Let u and r be the distance to move in the up and right directions. u=y2-y1 and r=x2-x1.
We have to move a total of u+r units. So the answer would be (u+r)!/u!r! since we are counting only the distinct paths. Each path from (x1,y1) to (x2,y2) may be expressed as a sequence of u+r steps consisting of U or R. If seq[i] has U then it means we moved up at the i th step. Similarly R is for right. The number of distinct paths would be the number of distinct arrangements of the sequence. On Sat, Jun 23, 2012 at 11:05 AM, Gobind Kumar Hembram <gobind....@gmail.com > wrote: > Given two positions in a 2-D matrix, say (x1, y1) and (x2, y2) where > x2>=x1 and y2>=y1. Find the total number of distinct paths between > (x1, y1) and (x2, y2). You can only move in right direction i.e. > positive x direction (+1, 0) or in up direction i.e. positive y > direction (0, +1) from any given position. > > Example: If the given coordinates are (3,3) and (5,5), the number of > distinct paths are 6 : one going through 3,5 ; one going through 5,3 > and four going through 4,4. > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
