sudoku.jl

### A Pluto.jl notebook ###
# v0.19.41

using Markdown
using InteractiveUtils

# ╔═╡ 0165319a-0082-11ef-3870-c156b946632d
using JuMP, CBLS

# ╔═╡ b96edc11-a727-45a8-83ae-d297efe24c8b
md"""
# Getting started with Constraint Programming!

This series of tutorial notebooks will bring you through the basic steps to formulate your problem as Constraint Programming Models.

In most of this tutorial, we will use CP solvers with an interface with the JuMP modeling language. We will rely mainly on the Constraint-based Local Search solver (*CBLS.jl*).
"""

# ╔═╡ f3cf35b7-3768-4e81-960b-0de664f11bbb
md"""
We will start with a simple puzzle game and some of its not that simple variants: the Sudoku.

(*From Wikipedia*)In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contains all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.

Thanks to TODO(cite correct contributor), we got a Sudoku pretty print in *ConstraintModels.jl*.
"""

# ╔═╡ f1469f7b-7015-44e6-9d65-6e20c3b6060f


# ╔═╡ 941b4622-f1d6-45ef-a278-1a774cbeb5be
md"""
Constraint Programming follows the *model-and-solve* approach. We first need to model our Sudoku problem. For this tutorial we use the JuMP modeling language with the CBLS solver.
"""

# ╔═╡ 3e44aa50-2bdb-4ae4-9f49-c5e48b5ee86a
m = JuMP.Model(CBLS.Optimizer)

# ╔═╡ 9ed0dc54-6193-4533-9b14-3e6436148f96
md"""
We can use the output of JuMP models to track the progress we make on our model by symply calling `m`.
"""

# ╔═╡ d07690f7-6e64-4ff3-af7f-54a89d3fda86
md"""
But what are the basis of CP models? It is quite simple:
1. A collection of variables X1,...,Xn = X with their domain
"""

# ╔═╡ 0bd29769-32e6-4e74-8b94-509b650651ed
@variable(m, 1 ≤ X[1:9, 1:9] ≤ 9, Int)

# ╔═╡ e4fc6f6b-2818-4cb4-a425-67f0bd49d3d5
m

# ╔═╡ 5df218df-b615-47eb-88bc-8b17a38e5cd9
md"""
We can see that we added, for each variable, 3 constraints. All 3 constraints are used to define the variable domain (here integer values within [1, 9]).

2. A collection of predicates, called constraints C1,...,Cn = C, over (subsets of) these variables

When modeling problems as CP, one might define and use their own predicates. However, a large collection of already defined constraints exists. One, if not the most, iconic global constraint is called AllDifferent. It ensures that all variables take distinct values.

Sudoku puzzles can be define using only this one constraint applied to different subsets of variables.
"""

# ╔═╡ 009c7898-d203-475a-b005-71ab92ecd7eb
for i in 1:9
        @constraint(m, X[i,:] in AllDifferent()) # rows
        @constraint(m, X[:,i] in AllDifferent()) # columns
end

# ╔═╡ 76cbf784-df24-4e38-a71e-38618e235ddc
m

# ╔═╡ a1d3e36c-0151-4e35-83b6-c9b801194178
md"""
We added 18 AllDifferent constraints, one for each column and row.

The last series of AllDifferent constraint is less straight forward. Nonetheless, the JuMP syntax allows us to work on a grid which alleviates its formulation. We need to ensure that each 3 × 3 subgrid (blocks) is filled with distinct values.
"""

# ╔═╡ 6d9e9d0d-f95b-4965-97cc-fc2eaae81c49
for i in 0:2, j in 0:2 # blocks
	@constraint(
		m,
		vec(X[(3i+1):(3(i+1)), (3j+1):(3(j+1))]) in AllDifferent(),
	) 
end

# ╔═╡ 94e11c4a-c558-47a8-8635-c1da1c4187c1
m

# ╔═╡ 96ce8df9-6316-4cfb-891d-7db10f2655fd
md"""
Finally, we added 9 AllDifferent constraints, one per block. Time to solve this model.
"""

# ╔═╡ f9a7ec2f-420e-4381-9b2b-101713ce0f93
optimize!(m)

# ╔═╡ 181d3e56-d645-448d-856a-8845c0fa17d8
md"""
Note that this is heuristic solver, we might not get a feasible solution! Let's check it out.

The `value` function print the value of a JuMP variable. We can cast it over a collection with the `value.` syntax.
"""

# ╔═╡ b88c5166-f333-4ff5-9b99-b1b6db779e29
value.(X)

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[[deps.Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[deps.Mocking]]
deps = ["Compat", "ExprTools"]
git-tree-sha1 = "4cc0c5a83933648b615c36c2b956d94fda70641e"
uuid = "78c3b35d-d492-501b-9361-3d52fe80e533"
version = "0.7.7"

[[deps.MozillaCACerts_jll]]
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version = "2023.1.10"

[[deps.MutableArithmetics]]
deps = ["LinearAlgebra", "SparseArrays", "Test"]
git-tree-sha1 = "c2e2d748aea87f006a87c1654878349baa04aaf0"
uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
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[[deps.NaNMath]]
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git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "1.0.2"

[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"

[[deps.OpenBLAS_jll]]
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uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.23+4"

[[deps.OpenLibm_jll]]
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uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.1+2"

[[deps.OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[deps.OrderedCollections]]
git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.6.3"

[[deps.Parsers]]
deps = ["Dates", "PrecompileTools", "UUIDs"]
git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.8.1"

[[deps.PatternFolds]]
deps = ["Intervals", "Lazy", "Random", "Reexport", "TestItemRunner", "TestItems"]
git-tree-sha1 = "d5ed514afa73b41c52a91bfb79f05da2d830fff4"
uuid = "c18a7f1d-76ad-4ce4-950d-5419b888513b"
version = "0.2.3"

[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.10.0"

[[deps.PooledArrays]]
deps = ["DataAPI", "Future"]
git-tree-sha1 = "36d8b4b899628fb92c2749eb488d884a926614d3"
uuid = "2dfb63ee-cc39-5dd5-95bd-886bf059d720"
version = "1.4.3"

[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.2.1"

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.4.3"

[[deps.PrettyTables]]
deps = ["Crayons", "LaTeXStrings", "Markdown", "PrecompileTools", "Printf", "Reexport", "StringManipulation", "Tables"]
git-tree-sha1 = "88b895d13d53b5577fd53379d913b9ab9ac82660"
uuid = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
version = "2.3.1"

[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[deps.Profile]]
deps = ["Printf"]
uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"

[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[deps.Random]]
deps = ["SHA"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[deps.RecipesBase]]
deps = ["PrecompileTools"]
git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.3.4"

[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.2.1"

[[deps.SentinelArrays]]
deps = ["Dates", "Random"]
git-tree-sha1 = "0e7508ff27ba32f26cd459474ca2ede1bc10991f"
uuid = "91c51154-3ec4-41a3-a24f-3f23e20d615c"
version = "1.4.1"

[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "66e0a8e672a0bdfca2c3f5937efb8538b9ddc085"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.2.1"

[[deps.SparseArrays]]
deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
version = "1.10.0"

[[deps.SpecialFunctions]]
deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "e2cfc4012a19088254b3950b85c3c1d8882d864d"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.3.1"

    [deps.SpecialFunctions.extensions]
    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"

    [deps.SpecialFunctions.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"

[[deps.StaticArraysCore]]
git-tree-sha1 = "36b3d696ce6366023a0ea192b4cd442268995a0d"
uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
version = "1.4.2"

[[deps.Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.10.0"

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.7.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "5cf7606d6cef84b543b483848d4ae08ad9832b21"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.34.3"

[[deps.StringManipulation]]
deps = ["PrecompileTools"]
git-tree-sha1 = "a04cabe79c5f01f4d723cc6704070ada0b9d46d5"
uuid = "892a3eda-7b42-436c-8928-eab12a02cf0e"
version = "0.3.4"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "7.2.1+1"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.3"

[[deps.TZJData]]
deps = ["Artifacts"]
git-tree-sha1 = "1607ad46cf8d642aa779a1d45af1c8620dbf6915"
uuid = "dc5dba14-91b3-4cab-a142-028a31da12f7"
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[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
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[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "OrderedCollections", "TableTraits"]
git-tree-sha1 = "cb76cf677714c095e535e3501ac7954732aeea2d"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.11.1"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.TestItemRunner]]
deps = ["Pkg", "TOML", "Test", "TestItems", "UUIDs"]
git-tree-sha1 = "cb2b53fd36a8fe20c0b9f55da6244eb4818779f5"
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version = "0.2.3"

[[deps.TestItems]]
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uuid = "1c621080-faea-4a02-84b6-bbd5e436b8fe"
version = "0.1.1"

[[deps.ThreadSafeDicts]]
git-tree-sha1 = "300b753c0a786ea43fdafc26a4e50b87fb58cd50"
uuid = "4239201d-c60e-5e0a-9702-85d713665ba7"
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[[deps.TimeZones]]
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git-tree-sha1 = "cc54d5c9803309474014a8955a96e4adcd11bcf4"
uuid = "f269a46b-ccf7-5d73-abea-4c690281aa53"
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weakdeps = ["RecipesBase"]

    [deps.TimeZones.extensions]
    TimeZonesRecipesBaseExt = "RecipesBase"

[[deps.Tokenize]]
git-tree-sha1 = "5b5a892ba7704c0977013bd0f9c30f5d962181e0"
uuid = "0796e94c-ce3b-5d07-9a54-7f471281c624"
version = "0.5.28"

[[deps.TranscodingStreams]]
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weakdeps = ["Random", "Test"]

    [deps.TranscodingStreams.extensions]
    TestExt = ["Test", "Random"]

[[deps.URIs]]
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[[deps.UUIDs]]
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uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.Unrolled]]
deps = ["MacroTools"]
git-tree-sha1 = "6cc9d682755680e0f0be87c56392b7651efc2c7b"
uuid = "9602ed7d-8fef-5bc8-8597-8f21381861e8"
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[[deps.Zlib_jll]]
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version = "1.2.13+1"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+1"

[[deps.nghttp2_jll]]
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uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"

[[deps.p7zip_jll]]
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uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"
"""

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