SueDeCoq

SueDeCoq is an analysis algorithm derived from the handle name "SueDeCoq" which first proposed this method. In order to understand SueDeCoq algorithm, some leap is necessary. Explain step by step using examples.
Many of the explanations here are based on the following HP.
http://hodoku.sourceforge.net/en/tech_misc.php#sdc

The following example is a basic SueDeCoq. In the left figure,
(1)Focus on r2c46 in block 2. There are four candidate numbers #1789 in these two cells, and candidate number # 78 is in r1c5 of the same block. Considering these three cells together, #19(78) is entered into the two cells of r2c46 (r2c46 is only one of #78 and not both).

(2)Considering the second line, since r2c9 has candidate number #19, #(19)78 will be included in 2 cells of r2C46 (r2c46 is only one of #19 and not both ).

When (1) and (2) are combined, #(19)(78) will be included in r2c46, and r2c46 is Locked of 2 numbers in 2 cells. However, one of the two number pairs is not decided.

In this state, #1 of r2c3 on the second is false because it breaks the Locked of the cell R2C46 in relation to r2c9 (the number entering r2c46 is insufficient). Likewise, #8 of r1c4 in block 2 breaks Locked of the cells r2c46 in relation to r1c5, so it can not be inserted (r1c4=#8 is false).

In the figure on the right, Focus on r3c123 in block 1. There are five candidate #12456 in these three cells. Considering the same as the left figure, r3c123 is Locked at #6(15)(24) (3 numbers for 3 cells). Therefore #24 of r3c67 breaks this Locked state(not enough numbers to enter r3c123), so it can be excluded from candidate numbers.

SueDeCoq (ALS Level-1)
ALS(block) : r13c3 r3c12 #12456
ALS(row) : r3c1238 #12456)

.2...3..4.4....25.6...243.8256..8....8..9..2....2..4868.463...2.63....4.9..7...6.
87........9.81.65....79...8.....67316..5.1..97124.....3...57....57.48.1........74

With reference to the concrete example above, Locked of SueDeCoq is defined. The following figure shows the configuration of the cell group appearing here.
(1)There is a cell group(ISPB) in the block and a cell group(ISPR) in the row (or column).
(2)The two cell groups are divided into a common part(IS) and other parts(PB and PR).
(3)The candidate digits of the disassembled cell group are IS_FreeB, PB_FreeB, PR_FreeB.
(4)PB_FreeBn, PR_FreeBn are candidate numbers of non-common parts (PB and PR).
(PB_FreeBn = PB_FreeB\IS_FreeB, PR_FreeBn = PR_FreeB\IS_FreeB \:Difference set)
(5)N is the number of candidate numbers in only the other part. (N=|PB_FreeBn|+|PR_FreeBn|)

Using these definitions, the analysis algorithm of SueDeCoq is

[1]In order for SueDeCoq to be established, Locked must be established first.

1. The number of cells of the common part IS is 2 or 3.
2. The other parts (PB, PR) are not empty.
3. There is no common candidate for common part and other parts (PB and PR).
4. |IS| = |IS_FreeB| - (|PB|+|PR|-N） (|A| is the number of elements of set A）

In the first example, it is as follows.
・There are 4 candidate numbers for the cells(=2) in the common part.
・In the cell outside the block, there are two same candidate numbers as the common part, and one candidate of the common part is restricted.
・Similarly, the cells in the block limit one of the candidate numbers of the common part.
・Other parts There are no unique candidate numbers for rows and blocks(N=0).
Therefore, the condition("2=4-1-1 + 0") is established and is Locked.

Here is an example of SueDeCoq with many cells.