Dynamic Programming and Knapsack Application

Question

Im studying dynamic programming and am looking to solve the following problem, which can be found here http://www.cs.berkeley.edu/~vazirani/algorithms/chap6.pdf:

You

Answer 1

optimize() {

Rectangle memo[width][height]
optimize(0,0,totalwidth, totalheight, memo)

}

optimize(x, y, width, height, memo) {

if memo[width][height] != null
    return memo[width][height]

rect = new Rectangle(width, height, value = 0)
for each pattern {

    //find vertical cut solution
    leftVerticalRect = optimize (x, y + pattern.height, pattern.width, height-pattern.height,memo)
    rightVerticalRect = optimize(x  + pattern.width, y, width-pattern.width, height)
    verticalcut = new Cut(x + pattern.width, y, x + pattern.width, y + height)

    //find horizontal cut solution
    topHorizontalRect = optimize ( --parameters-- )
    bottomHortizonalRect = optimize( --parameters--)
    horizontalcut = new Cut( --parameters--)

    //see which solution is more optimal
    if (leftVerticalRect.val + rightVerticalRect.val > topHorizontalRect.val + bottomHorizontalRect.val)
        subprobsolution = vertical cut solution
    else
        subprobsolution = horizontal cut solution

    //see if the solution found is greater than previous solutions to this subproblem
    if (subprobsolution.value + pattern.value > rect.value) {
        rect.subrect1 = subprobsolutionrect1
        rect.subrect2 = subprobsolutionrect2
        rect.pattern = pattern
        rect.cut = subprobsolutioncut
        rect.value = rect.subrect1.value + rect.subrect2.value + rect.pattern.value
    }
}

memo[width][height] = rect
return rect

}