Go implementation of Donald Knuth's Algorithm 7.2.2.1M for covering with multiplicities and colors. This implementation is based on the Algorithm M described in https://www-cs-faculty.stanford.edu/~knuth/fasc5c.ps.gz
package main
import (
"context"
"fmt"
"strings"
"time"
"github.com/sjnam/dlx"
)
func main() {
input := `
| A simple example of color controls
A B 2:3|C | X Y
A B X:0 Y:0
A C X:1 Y:1
C X:0
B X:1
C Y:1
`
mcc := dlx.NewMCC()
mcc.Debug = true
res := mcc.Dance(strings.NewReader(input))
for sol := range res.Solutions {
for _, opt := range sol {
fmt.Println(opt)
}
}
}
// (5 options, 3+2 items, 19 entries successfully read)
// [B X:1]
// [A C X:1 Y:1]
// [C Y:1]
// [null C]
// Altogether 1 solution 19 updates, 4 cleansings, 6 nodes.$ cd examples/langford
$ go run main.go 4
[2 3 4 2 1 3 1 4]
- 12 pieces: O P Q R S T U V W X Y Z
$ cd example/pentominoes
$ go run main.go 8x8.dlx
Solution: 1
P P P W U U U Y
P P W W U T U Y
Z W W T T T Y Y
Z Z Z T X Y
R R Z X X X
V R R S S S X Q
V R S S Q Q Q Q
V V V O O O O O
Solution: 2
W P P P U U U Y
W W P P U T U Y
Z W W T T T Y Y
Z Z Z T X Y
R R Z X X X
V R R S S S X Q
V R S S Q Q Q Q
V V V O O O O O
Solution: 3
V V V Z W W Q Q
V Z Z Z R W W Q
V Z P R R R W Q
O P P R X Q
O P P X X X
O U U S S S X T
O U S S Y T T T
O U U Y Y Y Y T
...
$ go run examples/queen/main.go 8
1:
Q . . . . . . .
. . . . . Q . .
. . . . . . . Q
. . Q . . . . .
. . . . . . Q .
. . . Q . . . .
. Q . . . . . .
. . . . Q . . .
2:
Q . . . . . . .
. . . . Q . . .
. . . . . . . Q
. . . . . Q . .
. . Q . . . . .
. . . . . . Q .
. Q . . . . . .
. . . Q . . . .
...
$ cd examples/sudoku
$ go run main.go puzzles.txt
Q[ 1]: ..43..2.9..5..9..1.7..6..43..6..2.8719...74...5..83...6.....1.5..35.869..4291.3..
A[ 1]: 864371259325849761971265843436192587198657432257483916689734125713528694542916378
Q[ 2]: .4.1...5.1.7..396.52...8..........17...9.68..8.3.5.62..9..6.5436...8.7..25..971..
A[ 2]: 346179258187523964529648371965832417472916835813754629798261543631485792254397186
Q[ 3]: 6..12.384..8459.72.....6..5...264.3..7..8...694...3...31.....5..897.....5.2...19.
A[ 3]: 695127384138459672724836915851264739273981546946573821317692458489715263562348197
Q[ 4]: 4972.....1..4....5....16.9862.3...4.3..9.......1.726....2..587....6....453..97.61
A[ 4]: 497258316186439725253716498629381547375964182841572639962145873718623954534897261
Q[ 5]: ..591.3.8..94.3.6..275..1...3....2.1...82...7..6..7..4....8....64.15.7..89....42.
A[ 5]: 465912378189473562327568149738645291954821637216397854573284916642159783891736425
...
Q[70098]: ..2.....9.3...25....61..37..........2..4..13...7..6.4...18.....76...54....9..76..
A[70098]: 472653819138792564956148372694531287285479136317286945521864793763915428849327651
Q[70099]: .3............1..87..58........24.5..4.8739....36.....9.......2..5..2.912.....7.4
A[70099]: 438297165659431278721586349167924853542873916893615427974168532385742691216359784
Solving took: 8.01462075s
$ cd examples/filomino
| ..3.3...3.
| ..131...43
| 64...141..
| .6...4.4..
| 64...141..
| ..434...12
| ..3.3...2.
| ..434...12
| 24...161..
| .2...6.6..
$ go run main.go 10x10.filomino.dlx
3 3 3 1 3 3 2 2 3 3
4 4 1 3 1 3 4 4 4 3
6 4 4 3 3 1 4 1 2 2
6 6 6 6 4 4 1 4 4 4
6 4 3 3 4 1 4 1 4 2
4 4 4 3 4 3 4 4 1 2
3 3 3 1 3 3 4 2 2 1
2 4 4 3 4 4 6 6 1 2
2 4 4 3 4 1 6 1 3 2
1 2 2 3 4 6 6 6 3 3
What is Word search? https://thewordsearch.com/
$ cd examples/wordsearch
$ go run main.go movie.txt 13 13
봄게하대위게하밀은마기생충
돼여힘다장시제국설국열차타
지변름의인여의변해밀양며신
가명호가도봄날은간다리생과
우량장인을원엽가더날파활함
물생화파괴겨강기휘마이의께
에인홍물밤골울기적올란발죄
빠한련과막것극그친인드견와
진콤낮동의태아구리씨그보벌
날달투나택시운전사고가녀이
다컴는억추의인살박쥐봄아카
웰수다오수정씨자금한절친바
복스시아오하행산부적의공공
$ go run main.go mathematicians.txt 15 15
H I L B E R T L C A N T O R O
X O L F W Q F F O H H C R I K
G T C A T A L A N R E T S D O
C T Q S M I N K O W S K I R T
G E S Y L V E S T E R V R A M
F N A W N O R R E P Y K T M E
S I A B E L U A D N A L V A L
J T W E I E R S T R A S S D L
S U I Z T I W R U H L X C A I
U D Z E C R E H S I A L G H N
B O R E L W D N A R T R E B X
D G R A M T S U I N E B O R F
R U N G E O J J E N S E N C X
F F O K R A M E E T I M R E H
E K N O P P L E S N E H X S N
Five people, from five different countries, have five different occupations, own five different pets, drink five different beverages, and live in a row of five different colored houses.
- The Englishman lives in a red house.
- The painter comes from Japan.
- The yellow house hosts a diplomat.
- The coffee-lover's house is green.
- The Norwegian's house is hte leftmost.
- The dog's owner is from Spain.
- The milk drinker lives in the middle house.
- The violinist drinks orange juice.
- The white house is just left of the green one.
- The Ukrainian drinks tea.
- The Norwegian lives next to the blue house.
- The sculptor breeds snails.
- The horse lives next to the diplomat.
- The nurse lives next to the fox.
Who trains the zebra, and who prefers to drink just plain water?
$ go run examples/zebra/main.go
Norway Ukraine England Spain Japan
diplomat nurse sculptor violinist painter
fox horse snail dog zebra
water tea milk orange coffee
yellow blue red white green
$ go run example/partridge/main.go
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟪🟪🟪🟪🟫🟫🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟪🟪🟪🟪🟫🟫🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟪🟪🟪🟪🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟪🟪🟪🟪🟧🟧🟧🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟪🟪🟪🟪🟧🟧🟧🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟪🟪🟪🟪🟧🟧🟧🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟪🟪🟪🟪⬛🟨🟨🟨🟨🟨🟨🟨
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨
🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨
🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨
🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟩🟩🟨🟨🟨🟨🟨🟨🟨
🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟩🟩🟪🟪🟪🟪🟧🟧🟧
🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟩🟩🟪🟪🟪🟪🟧🟧🟧
🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟩🟩🟪🟪🟪🟪🟧🟧🟧
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟩🟩🟩🟩🟩🟪🟪🟪🟪🟧🟧🟧
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟫🟫🟧🟧🟧
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟫🟫🟧🟧🟧
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩
🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩