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level 11
Sunnie😂
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难度系数评估体系(Sudoku Difficulty Rating System,简称SDRS),是一个以SE软件(Sudoku Explainer,数独分析器,目前最新版本为V1.2.9,后面简称SE软件)为基础测评的一个优化后的评估体系,它能相对比较精确地测试出标准数独的难度。
具体难度分析的方法如下:
将题目用带有难度系数评判的软件进行评测,每一步都以从低难度技巧到高难度技巧的过程搜索盘面内是否存在可用的情况,如果有,则使用掉它,并得到一个难度系数,然后进入第二步。从此我们可以看出,第一步取的是盘面内最小难度技巧的难度系数。同样,在第二步中,也按照第一步的过程获取最小的难度系数。最终,由软件获取到当前题目使用到的最难技巧,并以此技巧所对应的难度系数,作为整个题目的难度系数,此时称题目的难度为题目难度系数(SudokuExplainer Rating,SER或SR)。
具体的SE软件的技巧的难度参照表如下(左边是难度系数,右边是技巧名称):
l 1.0 Single
l 1.2 Hidden Single in box
l 1.5 Hidden Single in line
l 1.7 Direct Pointing
l 1.9 Direct Claiming
l 2.0 Direct Hidden Pair
l 2.3 Naked Single
l 2.5 Direct Hidden Triplet
l 2.6 Pointing
l 2.8 Claiming
l 3.0 Naked Pair
l 3.2 X-Wing
l 3.4 Hidden Pair
l 3.6 Naked Triplet
l 3.8 Swordfish
l 4.0 Hidden Triplet
l 4.2 XY-Wing
l 4.4 XYZ-Wing
l 4.4 W-Wing
l 4.5 UR Types 1, 2, 4
l 4.5 UR Type 3 with Hidden Pair
l 4.6 UR Type 3 with Naked Pair
l 4.6 UR Type 3 with Hidden Triplet
l 4.7 UR Type 3 with Naked Triplet
l 4.7 UR Type 3 with Hidden Quad
l 4.8 UR Type 3 with Naked Quad
l 4.6 UL Types 1, 2, 4 (6 cells)
l 4.7 UL Types 1, 2, 4 (8 cells)
l 4.8 UL Types 1, 2, 4 (10 cells)
l 4.9 UL Types 1, 2, 4 (12 cells)
l 5.0 UL Types 1, 2, 4 (14 cells)
l 5.1 UL Types 1, 2, 4 (16 cells)
l 4.6 UL Type 3 with Hidden Pair (6cells)
l 4.7 UL Type 3 with Hidden Pair (8cells)
l 4.7 UL Type 3 with Hidden Triplet (6cells)
l 4.8 UL Type 3 with Hidden Triplet (8cells)
l 4.8 UL Type 3 with Hidden Quad (6cells)
l 4.9 UL Type 3 with Hidden Quad (8cells)
l 4.7 UL Type 3 with Naked Pair (6cells)
l 4.8 UL Type 3 with Naked Pair (8cells)
l 4.9 UL Type 3 with Naked Pair (10cells)
l 5.0 UL Type 3 with Naked Pair (12cells)
l 4.8 UL Type 3 with Naked Triplet (6cells)
l 4.9 UL Type 3 with Naked Triplet (8cells)
l 4.9 UL Type 3 with Naked Quad (6cells)
l 5.0 UL Type 3 with Naked Quad (8cells)
l 5.0 Naked Quad
l 5.2 Jellyfish
l 5.4 Hidden Quad
l 5.6 Bivalue Universal Graves Type 1
l 5.7 Bivalue Universal Graves Type 2
l 5.7 Bivalue Universal Graves Type 4
l 5.8 Bivalue Universal Graves Type 3with Naked Pair
l 5.9 Bivalue Universal Graves Type 3with Naked Triplet
l 6.0 Bivalue Universal Graves Type 3with Naked Quad
l 6.1 Bivalue Universal Graves Type 3with Naked Quint
l 6.2 Aligned Pair Exclusion
l 6.5 Bidirectional X-Cycle (6 cells)
l 6.6 Bidirectional X-Cycle (8 cells)
l 6.6 Turbot Fish
l 6.6 Forcing X-chain (5-6 nodes)
l 6.7 Forcing X-Chain (7-8 nodes)
l 6.8 Forcing X-Chain (9-12 nodes)
l 6.9 Forcing X-Chain (13-16 nodes)
l 6.5 Bidirectional Y-cycle (3 cells)
l 6.6 Bidirectional Y-cycle (4 cells)
l 6.7 Bidirectional Y-cycle (5 cells)
l 6.8 Bidirectional Y-cycle (6-7 cells)
l 6.9 Bidirectional Y-cycle (8-9 cells)
l 7.0 Bidirectional Y-cycle (10-13cells)
l 7.0 Bidirectional Cycle (6 nodes)
l 7.1 Bidirectional Cycle (8 nodes)
l 7.2 Bidirectional Cycle (10 nodes)
l 7.3 Bidirectional Cycle (12 nodes)
l 7.0 Forcing Chain (5 nodes)
l 7.1 Forcing Chain (7 nodes)
l 7.2 Forcing Chain (9 nodes)
l 7.3 Forcing Chain (11-13 nodes)
l 7.4 Forcing Chain (15-17 nodes)
l 7.5 Forcing Chain (19-25 nodes)
l 7.6 Forcing Chain (27-more nodes)
l 7.5 Aligned Triplet Exclusion
l 7.6 Nishio Forcing Chain (5-6 nodes)
l 7.7 Nishio Forcing Chain (7-8 nodes)
l 7.8 Nishio Forcing Chain (9-12 nodes)
l 7.9 Nishio Forcing Chain (13-16nodes)
l 8.0 Nishio Forcing Chain (17-24nodes)
l 8.1 Nishio Forcing Chain (25-36nodes)
l 8.2 Multiple (7-8 nodes) RegionForcing Chains
l 8.3 Multiple (9-12 nodes) Cell/RegionForcing Chains
l 8.4 Multiple (13-16 nodes)Cell/Region Forcing Chains
l 8.5 Multiple (17-24 nodes)Cell/Region Forcing Chains
l 8.6 Multiple (25-36 nodes)Cell/Region Forcing Chains
l 8.6 Dynamic (5-6 nodes) Cell/RegionForcing Chains
l 8.7 Dynamic (7-8 nodes) Cell/RegionForcing Chains
l 8.8 Dynamic (9-12 nodes) CRCD ForcingChains
l 8.9 Dynamic (13-16 nodes) CRCDForcing Chains
l 9.0 Dynamic (17-24 nodes) CRCDForcing Chains
l 9.1 Dynamic (25-36 nodes) CRCDForcing Chains
l 9.2 Dynamic (37-48 nodes) CRCDForcing Chains
l 9.3 Dynamic (49-72 nodes) CRCDForcing Chains
l 9.4 Dynamic (73-96 nodes) CRCDForcing Chains
l 9.3 Dynamic + (9-12 nodes) CRCDForcing Chains
l 9.4 Dynamic + (13-16 nodes) CRCDForcing Chains
l 9.5 Dynamic + (17-24 nodes) CRCDForcing Chains
l 9.6 Dynamic + (25-36 nodes) CRCDForcing Chains
l 9.7 Dynamic + (37-48 nodes) CRCD ForcingChains
l 9.8 Dynamic + (49-72 nodes) CRCDForcing Chains
l 9.9 Dynamic + (73-96 nodes) CRCDForcing Chains
l 10.0 Dynamic + (97-144 nodes) CRCDForcing Chains
l 10.1 Dynamic + (145-192 nodes) CRCDForcing Chains
l 10.0 Dynamic + Forcing Chains (17-24nodes) CRCD Forcing Chains
l 10.1 Dynamic + Forcing Chains (25-36nodes) CRCD Forcing Chains
l 10.2 Dynamic + Forcing Chains (37-48nodes) CRCD Forcing Chains
l 10.3 Dynamic + Forcing Chains (49-72nodes) CRCD Forcing Chains
l 10.4 Dynamic + Forcing Chains (73-96 nodes)CRCD Forcing Chains
l 10.5 Dynamic + Forcing Chains (97-144nodes) CRCD Forcing Chains
l 10.6 Dynamic + Forcing Chains(145-192 nodes) CRCD Forcing Chains
l 10.7 Dynamic + Forcing Chains(193-288 nodes) CRCD Forcing Chains
l 10.8 Dynamic + Forcing Chains(289-384 nodes) CRCD Forcing Chains
l 10.9 Dynamic + Multiple ForcingChains (73-96 nodes) CRCD Forcing Chains
l 11.0 Dynamic + Multiple ForcingChains (97-144 nodes) CRCD Forcing Chains
l 11.1 Dynamic + Multiple ForcingChains (145-192 nodes) CRCD Forcing Chains
l 11.2 Dynamic + Multiple ForcingChains (193-288 nodes) CRCD Forcing Chains
l 11.3 Dynamic + Multiple ForcingChains (289-384 nodes) CRCD Forcing Chains
l 11.4 Dynamic + Multiple ForcingChains (385-576 nodes) CRCD Forcing Chains
l 11.4 Dynamic + Dynamic Forcing Chains(73-96 nodes) CRCD Forcing Chains
l 11.5 Dynamic + Dynamic Forcing Chains(97-144 nodes) CRCD Forcing Chains
l 11.6 Dynamic + Dynamic Forcing Chains(145-192 nodes) CRCD Forcing Chains
l 11.7 Dynamic + Dynamic Forcing Chains(193-288 nodes) CRCD Forcing Chains
l 11.8 Dynamic + Dynamic Forcing Chains(289-384 nodes) CRCD Forcing Chains
l 11.9 Dynamic + Dynamic Forcing Chains(385-576 nodes) CRCD Forcing Chains
l 12.0 Dynamic + Dynamic Forcing Chains(577-more nodes) CRCD Forcing Chains
这部分均来自SDRS。英语并没有翻译成中文。目前仅作参考。
另外,在SDRS里,还有一些定义。
魔术格(Magic Cell):
魔术格是指,当前数独盘面中,一旦得出某一个位置上的数值后,全盘立马变为非常简单的题目,那么这个位置被称为魔术格。但要注意的是,魔术格不是每一个数独盘面都存在的,而且,即使有魔术格,但也不一定是“单阶魔术格”(详细内容请参考下面对“阶魔术格”的定义)。也就是说,有一些数独盘面存在魔术格,但也不能一气呵成,还必须进行数次猜解才能够完成整个题目。通常来说,魔术格本身是不可能看出来的,只能靠运气,而且您可能需要买彩票的那种运气才能够猜对。
阶魔术格:
魔术格很多时候都是不能完成全盘的,但有一些神奇的魔术格,可以把当前可能相对较难的题目变成一个相对简单的题目,但只能完成一部分。这个时候就可能存在第二次的魔术格,此时称其为“二阶魔术格”,同理,可能还存在“三阶魔术格”。但请记住的是,所有题一定存在魔术格,在当前盘势若有单阶魔术格,则其魔术格可能不只一个。如果有三阶魔术格的话,如果还想着猜的话,绝对会痛不欲生。
精简题:
精简题是指,题目的所有提示数都不能缺少。任何一个提示数的缺少都能导致题目出现多解的情况。
珍珠系数(Pearl Rating,简称PR):
珍珠系数是指,题目第一步的难度系数,不管第一步是排除法还是候选数技巧。
钻石系数(Diamond Rating,简称DR):
钻石系数是指,题目中第一个出数的前一步的难度系数。也就是说,如果说,一个题目的第一个出数是靠X-Wing(二链列)出数的,那么PR=3.2。
珍珠题:
珍珠题是指,题目的第一步必须是候选数技巧,或者说,题目的第一步不能通过直接出数的形式直接得到。也就是说,珍珠系数必然会大于2.5(上述的表格已经给出了)。
极限珍珠题:
极限珍珠题是指,题目的第一个出数之前的那个候选数技巧,它的难度系数等于题目的难度系数的题。这个时候,SER=PR。
钻石题:
钻石题是指,题目第一步的难度系数等于题目难度系数的题。这个时候,SER=PR=DR。
(后续还会更新,希望大家前来阅读并且指正说法。)
2017年01月07日 14点01分
1
具体难度分析的方法如下:
将题目用带有难度系数评判的软件进行评测,每一步都以从低难度技巧到高难度技巧的过程搜索盘面内是否存在可用的情况,如果有,则使用掉它,并得到一个难度系数,然后进入第二步。从此我们可以看出,第一步取的是盘面内最小难度技巧的难度系数。同样,在第二步中,也按照第一步的过程获取最小的难度系数。最终,由软件获取到当前题目使用到的最难技巧,并以此技巧所对应的难度系数,作为整个题目的难度系数,此时称题目的难度为题目难度系数(SudokuExplainer Rating,SER或SR)。
具体的SE软件的技巧的难度参照表如下(左边是难度系数,右边是技巧名称):
l 1.0 Single
l 1.2 Hidden Single in box
l 1.5 Hidden Single in line
l 1.7 Direct Pointing
l 1.9 Direct Claiming
l 2.0 Direct Hidden Pair
l 2.3 Naked Single
l 2.5 Direct Hidden Triplet
l 2.6 Pointing
l 2.8 Claiming
l 3.0 Naked Pair
l 3.2 X-Wing
l 3.4 Hidden Pair
l 3.6 Naked Triplet
l 3.8 Swordfish
l 4.0 Hidden Triplet
l 4.2 XY-Wing
l 4.4 XYZ-Wing
l 4.4 W-Wing
l 4.5 UR Types 1, 2, 4
l 4.5 UR Type 3 with Hidden Pair
l 4.6 UR Type 3 with Naked Pair
l 4.6 UR Type 3 with Hidden Triplet
l 4.7 UR Type 3 with Naked Triplet
l 4.7 UR Type 3 with Hidden Quad
l 4.8 UR Type 3 with Naked Quad
l 4.6 UL Types 1, 2, 4 (6 cells)
l 4.7 UL Types 1, 2, 4 (8 cells)
l 4.8 UL Types 1, 2, 4 (10 cells)
l 4.9 UL Types 1, 2, 4 (12 cells)
l 5.0 UL Types 1, 2, 4 (14 cells)
l 5.1 UL Types 1, 2, 4 (16 cells)
l 4.6 UL Type 3 with Hidden Pair (6cells)
l 4.7 UL Type 3 with Hidden Pair (8cells)
l 4.7 UL Type 3 with Hidden Triplet (6cells)
l 4.8 UL Type 3 with Hidden Triplet (8cells)
l 4.8 UL Type 3 with Hidden Quad (6cells)
l 4.9 UL Type 3 with Hidden Quad (8cells)
l 4.7 UL Type 3 with Naked Pair (6cells)
l 4.8 UL Type 3 with Naked Pair (8cells)
l 4.9 UL Type 3 with Naked Pair (10cells)
l 5.0 UL Type 3 with Naked Pair (12cells)
l 4.8 UL Type 3 with Naked Triplet (6cells)
l 4.9 UL Type 3 with Naked Triplet (8cells)
l 4.9 UL Type 3 with Naked Quad (6cells)
l 5.0 UL Type 3 with Naked Quad (8cells)
l 5.0 Naked Quad
l 5.2 Jellyfish
l 5.4 Hidden Quad
l 5.6 Bivalue Universal Graves Type 1
l 5.7 Bivalue Universal Graves Type 2
l 5.7 Bivalue Universal Graves Type 4
l 5.8 Bivalue Universal Graves Type 3with Naked Pair
l 5.9 Bivalue Universal Graves Type 3with Naked Triplet
l 6.0 Bivalue Universal Graves Type 3with Naked Quad
l 6.1 Bivalue Universal Graves Type 3with Naked Quint
l 6.2 Aligned Pair Exclusion
l 6.5 Bidirectional X-Cycle (6 cells)
l 6.6 Bidirectional X-Cycle (8 cells)
l 6.6 Turbot Fish
l 6.6 Forcing X-chain (5-6 nodes)
l 6.7 Forcing X-Chain (7-8 nodes)
l 6.8 Forcing X-Chain (9-12 nodes)
l 6.9 Forcing X-Chain (13-16 nodes)
l 6.5 Bidirectional Y-cycle (3 cells)
l 6.6 Bidirectional Y-cycle (4 cells)
l 6.7 Bidirectional Y-cycle (5 cells)
l 6.8 Bidirectional Y-cycle (6-7 cells)
l 6.9 Bidirectional Y-cycle (8-9 cells)
l 7.0 Bidirectional Y-cycle (10-13cells)
l 7.0 Bidirectional Cycle (6 nodes)
l 7.1 Bidirectional Cycle (8 nodes)
l 7.2 Bidirectional Cycle (10 nodes)
l 7.3 Bidirectional Cycle (12 nodes)
l 7.0 Forcing Chain (5 nodes)
l 7.1 Forcing Chain (7 nodes)
l 7.2 Forcing Chain (9 nodes)
l 7.3 Forcing Chain (11-13 nodes)
l 7.4 Forcing Chain (15-17 nodes)
l 7.5 Forcing Chain (19-25 nodes)
l 7.6 Forcing Chain (27-more nodes)
l 7.5 Aligned Triplet Exclusion
l 7.6 Nishio Forcing Chain (5-6 nodes)
l 7.7 Nishio Forcing Chain (7-8 nodes)
l 7.8 Nishio Forcing Chain (9-12 nodes)
l 7.9 Nishio Forcing Chain (13-16nodes)
l 8.0 Nishio Forcing Chain (17-24nodes)
l 8.1 Nishio Forcing Chain (25-36nodes)
l 8.2 Multiple (7-8 nodes) RegionForcing Chains
l 8.3 Multiple (9-12 nodes) Cell/RegionForcing Chains
l 8.4 Multiple (13-16 nodes)Cell/Region Forcing Chains
l 8.5 Multiple (17-24 nodes)Cell/Region Forcing Chains
l 8.6 Multiple (25-36 nodes)Cell/Region Forcing Chains
l 8.6 Dynamic (5-6 nodes) Cell/RegionForcing Chains
l 8.7 Dynamic (7-8 nodes) Cell/RegionForcing Chains
l 8.8 Dynamic (9-12 nodes) CRCD ForcingChains
l 8.9 Dynamic (13-16 nodes) CRCDForcing Chains
l 9.0 Dynamic (17-24 nodes) CRCDForcing Chains
l 9.1 Dynamic (25-36 nodes) CRCDForcing Chains
l 9.2 Dynamic (37-48 nodes) CRCDForcing Chains
l 9.3 Dynamic (49-72 nodes) CRCDForcing Chains
l 9.4 Dynamic (73-96 nodes) CRCDForcing Chains
l 9.3 Dynamic + (9-12 nodes) CRCDForcing Chains
l 9.4 Dynamic + (13-16 nodes) CRCDForcing Chains
l 9.5 Dynamic + (17-24 nodes) CRCDForcing Chains
l 9.6 Dynamic + (25-36 nodes) CRCDForcing Chains
l 9.7 Dynamic + (37-48 nodes) CRCD ForcingChains
l 9.8 Dynamic + (49-72 nodes) CRCDForcing Chains
l 9.9 Dynamic + (73-96 nodes) CRCDForcing Chains
l 10.0 Dynamic + (97-144 nodes) CRCDForcing Chains
l 10.1 Dynamic + (145-192 nodes) CRCDForcing Chains
l 10.0 Dynamic + Forcing Chains (17-24nodes) CRCD Forcing Chains
l 10.1 Dynamic + Forcing Chains (25-36nodes) CRCD Forcing Chains
l 10.2 Dynamic + Forcing Chains (37-48nodes) CRCD Forcing Chains
l 10.3 Dynamic + Forcing Chains (49-72nodes) CRCD Forcing Chains
l 10.4 Dynamic + Forcing Chains (73-96 nodes)CRCD Forcing Chains
l 10.5 Dynamic + Forcing Chains (97-144nodes) CRCD Forcing Chains
l 10.6 Dynamic + Forcing Chains(145-192 nodes) CRCD Forcing Chains
l 10.7 Dynamic + Forcing Chains(193-288 nodes) CRCD Forcing Chains
l 10.8 Dynamic + Forcing Chains(289-384 nodes) CRCD Forcing Chains
l 10.9 Dynamic + Multiple ForcingChains (73-96 nodes) CRCD Forcing Chains
l 11.0 Dynamic + Multiple ForcingChains (97-144 nodes) CRCD Forcing Chains
l 11.1 Dynamic + Multiple ForcingChains (145-192 nodes) CRCD Forcing Chains
l 11.2 Dynamic + Multiple ForcingChains (193-288 nodes) CRCD Forcing Chains
l 11.3 Dynamic + Multiple ForcingChains (289-384 nodes) CRCD Forcing Chains
l 11.4 Dynamic + Multiple ForcingChains (385-576 nodes) CRCD Forcing Chains
l 11.4 Dynamic + Dynamic Forcing Chains(73-96 nodes) CRCD Forcing Chains
l 11.5 Dynamic + Dynamic Forcing Chains(97-144 nodes) CRCD Forcing Chains
l 11.6 Dynamic + Dynamic Forcing Chains(145-192 nodes) CRCD Forcing Chains
l 11.7 Dynamic + Dynamic Forcing Chains(193-288 nodes) CRCD Forcing Chains
l 11.8 Dynamic + Dynamic Forcing Chains(289-384 nodes) CRCD Forcing Chains
l 11.9 Dynamic + Dynamic Forcing Chains(385-576 nodes) CRCD Forcing Chains
l 12.0 Dynamic + Dynamic Forcing Chains(577-more nodes) CRCD Forcing Chains
这部分均来自SDRS。英语并没有翻译成中文。目前仅作参考。
另外,在SDRS里,还有一些定义。
魔术格(Magic Cell):
魔术格是指,当前数独盘面中,一旦得出某一个位置上的数值后,全盘立马变为非常简单的题目,那么这个位置被称为魔术格。但要注意的是,魔术格不是每一个数独盘面都存在的,而且,即使有魔术格,但也不一定是“单阶魔术格”(详细内容请参考下面对“阶魔术格”的定义)。也就是说,有一些数独盘面存在魔术格,但也不能一气呵成,还必须进行数次猜解才能够完成整个题目。通常来说,魔术格本身是不可能看出来的,只能靠运气,而且您可能需要买彩票的那种运气才能够猜对。
阶魔术格:
魔术格很多时候都是不能完成全盘的,但有一些神奇的魔术格,可以把当前可能相对较难的题目变成一个相对简单的题目,但只能完成一部分。这个时候就可能存在第二次的魔术格,此时称其为“二阶魔术格”,同理,可能还存在“三阶魔术格”。但请记住的是,所有题一定存在魔术格,在当前盘势若有单阶魔术格,则其魔术格可能不只一个。如果有三阶魔术格的话,如果还想着猜的话,绝对会痛不欲生。
精简题:
精简题是指,题目的所有提示数都不能缺少。任何一个提示数的缺少都能导致题目出现多解的情况。
珍珠系数(Pearl Rating,简称PR):
珍珠系数是指,题目第一步的难度系数,不管第一步是排除法还是候选数技巧。
钻石系数(Diamond Rating,简称DR):
钻石系数是指,题目中第一个出数的前一步的难度系数。也就是说,如果说,一个题目的第一个出数是靠X-Wing(二链列)出数的,那么PR=3.2。
珍珠题:
珍珠题是指,题目的第一步必须是候选数技巧,或者说,题目的第一步不能通过直接出数的形式直接得到。也就是说,珍珠系数必然会大于2.5(上述的表格已经给出了)。
极限珍珠题:
极限珍珠题是指,题目的第一个出数之前的那个候选数技巧,它的难度系数等于题目的难度系数的题。这个时候,SER=PR。
钻石题:
钻石题是指,题目第一步的难度系数等于题目难度系数的题。这个时候,SER=PR=DR。
(后续还会更新,希望大家前来阅读并且指正说法。)