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16 Queens Problem - trial 1

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16 QUEENS PROBLEM USING CSP – I K. INIYA III CSE SRI VIDYA COLLEGE OF ENGINEERING AND TECHNOLOGY, VIRUDHUNAGAR
Transcript
Page 1: 16 Queens Problem - trial 1

16 QUEENS PROBLEM USING CSP – I K. INIYA

III CSESRI VIDYA COLLEGE OF ENGINEERING AND

TECHNOLOGY, VIRUDHUNAGAR

Page 2: 16 Queens Problem - trial 1

The Queen can move any number of vacant squares diagonally, horizontally and vertically.

RULES:

Page 3: 16 Queens Problem - trial 1

Place 16 Queen’s in 16X16 Chess Board with no interaction between other Queen’s.

Use Constraint Satisfaction Problems (CSPs) Concept to Solve this Problem.

CONT.,

Page 4: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

16X16 CHESS BOARD

PLEASE HELP ME TO FIND

THE RIGHT

SOLUTION

Page 5: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

CONSTRAINTS

Page 6: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE 1ST QUEEN IN (1,1)

Page 7: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{2,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}{2,3,5,6,7,8,9,10,11,12,13

, 14,15,16

}{2,3,4,6,7,8,9,10,11,12,13

, 14,15,16

}{2,3,4,5,7,8,9,10,11,12,13

, 14,15,16

}{2,3,4,5,6,8,9,10,11,12,13

, 14,15,16

}

{2,3,4,5,6,7,9,10,11,12,13

, 14,15,16

}

{2,3,4,5,6,7,8,10,11,12,13

, 14,15,16

}

{2,3,4,5,6,7,8,9,11,12,13, 14,15,16

}

{2,3,4,5,6,7,8,9,1

0, 11,12,14,15,16}

{2,3,4,5,6,7,8,9,10, 11,13, 14,15,16

}{2,3,4,5,6,7,8,9,10, 11,13, 14,15,16

}

{2,3,4,5,6,7,8,9,1

0, 11,12,13, 15,16}

{2,3,4,5,6,7,8,9,1

0, 11,12,13, 14,16}

{2,3,4,5,6,7,8,9,10,11,12,

13, 14,15}

TRIAL 1:PLACE 1ST QUEEN IN (1,1)

Page 8: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE2N

D QUEEN IN(2,3)

Page 9: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{5,6,7,8,9,10,11,12,13,

14,15,16} {2,6,7,8,

9,10,11,12,13,

14,15,16}

{2,4,7,8,9,10,11,12,13,

14,15,16}

{2,4,5,8,9,10,11,12,13,

14,15,16}

{2,4,5,6,9,10,11,12,13,

14,15,16}

{2,4,5,6,7,10,11,12,13,

14,15,16}

{2,4,5,6,7,8,11,1

2,13, 14,15,16

}

{2,4,5,6,7,8,9,12,

13, 14,15,16

}

{2,4,5,6,7,8,9,10, 11,12,15

,16}

{2,4,5,6,7,8,9,10,

11, 14,15,16

}{2,4,5,6,7,8,9,10,

13, 14,15,16

}

{2,4,5,6,7,8,9,10,

11,12, 13,16}

{2,4,5,6,7,8,9,10, 11,12,13

, 14}

{2,4,5,6,7,8,9,10,11,12,13, 14,15}

TRIAL 1:PLACE2N

D QUEEN IN(2,3)

Page 10: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE 3RD QUEEN IN(3,5)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Page 11: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{5,6,7,8,9,10,11,12,13,

14,15,16} {2,7,8,9,

10,11,12,13,

14,15,16}

{2,4,8,9, 10,11,12

,13, 14,15,16

}

{4,9,10,11,12,13

, 14,15,16

}{2,4,6,10,11,12,

13, 14,15,16

}{2,4,6,7, 11,12,13

, 14,15,16

}

{2,4,6,7,8, 12,13, 14,15,16

}

{2,4,6,7,8,9,13,

14,15,16}

{2,4,6,7,8,9,10,

11,12,16}

{2,4,6,7,8,9,10,

11,15,16}

{2,4,6,7,8,9,10,1

4, 15,16}

{2,4,6,7,8,9,10, 11,12}

{2,4,6,7,8,9,10,

11,12,13, 14}

{2,4,6,7,8,9,10,11,12,13, 14,15}

TRIAL 1:PLACE 3RD QUEEN IN(3,5)

Page 12: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE 4TH QUEEN IN(4,7)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Page 13: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{5,6,7,8,9,10,11,12,13,

14,15,16} {2,7,8,9,

10,11,12,13,

14,15,16}

{2,4,9, 10,11,12

,13, 14,15,16

}

{4,10,11, 12,13, 14,15,16

}

{2,6,11,12,13,

14,15,16}{2,4,6,1

2,13, 14,15,16

}

{4,6,8,13,

14,15,16}

{2,4,6,8,9,14,15,

16}

{2,4,6,8,9,10,

11,12}

{2,4,6,8,9,10,

11,16}

{2,4,6,8,9,10,

15,16}

{2,4,6,8,9,10,

11,12,13}

{2,4,6,8,9,10,

11,12,13,14}

{2,4,6,8,9,10,11,12,13, 14,15}

TRIAL 1:PLACE 4TH QUEEN IN(4,7)

Page 14: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE 5TH QUEEN IN(5,9)

Page 15: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{5,6,7,8,9,10,11,12,13,

14,15,16} {2,7,8,9,

10,11,12,13,

14,15,16}

{2,4,9, 10,11,12

,13, 14,15,16

}

{4,11, 12,13,

14,15,16}

{2,6,12, 13,

14,15,16}{2,4,13,

14,15,16}

{4,6,8, 14,15,16

}

{2,6,8,15,16}

{2,4,6,8,10,

11,12}

{4,6,8,10, 11}

{2,4,6,8, 10,16}

{2,4,6,8, 10,

11,12,13}

{2,4,6,8, 10,

11,12,13,14}

{2,4,6,8, 10,11,12

,13, 14,15}

TRIAL 1:PLACE 5TH QUEEN IN(5,9)

Page 16: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE 6TH QUEEN IN(6,11)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Page 17: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{5,6,7,8,9,10,11,12,13,

14,15,16} {2,7,8,9,

10,11,12,13,

14,15,16}

{2,4,9, 10,11,12

,13, 14,15,16

}

{4,11, 12,13,

14,15,16}

{2,6,13, 14,15,16

}

{2,4,14,15,16}{4,6,15,

16}

{2,6,8,16}

{2,6,8,10,12}

{4,6,8,10 }

{2,4,8, 10}

{2,4,6,8, 10,

12,13}

{4,6,8, 10,

12,13,14}

{2,4,6,8, 10,12,13, 14,15}

TRIAL 1:PLACE 6TH QUEEN IN(6,11)

Page 18: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE 7TH QUEEN IN(7,13)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Page 19: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{5,6,7,8,9,10,11,12,13,

14,15,16} {2,7,8,9,

10,11,12,13,

14,15,16}

{2,4,9, 10,11,12

,13, 14,15,16

}

{4,11, 12,13,

14,15,16}

{2,6,13, 14,15,16

}

{2,4, 15,16}{4,6,

16}

{2,6,8}

{2,6,8,10,12}

{4,6,10 }

{2,4,8, 10}

{2,4,8, 10, 12}

{4,6,8, 10,

12,14}

{2,6,8, 10,12, 14,15}

TRIAL 1:PLACE 7TH QUEEN IN(7,13)

Page 20: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE 8TH QUEEN IN(8,15)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Page 21: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{5,6,7,8,9,10,11,12,13,

14,15,16} {2,7,8,9,

10,11,12,13,

14,15,16}

{2,4,9, 10,11,12

,13, 14,15,16

}

{4,11, 12,13,

14,15,16}

{2,6,13, 14,15,16

}

{2,4, 15,16}

{4,6}

{2,6,8}

{2,6,8,12}

{4,6,10 }

{2,4,8, 10}

{2,4,8, 10, 12}

{4,6, 10, 12,14}

{2,6,8, 10,12,

14}TRIAL 1:PLACE 8TH QUEEN IN(8,15)

Page 22: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE 9TH QUEEN IN(9,4)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Page 23: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{5,6,7,8,9,10,11,12,13,

14,15,16} {2,7,8,9,

10,11,12,13,

14,15,16}

{2,4,9, 10,11,12

,13, 14,15,16

}

{4,11, 12,13,

14,15,16}

{2,6,13, 14,15,16

}

{2,4, 15,16}

{4,6}

{2,6,8}

{2,6,12}

{6,10 }

{8, 10}

{2,8, 10, 12}

{6, 12,14}

{2,6,8,10,12,14}TRIAL

1:PLACE 9TH QUEEN IN(9,4)

Page 24: 16 Queens Problem - trial 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

TRIAL 1:PLACE 10TH QUEEN IN(10,2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Page 25: 16 Queens Problem - trial 1

X13

X9

X1

X5

X16

X8

X7

X15

X6

X14

X3

X11

X4

X12

X2

X10

{1,2,3,4,5,6,7,8,9,10,11,1

2,13, 14,15,16

}

{3,4,5,6,7,8,9,10,11,12,13

, 14,15,16

}

{5,6,7,8,9,10,11,12,13,

14,15,16} {2,7,8,9,

10,11,12,13,

14,15,16}

{2,4,9, 10,11,12

,13, 14,15,16

}

{4,11, 12,13,

14,15,16}

{2,6,13, 14,15,16

}

{2,4, 15,16}

{4,6}

{2,6,8}

{6,12}

{6,10 }

{ }

{8, 10, 12}

{6, 12,14}

{6,10,12, 14}TRIAL

1:PLACE 10TH QUEEN IN(10,2)

TRIAL 1 FAILS IN THE 10TH POSITION SO, I TAKE TRIAL 2

OH! NO IT FAILS

Page 26: 16 Queens Problem - trial 1

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