Google Treasure Hunt 2008--Robot Problem

Question

A robot is located at the top-left corner of a65 x45 grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

Note: The grid below is 7x3, and is used to illustrate the problem. It is not drawn to scale.

*Image not to scale.

How many possible unique paths are there?
(Note: Answer must be an exact, decimal representation of the number.)

Your answer:

For a M*N grid,the result is as simple as (N+M-2)!/(N-1)!/(M-1)!

1. 1. Function G_C_D(ByValxAsLong,ByValyAsLong)AsLong'GETGreatestCommonDivisor
   2. DimtempAsLong
   3. Ifx>yThentemp=x:x=y:y=temp'LETX<Y
   4. Do
   5. temp=yModx
   6. Iftemp=0ThenG_C_D=x:ExitFunction
   7. y=x
   8. x=temp
   9. Loop
   10. EndFunction
   12. FunctionRobot(ByValNAsLong,ByValmAsLong)AsString
   13. Ifm=1ThenRobot=1:ExitFunction
   14. DimS()AsString,result()AsLong,nn(),nm(),iAsLong,jAsLong,kAsLong,tempAsLong,numlenAsLong,lastAsLong
   15. ReDimnn(1Tom-1)
   16. ReDimnm(1Tom-1)
   17. Fori=1Tom-1
   18. nn(i)=N+m-1-i'(n+m-2)(n+m-3)*....(n-1)
   19. nm(i)=i'1*2*3*...*(m-1)
   20. Next
   22. j=1
   23. DoWhilej<m-1
   24. j=j+1
   25. Fori=1Tom-1
   26. temp=G_C_D(nm(j),nn(i))'GreatestCommonDivisor
   27. Iftemp>1Thennn(i)=nn(i)/temp:nm(j)=nm(j)/temp
   28. Ifnm(j)=1ThenExitFor
   29. Next
   30. Loop
   31. k=0
   32. Fori=1Tom-1
   33. Ifnn(i)>1Then
   34. k=k+1
   35. nn(k)=nn(i)
   36. EndIf
   37. Next
   38. ReDimPreservenn(1Tok)
   40. numlen=1
   41. ReDimresult(1Tonumlen)
   42. result(1)=1
   43. i=0
   44. DoWhilei<k
   45. i=i+1
   46. last=0
   47. Forj=1Tonumlen
   48. temp=result(j)*nn(i)+last
   49. result(j)=tempMod100000
   50. last=temp\100000
   51. Next
   52. DoWhileNotlast=0
   53. ReDimPreserveresult(1Tonumlen+1)
   54. result(numlen+1)=lastMod100000
   55. last=last\100000
   56. numlen=UBound(result)
   57. Loop
   58. Loop
   60. ReDimS(1Tonumlen)
   61. Fori=2Tonumlen
   62. S(i)=Format(result(numlen+1-i),"00000")
   63. Next
   64. S(1)=result(numlen)
   65. Erasenn()
   66. Robot=Join(S,"")
   67. EndFunction
   69. PrivateSubCommand1_Click()
   70. MsgBoxRobot(65,45)
   71. EndSub

It returns:

3927192747782241611458841012775

Later , I use 3 lines python codes to solve it：

1. fac=lambdan:[1,0][n>0]orfac(n-1)*n
2. robot=lambdam,n:fac(m+n-2)/(fac(m-1)*fac(n-1))
3. printrobot(65,45)

Conclusion:

It seemsVB is the worst choice for numbers calculating.