project euler – Problem 15

November 8, 2011
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Starting in the top left corner of a 2x2 grid, there are 6 routes (without backtracking) to the bottom right corner.

How many routes are there through a 20x20 grid?

Using recursive algorithm can solved this problem well. For optimized the running time, I use a matrix to cache previously called functions, as I did in Problem 164.

?View Code RSPLUS

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find.routes.internal <- function(x,y) {
    cnt <- cacheMat[x+1,y+1]
    if (cnt != 0)
        return(cnt)
 
    if (y >0)
        cnt <- cnt+find.routes.internal(x,y-1)
    if (x >0)
        cnt <- cnt+find.routes.internal(x-1,y)
    if (x ==0 && y ==0)
        cnt <- cnt+1
 
    cacheMat[x+1,y+1] <<- cnt
 
    return(cnt)
}
 
find.routes <- function(x,y) {
    cacheMat <- matrix(0, nrow=x+1, ncol=y+1)
    cnt <- find.routes.internal(x,y)
    return(cnt)
}

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