Assignment -1 Name LALIT

RollNo. B10061

Branch EE

The whole problem is divided into following parts :-

1. Initial state

2. Operators Defining legal moves

3. H – Value Comparison(Heuristic function)

4. MoveGen function

5. Goal test

Initial State

B B B W W W E

Description:-

There are three black tiles(B), three white tiles(W) and an empty cell(E). The Puzzle has the

following moves(Legal Moves):

H1 and H2 are the operators for defining the legal moves.

H1 A tile may move into an adjacent empty cell with unit cost

H2A tile may hop over at most two other tiles into an empty cell with a cost equal to

the number of tiles hopped over

Goal:-

The goal of the puzzle is to have all of the white tiles to the left of all of the black tiles (without

regard to the position of empty cell) i.e.

W W W B B B E

Solution :-

P is one (1) for every level of the tree

Operators defining Legal moves.

The heuristic function is given by :-

Q no. of tiles hopped over

R no. of tiles out of place

S = Q+R

T = P+S

No. of moves/Nodes available will be decided according to the value of T we are getting; the

lesser the value or lower the cost, the more good will be the node to choose for Goal

Attainment.

Initial state Tile hoped (Q) Out of place (R) T=P+S

BBBWWWE - 6 6+1

This is the best node with lowest heuristic

BBBWWEW 0 6 7

S is 1 for this part of the tree

BBBWEWW 1 6 8

A TILE CAN HOP ATMOST TWO TILES

BBBEWWW 2 6 9

Best node in level two P is 2

BBBWWEW 0 6 8

BBBEWWW 1 6 9

BBEBWWW 2 5 9

Best node in level two P is 3

BBBWEWW - 6 9

BBBEWWW 1 5 9

BBEBWWW 1 5 9

BEBBWWW 2 5 10

The search goes in this way and the search tree is as follows :-

P=24 GOAL ATTAINED

P=23

P=22

P=21

P=20

P=19

P=18

P=17

P=16

P=15

P=14

P=13

P=12

P=11

P=10

P=8

P=8

P=7 (nodes with lowset h value only)

P=6

P=5

P=4

P=3

P=2

P=1

Initial State BBBWWWE

BBBWWEW

(Q=0;R=6,T=7)

BBBWEWW

BBBEWWW BBEWBWW

EBBWBWW BBWEBWW

BEWBBWW

EBWBBWW BWEBBWW

BWWBBEW

BWWBEBW

BWWWEBBW

EWWBBBW

WWEBBBW

WWBEBBW

WWBBEBW

WWBBBEW

WWBBBWE

WWBBEWB

WWBBWEB

WWBEWBB

WWBWEBB

WWEWBBB

WWWEBBB

WWWBEBB

WWWBBEB

WWWBBBE

BBWEBWW

BBEWBWW BBWBEWW

BBBWEWW

BEBWBWW

BBBEWWW BBEWWBW

BBBWEWW

(Q=1;R=6;T=8)

BBBEWWW

(T=9)

MoveGen() function: -

It has to search for lowest ‘T’ and follow it in that node(with minimum T) and search further for the

lowest one till the goal is attained.

Pseudocode for it

Node1 is the parent node or the initial state of our problem

Function Expand(node,problem), Returns (set of nodes )

In expand, we are opening a node and comparing it with the solution of problem and then calculating

the value of ‘T’ or the path cost.

For each calculate ‘T’ and in MinFn Expand(node,problem) // Expand the node with minimum ‘T’

Here, MinFn is used to to expand the node with minimum T

And in this way search goes on with minimum ‘T’ and comparing it with solution required.

T the value of ‘T’ can be calculated by;

T=P+S

Q no. of tiles hopped over

R no. of tiles out of place

S = Q+R

Goal-Test: -

It is simply a compare and return type function

If (nodex==solution)

thenReturn(nodex)

Else

MoveGen(nodex, problem)