project euler – Problem 15
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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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | 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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