(0.914780)
177    {Va: n=12, w=8, a1=2,b1=4, a2=1, b2=7, t=0.314571}    0.085320(0.911091)
177    {Va: n=12, w=8, a1=2,b1=5, a2=1, b2=6, t=0.314571}    0.085320(0.911091)
177    {Va: n=12, w=8, a1=2,b1=6, a2=1, b2=5, t=0.314571}    0.085320(0.911091)
177    {Va: n=12, w=8, a1=2,b1=7, a2=1, b2=4, t=0.314571}    0.085320(0.911091)
178    {Va: n=12, w=14, a1=1,b1=3, a2=1, b2=2, t=0.303058}    0.085095(0.911407)
188    {Va: n=12, w=15, a1=7,b1=1, a2=3, b2=1, t=0.201595}    0.083632(0.929786)
188    {Va: n=12, w=15, a1=8,b1=1, a2=2, b2=1, t=0.201595}    0.083632(0.929786)
200以内的，试验一下看看

mathe · 发表于 2021-1-1 14:41:29

122 {Va: n=10, w=9, a1=5,b1=2, a2=3, b2=3, t=0.317272} 0.101907(0.895885)

mathe · 发表于 2021-1-1 14:50:19

应该还有可能存在单侧正放正方形的可能

mathe · 发表于 2021-1-1 15:01:41

代码放在了 https://gitee.com/zhaohuidu/a4square 大家可以自己改进, 并且进行代码合并

dlpg070 · 发表于 2021-1-1 21:08:58

本帖最后由 dlpg070 于 2021-1-1 21:13 编辑

mathe 发表于 2021-1-1 15:01
代码放在了 https://gitee.com/zhaohuidu/a4square 大家可以自己改进, 并且进行代码合并

20210101版的几个统计结果:
新增Va Vs 成果斐然,但斜排为主的混排,还有许多更优解待发现

Va: 73  战果不错
Vs:  3
V: 232 30301218版 291 减少了
Cm  98 -19
Cm2  19

可能有较大改进的例子:
例如:n=86  Va Vs 不如 V,新类型结果至少不低于 V
V 第2,3  Vs:第4,Va:第5
86 8*11-2    0.125000(0.950175)
86 {V: n=8,u=14,w=11,s=6,t=0.060369}    0.124289(0.939398)
86 {V: n=8,u=14,w=11,s=7,t=0.060369}    0.124289(0.939398)
86    {Vs: n=9, w=1, s=1, a1=8, b1=10, t=0.551553}    0.122109(0.906729)
86    {Va: n=9, w=1, a1=8,b1=9, a2=1, b2=1, t=0.541987}    0.121566(0.898680)

更明显的例子:
n=90  斜排为主的混排,应该比V好,我的初步计算甚至优于 Cm ,Cu2
但是这个版本,Va Vs没有上榜前8名
90 {Cm 8*11-6+8}    0.118766(0.897660)
90 {Cu2 8*11} t=0.261593    0.118638(0.895732)
90 8*11+2    0.118261(0.890048)
90 8*12-6    0.117851(0.883883)
90 {H: n=12,u=24,w=7,s=12,t=0.130000}    0.117573(0.879718)

n=91 Vs 第7,Va第8
91 {Cm2 8*11-6+9, t=0.517590}    0.118737(0.907191)
91 8*11+3    0.118261(0.899938)
91 8*12-5    0.117851(0.893704)
91 {H: n=12,u=20,w=8,s=8,t=0.070000}    0.117454(0.887694)
91 {H: n=12,u=20,w=8,s=9,t=0.070000}    0.117454(0.887694)
91 {H: n=12,u=20,w=8,s=10,t=0.070000}    0.117454(0.887694)
91    {Vs: n=10, w=1, s=2, a1=8, b1=10, t=0.655912}    0.117167(0.883363)
91    {Va: n=10, w=1, a1=6,b1=10, a2=1, b2=2, t=0.654856}    0.117091(0.882206)

原因?

dlpg070 · 发表于 2021-1-2 16:10:50

本帖最后由 dlpg070 于 2021-1-2 19:11 编辑

dlpg070 发表于 2021-1-1 21:08
20210101版的几个统计结果:
新增Va Vs 成果斐然,但斜排为主的混排,还有许多更优解待发现

Va优秀解排行榜第1名清单:
1 共73项
2 200以内与 mathe 181#一致
3 549---999 没有处理Va,实际清单还有许多项,远大于73
4 较认真分析了 Va 处理部分
没有发现明显bug,很优秀,
发现 n=86 Va不如V的原因:Va算法假定上下至少有1个平放正方形,而86不能满足要求
n=99  Va已经处理,跃居第2名,不及Cm
90 91 未见改进可能
5 可见的急切的改进是:增加 n,w 搜索范围,处理1---999全范围

  55  27    {Va: n= 5, w= 4, a1= 2,b1= 2, a2= 2, b2= 1, t=0.44785717834}    0.20243240843(0.78236398584)
117  58    {Va: n= 7, w= 8, a1= 3,b1= 1, a2= 2, b2= 1, t=0.34070935608}    0.14426307248(0.85353896250)
119  59    {Va: n= 7, w= 8, a1= 4,b1= 1, a2= 1, b2= 1, t=0.34070935608}    0.14426307248(0.86825515151)
157  78    {Va: n= 8, w= 9, a1= 2,b1= 2, a2= 2, b2= 1, t=0.31878049953}    0.12641657126(0.88142957565)
237 118    {Va: n=10, w=10, a1= 5,b1= 1, a2= 2, b2= 3, t=0.37202310133}    0.10331176805(0.89056699835)
245 122    {Va: n=10, w= 9, a1= 5,b1= 2, a2= 3, b2= 3, t=0.31727203017}    0.10190692271(0.89588488115)
247 123    {Va: n=10, w= 9, a1= 3,b1= 3, a2= 2, b2= 3, t=0.30663271247}    0.10167350500(0.89909525187)
255 127    {Va: n=10, w=11, a1= 6,b1= 1, a2= 3, b2= 2, t=0.23530361176}    0.10042606493(0.90569425851)
307 153    {Va: n=11, w=14, a1= 2,b1= 2, a2= 1, b2= 1, t=0.25461997715}    0.09176646003(0.91105456895)
309 154    {Va: n=11, w=13, a1= 6,b1= 1, a2= 5, b2= 1, t=0.24708869543}    0.09165485709(0.91478006576)
355 177    {Va: n=12, w= 8, a1= 2,b1= 4, a2= 1, b2= 7, t=0.31457051429}    0.08532015299(0.91109050272)
357 178    {Va: n=12, w=14, a1= 1,b1= 3, a2= 1, b2= 2, t=0.30305836750}    0.08509494659(0.91140738763)
377 188    {Va: n=12, w=15, a1= 7,b1= 1, a2= 3, b2= 1, t=0.20159486541}    0.08363152208(0.92978568042)
435 217    {Va: n=13, w=13, a1= 4,b1= 3, a2= 4, b2= 3, t=0.24058537771}    0.07773720190(0.92726217611)
437 218    {Va: n=13, w=14, a1= 4,b1= 3, a2= 4, b2= 2, t=0.22118711211}    0.07750329009(0.92593771499)
441 220    {Va: n=13, w=15, a1= 8,b1= 1, a2= 5, b2= 2, t=0.19682469670}    0.07725253848(0.92839587254)
443 221    {Va: n=13, w=14, a1= 2,b1= 3, a2= 1, b2= 3, t=0.19408650622}    0.07722731861(0.93200702959)
445 222    {Va: n=13, w=14, a1= 1,b1= 3, a2= 1, b2= 3, t=0.16440889245}    0.07699196826(0.93052666165)
497 248    {Va: n=14, w=16, a1= 3,b1= 3, a2= 3, b2= 2, t=0.27481194996}    0.07274825926(0.92807247985)
501 250    {Va: n=14, w=15, a1= 7,b1= 2, a2= 7, b2= 2, t=0.25049642581}    0.07240637973(0.92678432117)
503 251    {Va: n=14, w=16, a1= 7,b1= 2, a2= 7, b2= 1, t=0.24671346104}    0.07235731727(0.92923088631)
513 256    {Va: n=14, w=14, a1= 8,b1= 2, a2= 3, b2= 4, t=0.19718927747}    0.07181529992(0.93359587578)
515 257    {Va: n=14, w=15, a1= 8,b1= 2, a2= 3, b2= 3, t=0.18989185064}    0.07175094920(0.93556383852)
517 258    {Va: n=14, w=16, a1= 8,b1= 2, a2= 3, b2= 2, t=0.18286752140}    0.07169271859(0.93768033137)
519 259    {Va: n=14, w=18, a1= 8,b1= 1, a2= 3, b2= 1, t=0.16953283218}    0.07159214086(0.93867546257)
521 260    {Va: n=14, w=19, a1= 3,b1= 1, a2= 2, b2= 1, t=0.16625609654}    0.07156941552(0.94170156281)
565 282    {Va: n=15, w=15, a1= 8,b1= 2, a2= 7, b2= 3, t=0.28781199636}    0.06818090275(0.92695703531)
577 288    {Va: n=15, w=18, a1= 6,b1= 2, a2= 6, b2= 1, t=0.25557263896}    0.06772507476(0.93406366022)
579 289    {Va: n=15, w=19, a1= 6,b1= 1, a2= 6, b2= 1, t=0.25062237238}    0.06766183337(0.93555724747)
595 297    {Va: n=15, w=18, a1=10,b1= 1, a2= 4, b2= 2, t=0.17970841374}    0.06694703866(0.94124827619)
599 299    {Va: n=15, w=18, a1= 9,b1= 1, a2= 6, b2= 2, t=0.14547582683}    0.06672663677(0.94135766175)
601 300    {Va: n=15, w=20, a1= 4,b1= 1, a2= 4, b2= 1, t=0.14368998657}    0.06671732203(0.94424233595)
663 331    {Va: n=16, w=17, a1= 7,b1= 3, a2= 4, b2= 3, t=0.23551335757}    0.06332457660(0.93855037010)
667 333    {Va: n=16, w=19, a1= 7,b1= 2, a2= 4, b2= 2, t=0.22060429954}    0.06316694168(0.93952628870)
669 334    {Va: n=16, w=17, a1= 1,b1= 4, a2= 1, b2= 4, t=0.21046693406}    0.06306819680(0.93940376664)
677 338    {Va: n=16, w=20, a1= 3,b1= 2, a2= 3, b2= 2, t=0.18233940127}    0.06282951903(0.94347234082)
743 371    {Va: n=17, w=18, a1= 9,b1= 1, a2= 8, b2= 4, t=0.24950287933}    0.05980674448(0.93833785481)
745 372    {Va: n=17, w=19, a1= 9,b1= 1, a2= 8, b2= 3, t=0.24648734038}    0.05977221188(0.93978086173)
755 377    {Va: n=17, w=21, a1= 6,b1= 2, a2= 3, b2= 2, t=0.21834145528}    0.05947779349(0.94305288877)
759 379    {Va: n=17, w=20, a1= 8,b1= 1, a2= 6, b2= 3, t=0.20318205559}    0.05933982981(0.94366273433)
761 380    {Va: n=17, w=20, a1= 7,b1= 2, a2= 7, b2= 2, t=0.20318205559}    0.05933982981(0.94615260962)
763 381    {Va: n=17, w=21, a1= 7,b1= 2, a2= 7, b2= 1, t=0.19922513765}    0.05930616409(0.94756638924)
771 385    {Va: n=17, w=20, a1=10,b1= 2, a2= 5, b2= 2, t=0.16356252809}    0.05904601910(0.94913278926)
777 388    {Va: n=17, w=20, a1= 8,b1= 2, a2= 8, b2= 2, t=0.12430548985}    0.05884840539(0.95013677200)
835 417    {Va: n=18, w=22, a1= 6,b1= 1, a2= 5, b2= 3, t=0.25352059559}    0.05657564287(0.94380017225)
855 427    {Va: n=18, w=21, a1= 9,b1= 2, a2= 8, b2= 2, t=0.19636612457}    0.05602497200(0.94771155001)
857 428    {Va: n=18, w=20, a1= 1,b1= 4, a2= 1, b2= 4, t=0.19594219621}    0.05602160924(0.94981698398)
861 430    {Va: n=18, w=21, a1= 9,b1= 2, a2= 9, b2= 2, t=0.17078219287}    0.05584067932(0.94810152201)
865 432    {Va: n=18, w=25, a1= 3,b1= 1, a2= 3, b2= 1, t=0.16852947784}    0.05582625826(0.95201938102)
873 436    {Va: n=18, w=25, a1= 2,b1= 1, a2= 2, b2= 1, t=0.12564389308}    0.05560676662(0.95329381880)
875 437    {Va: n=18, w=24, a1= 2,b1= 2, a2= 2, b2= 1, t=0.12478276087}    0.05560342303(0.95536537120)
877 438    {Va: n=18, w=23, a1= 2,b1= 2, a2= 2, b2= 2, t=0.12394880958}    0.05560022465(0.95744140598)
939 469    {Va: n=19, w=21, a1= 7,b1= 3, a2= 7, b2= 3, t=0.23417017898}    0.05343743471(0.94699796932)
941 470    {Va: n=19, w=22, a1= 8,b1= 2, a2= 6, b2= 3, t=0.22945352817}    0.05339179027(0.94739661095)
943 471    {Va: n=19, w=23, a1= 7,b1= 2, a2= 7, b2= 2, t=0.22489545979}    0.05334888123(0.94788694508)
945 472    {Va: n=19, w=24, a1=10,b1= 2, a2= 4, b2= 1, t=0.22048825170}    0.05330851022(0.94846234213)
947 473    {Va: n=19, w=24, a1= 3,b1= 2, a2= 2, b2= 3, t=0.21603162061}    0.05326879991(0.94905628206)
957 478    {Va: n=19, w=26, a1= 2,b1= 2, a2= 2, b2= 1, t=0.18481558963}    0.05302171208(0.95021174239)
959 479    {Va: n=19, w=23, a1= 8,b1= 2, a2= 7, b2= 2, t=0.18379305190}    0.05301452949(0.95194167067)
961 480    {Va: n=19, w=23, a1= 2,b1= 4, a2= 2, b2= 2, t=0.17758275963}    0.05297213737(0.95240404840)
963 481    {Va: n=19, w=23, a1= 2,b1= 3, a2= 2, b2= 3, t=0.17758275963}    0.05297213737(0.95438822351)
967 483    {Va: n=19, w=26, a1= 5,b1= 1, a2= 4, b2= 1, t=0.15439230077}    0.05283240383(0.95330720489)
1047 523    {Va: n=20, w=27, a1= 2,b1= 2, a2= 1, b2= 2, t=0.22227830487}    0.05068833000(0.95017293789)
1049 524    {Va: n=20, w=26, a1= 6,b1= 2, a2= 6, b2= 1, t=0.21970003989}    0.05066576283(0.95114222198)
1051 525    {Va: n=20, w=25, a1= 2,b1= 3, a2= 1, b2= 3, t=0.21438853183}    0.05062039513(0.95125152755)
1053 526    {Va: n=20, w=24, a1= 2,b1= 3, a2= 1, b2= 4, t=0.21101737559}    0.05059238280(0.95200891408)
1067 533    {Va: n=20, w=25, a1= 4,b1= 3, a2= 3, b2= 2, t=0.17795984649}    0.05034952675(0.95543907067)
1071 535    {Va: n=20, w=24, a1=10,b1= 2, a2= 9, b2= 2, t=0.15744117519}    0.05022746534(0.95437995563)
1073 536    {Va: n=20, w=28, a1= 3,b1= 1, a2= 3, b2= 1, t=0.15531188715}    0.05021604219(0.95572897531)
1079 539    {Va: n=20, w=24, a1= 3,b1= 3, a2= 2, b2= 3, t=0.13203285105}    0.05010628562(0.95688156274)
1083 541    {Va: n=20, w=26, a1= 2,b1= 1, a2= 1, b2= 3, t=0.11105822080}    0.05003097543(0.95754723743)
1085 542    {Va: n=20, w=25, a1= 2,b1= 1, a2= 1, b2= 4, t=0.11056396162}    0.05002946881(0.95925941898)
1087 543    {Va: n=20, w=25, a1= 2,b1= 2, a2= 1, b2= 3, t=0.11056396162}    0.05002946881(0.96102927031)

mathe · 发表于 2021-1-2 16:29:37

文件
https://gitee.com/zhaohuidu/a4square/blob/master/sqrt2.out
第5888行给出了998 {Va: n=27, w=35, a1=17,b1=1, a2=10, b2=2, t=0.092274} 0.037068(0.969659)

dlpg070 · 发表于 2021-1-2 19:53:27

本帖最后由 dlpg070 于 2021-1-2 19:54 编辑

mathe 发表于 2021-1-2 16:29
文件
https://gitee.com/zhaohuidu/a4square/blob/master/sqrt2.out
第5888行给出了998 {Va: n=27, w=35 ...

修改 EN=15 重新计算 Va处理到1---999
统计:
V: 139
Va:177
Tk: 36
Cm: 75
Cm2:19
Cu2: 6
V已经被Va打败,符合预期,可喜可贺

dlpg070 · 发表于 2021-1-2 20:27:50

本帖最后由 dlpg070 于 2021-1-2 20:36 编辑

mathe 发表于 2021-1-2 16:29
文件
https://gitee.com/zhaohuidu/a4square/blob/master/sqrt2.out
第5888行给出了998 {Va: n=27, w=35 ...

sqrt2_1_20210101.zip (17.66 KB, 下载次数: 0)
优秀解排行表文件存于附件,可能有误请指正
sqrt2.out:
998    {Va: n=27, w=35, a1=17,b1=1, a2=10, b2=2, t=0.092274}    0.037068(0.969659)
998    {Va: n=27, w=35, a1=18,b1=1, a2=9, b2=2, t=0.092274}    0.037068(0.969659)
998    {Va: n=27, w=35, a1=19,b1=1, a2=8, b2=2, t=0.092274}    0.037068(0.969659)
998    {Va: n=27, w=35, a1=20,b1=1, a2=7, b2=2, t=0.092274}    0.037068(0.969659)
998 {V: n=27,u=27,w=38,s=6,t=0.091871}    0.037067(0.969616)
我计算
998 {V: n=27,u=27,w=38,s= 6,t=0.09187139162}    0.03706740819(0.96961647160)
a 小数点后第7位有差别
到底算 Va 优还是 V 优?

uk702 · 发表于 2021-1-3 07:41:59

本帖最后由 uk702 于 2021-1-3 07:55 编辑

n = 100、101 可能有改进空间。
应该也不可能了，9*11 意味着水平要排 9 个，因此不可能超过 1/9 = 0.11111...，目前 n = 101 的最佳值已经为 0.111793 > 0.1111... .
就不知道改成 8*12+4、8*12+5 之后，那个 +4、+5 还有没有其它排法。

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