Constraint Satisfaction Problems - Homework | CS 3600, Assignments of Computer Science

Material Type: Assignment; Professor: Riedl; Class: Intro-Artificial Intell; Subject: Computer Science; University: Georgia Institute of Technology-Main Campus; Term: Spring 2009;

Typology: Assignments

Pre 2010

Uploaded on 08/05/2009

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๎˜ƒ๎˜6933๎˜-๎˜๎˜†๎˜Ÿ๎˜๎˜–&๎˜Ÿ!๎˜›๎˜5+8๎˜-๎˜๎˜ƒ๎˜Ÿ๎˜ž"#!๎˜’๎˜š๎˜ž#๎˜๎˜๎˜’#๎˜š"๎˜—๎˜’๎˜”#๎˜š๎˜Ÿ๎˜ž๎˜๎˜‹!๎˜Ÿ๎˜“๎˜œ๎˜–๎˜"๎˜.๎˜…๎˜„๎˜‚๎˜‡๎˜†๎˜๎˜„๎˜ƒ/
๎˜Ž๎˜™๎˜š"๎˜๎˜š"๎˜๎˜’๎˜"๎˜’๎˜ ๎˜œ๎˜–๎˜"๎˜Ÿ๎˜œ$#๎˜š๎˜Ÿ๎˜ž๎˜๎˜—๎˜Ÿ!๎˜#๎˜™๎˜š"๎˜ !๎˜Ÿ๎˜“๎˜œ๎˜–๎˜+๎˜๎˜๎˜ˆ๎˜’๎˜ž'๎˜ ๎˜Ÿ""๎˜š๎˜“๎˜œ๎˜–๎˜"๎˜Ÿ๎˜œ$#๎˜š๎˜Ÿ๎˜ž"๎˜๎˜’๎˜ž๎˜•๎˜"#๎˜– "๎˜๎˜’!๎˜–๎˜ ๎˜Ÿ""๎˜š๎˜“๎˜œ๎˜–+
4+ ๎˜ƒ๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜#๎˜™๎˜–๎˜๎˜‘6๎˜%๎˜’!๎˜š๎˜’๎˜“๎˜œ๎˜–+๎˜๎˜๎˜‡#"๎˜๎˜•๎˜Ÿ๎˜๎˜’๎˜š๎˜ž๎˜๎˜š"๎˜03)๎˜41+
5+ ๎˜ƒ๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜#๎˜™๎˜–๎˜%๎˜’๎˜œ$๎˜–๎˜4๎˜๎˜—๎˜Ÿ!๎˜๎˜‘6+๎˜๎˜.๎˜๎˜–๎˜๎˜”๎˜’๎˜ž2#๎˜๎˜”๎˜™๎˜Ÿ"๎˜–๎˜3)๎˜๎˜š#๎˜&๎˜Ÿ$๎˜œ๎˜•๎˜ž2#๎˜"$!%๎˜š%๎˜–๎˜๎˜—๎˜Ÿ!&๎˜’!๎˜•๎˜๎˜”๎˜™๎˜–๎˜”๎˜›๎˜š๎˜ž๎˜˜)๎˜๎˜“๎˜–๎˜”๎˜’$"๎˜–
๎˜š#๎˜&๎˜Ÿ$๎˜œ๎˜•๎˜๎˜—๎˜Ÿ!๎˜”๎˜–๎˜๎˜…๎˜#๎˜Ÿ๎˜๎˜“๎˜–๎˜3)๎˜๎˜’๎˜ž๎˜•๎˜๎˜œ๎˜–๎˜’๎˜•๎˜š๎˜ž๎˜˜๎˜๎˜•๎˜š๎˜˜๎˜š#"๎˜๎˜$"#๎˜๎˜“๎˜–๎˜๎˜ž๎˜Ÿ๎˜ž,(๎˜–!๎˜Ÿ/+
6+ ๎˜ƒ๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜๎˜…)๎˜๎˜“๎˜–๎˜”๎˜’$"๎˜–๎˜๎˜š#๎˜๎˜Ÿ๎˜ž๎˜œ'๎˜๎˜™๎˜’"๎˜๎˜Ÿ๎˜ž๎˜–๎˜!๎˜–๎˜๎˜’๎˜š๎˜ž๎˜š๎˜ž๎˜˜๎˜%๎˜’๎˜œ$๎˜–+
7+ ๎˜ƒ๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜#๎˜™๎˜–๎˜%๎˜’๎˜œ$๎˜–๎˜4๎˜๎˜—๎˜Ÿ!๎˜๎˜…+
8+ ๎˜‰๎˜Ÿ&๎˜๎˜‘5๎˜๎˜’๎˜ž๎˜•๎˜๎˜‘4๎˜๎˜’!๎˜–๎˜#๎˜š๎˜–๎˜•๎˜๎˜—๎˜Ÿ!๎˜๎˜๎˜š๎˜ž๎˜š๎˜$๎˜๎˜!๎˜–๎˜๎˜’๎˜š๎˜ž๎˜š๎˜ž๎˜˜๎˜%๎˜’๎˜œ$๎˜–"๎˜๎˜’#๎˜5*๎˜๎˜’!๎˜“๎˜š#!๎˜’!๎˜š๎˜œ'๎˜๎˜”๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜๎˜‘5+
9+ ๎˜„๎˜š#๎˜™๎˜–!๎˜%๎˜’๎˜œ$๎˜–๎˜"$!%๎˜š%๎˜–"๎˜๎˜—๎˜Ÿ!&๎˜’!๎˜•๎˜๎˜”๎˜™๎˜–๎˜”๎˜›๎˜š๎˜ž๎˜˜)๎˜"๎˜Ÿ๎˜๎˜’!๎˜“๎˜š#!๎˜’!๎˜š๎˜œ'๎˜๎˜”๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜3๎˜๎˜—๎˜Ÿ!๎˜๎˜‘5+
:+ ๎˜‰๎˜Ÿ&๎˜๎˜‘4๎˜๎˜™๎˜’"๎˜#๎˜™๎˜–๎˜๎˜๎˜š๎˜ž๎˜š๎˜$๎˜๎˜!๎˜–๎˜๎˜’๎˜š๎˜ž๎˜š๎˜ž๎˜˜๎˜%๎˜’๎˜œ$๎˜–"+
;+ ๎˜‚๎˜˜๎˜’๎˜š๎˜ž)๎˜๎˜’!๎˜“๎˜š#!๎˜’!๎˜š๎˜œ'๎˜๎˜”๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜3๎˜๎˜—๎˜Ÿ!๎˜#๎˜™๎˜–๎˜%๎˜’๎˜œ$๎˜–๎˜๎˜Ÿ๎˜—๎˜๎˜‘4+
<+ ๎˜Ž๎˜™๎˜–๎˜%๎˜’!๎˜š๎˜’๎˜“๎˜œ๎˜–๎˜๎˜Š๎˜๎˜$"#๎˜๎˜“๎˜–๎˜๎˜’๎˜ž๎˜๎˜–%๎˜–๎˜ž๎˜๎˜ž$๎˜๎˜“๎˜–!๎˜.๎˜“๎˜–๎˜”๎˜’$"๎˜–๎˜๎˜š#๎˜๎˜š"๎˜#๎˜™๎˜–๎˜"$๎˜๎˜๎˜Ÿ๎˜—๎˜๎˜Ž๎˜=๎˜๎˜Ž๎˜๎˜œ๎˜–""๎˜#๎˜™๎˜’๎˜ž๎˜8
.๎˜“๎˜–๎˜”๎˜’$"๎˜–๎˜๎˜Š๎˜=๎˜๎˜Š๎˜>๎˜๎˜Œ๎˜=๎˜43๎˜๎˜Š/+๎˜๎˜๎˜Ž๎˜™๎˜’#๎˜๎˜๎˜’๎˜›๎˜–"๎˜๎˜š#๎˜๎˜๎˜Ÿ"#๎˜๎˜”๎˜Ÿ๎˜ž"#!๎˜’๎˜š๎˜ž๎˜–๎˜•/+
43+ ๎˜‚!๎˜“๎˜š#!๎˜’!๎˜š๎˜œ'๎˜๎˜”๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜7๎˜๎˜’"๎˜#๎˜™๎˜–๎˜%๎˜’๎˜œ$๎˜–๎˜๎˜Ÿ๎˜—๎˜๎˜Š+
44+ ๎˜Œ๎˜๎˜ž๎˜Ÿ&๎˜๎˜Ÿ๎˜ž๎˜œ'๎˜๎˜™๎˜’"๎˜4๎˜!๎˜–๎˜๎˜’๎˜š๎˜ž๎˜š๎˜ž๎˜˜๎˜%๎˜’๎˜œ$๎˜–+
45+ ๎˜ƒ๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜#๎˜™๎˜–๎˜%๎˜’๎˜œ$๎˜–๎˜๎˜Ÿ๎˜—๎˜;๎˜๎˜—๎˜Ÿ!๎˜๎˜Œ+
46+ ๎˜Ž๎˜๎˜ž๎˜Ÿ&๎˜๎˜Ÿ๎˜ž๎˜œ'๎˜๎˜™๎˜’"๎˜4๎˜!๎˜–๎˜๎˜’๎˜š๎˜ž๎˜š๎˜ž๎˜˜๎˜%๎˜’๎˜œ$๎˜–+
47+ ๎˜ƒ๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜#๎˜™๎˜–๎˜%๎˜’๎˜œ$๎˜–๎˜:๎˜๎˜—๎˜Ÿ!๎˜๎˜Ž+
48+ ๎˜๎˜๎˜$"#๎˜๎˜“๎˜–๎˜๎˜’๎˜ž๎˜๎˜–%๎˜–๎˜ž๎˜๎˜ž$๎˜๎˜“๎˜–!๎˜๎˜œ๎˜–""๎˜#๎˜™๎˜’๎˜ž๎˜<*๎˜๎˜”๎˜™๎˜Ÿ๎˜Ÿ"๎˜–๎˜๎˜+
49+ ๎˜Ž๎˜™๎˜–๎˜๎˜Ÿ๎˜ž๎˜œ'๎˜%๎˜’๎˜œ$๎˜–๎˜๎˜—๎˜Ÿ!๎˜๎˜๎˜#๎˜™๎˜’#๎˜"$!%๎˜š%๎˜–"๎˜๎˜—๎˜Ÿ!&๎˜’!๎˜•๎˜๎˜”๎˜™๎˜–๎˜”๎˜›๎˜š๎˜ž๎˜˜๎˜๎˜š"๎˜9+
4:+ ๎˜Ž๎˜™๎˜–๎˜๎˜Ÿ๎˜ž๎˜œ'๎˜%๎˜’!๎˜š๎˜’๎˜“๎˜œ๎˜–๎˜๎˜œ๎˜–๎˜—#๎˜๎˜š"๎˜๎˜+
4;+ ๎˜Ž๎˜™๎˜–๎˜๎˜Ÿ๎˜ž๎˜œ'๎˜%๎˜’๎˜œ$๎˜–๎˜๎˜œ๎˜–๎˜—#๎˜๎˜—๎˜Ÿ!๎˜๎˜๎˜๎˜š"๎˜6+
4<+ ๎˜๎˜–๎˜๎˜™๎˜’%๎˜–๎˜๎˜’!!๎˜š%๎˜–๎˜•๎˜๎˜’#๎˜๎˜’๎˜"๎˜Ÿ๎˜œ$#๎˜š๎˜Ÿ๎˜ž+

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CS3600 - Homework 2.5 - Constraint Satisfaction Problems (solution) This is a sample solution for this problem. Many possible solutions and steps are possible. 1. Choose the X; variable. Its domain is {0, 1}. 2. Choose the value 1 for X3. (We can't chose 0, it wouldn't survive forward checking, because it would force F to be 0, and leading digits must be non-zero). 3. Choose F, because it only has one remaining value. 4. Choose the value 1 for F. 5. Now X;and X;, are tied for minimum remaining values at 2; arbitrarily choose X2. 6. Either value survives forward checking, so arbitrarily choose 0 for X2. 7. Now X;has the minimum remaining values. 8. Again, arbitrarily choose 0 for the value of X;. 9. The variable O must be an even number (because it is the sum of T + T less than 5 (because 0 +0 = R+100). That makes it most constrained). 10. Arbitrarily choose 4 as the value of 0. 11. R now only has 1 remaining value. 12. Choose the value of 8 for R. 13.T now only has 1 remaining value. 14. Choose the value 7 for T. 15.U must be an even number less than 9; choose U. 16. The only value for U that survives forward checking is 6. 17. The only variable left is W. 18. The only value left for W is 3. 19. We have arrived at a solution.