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Backtracking

Backtracking. Introduction. Systematic way to do an exhaustive search Take advantage of pruning when possible. Turnpike Reconstruction Problem. Given |D| distances, determine x coordinates for points lying on x-axis |D|=N(N-1)/2

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Backtracking

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  1. Backtracking

  2. Introduction • Systematic way to do an exhaustive search • Take advantage of pruning when possible

  3. Turnpike Reconstruction Problem • Given |D| distances, determine x coordinates for points lying on x-axis • |D|=N(N-1)/2 • Easy to go from points to distances in O(N2) – distances to points is worst-case exponential

  4. Turnpike Reconstruction Problem • N = 6 • Should largest distance be placed on left or right side? • if 1 only, place • if both, choose 1 – if it does not lead to a solution, try the other • if neither, no solution to current configuration – backtrack x1 = 0 x6 = 10 D = {1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 8, 10}

  5. Turnpike Reconstruction Problem x1 = 0 x6 = 10 D = {1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 8, 10} x1=0 x6=10 x5=8 x4=7 x2=3 x3=6 x2=4 x3=4 x4=6 x3=5

  6. TicTacToe • Idea: for each possible move, determine outcome assuming player and computer will choose optimal subsequent moves • http://www.ocf.berkeley.edu/~yosenl/extras/alphabeta/alphabeta.html • Minimax strategy – human win = -1 and computer win = 1 – human tries to minimize value of play while computer tries to maximize value of play

  7. findCompMove if(full) value = DRAW else if comp wins value = COMP_WIN else value = COMP_LOSS bestMove = 1 for (i 1->n) if empty place rval= findHumanMove unplace if rval > value value = rval bestMove = i findHumanMove if(full) value = DRAW else if comp wins value = COMP_LOSS else value = COMP_WIN bestMove = 1 for (i 1->n) if empty place rval= findCompMove unplace if rval < value value = rval bestMove = i TicTacToe

  8. Game Tree • Levels alternate min/max • If solution is obvious – prune • Example • 44 (max) • 44 (min) • 44 (max) • 27 • 44 • 68 • 68 • C • 40

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