Following question was asked in a coding interview.how to solve it with out using dynamic programming?

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Following question was asked in a coding interview.how to solve it with out using dynamic programming?

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Auto comment: topic has been updated by leninkumar31 (previous revision, new revision, compare).To reach from (0,0) to (X,Y) you need to go right X steps and go up Y steps. Let's regard a step as an arrow. If there is no building, you can make combinations of X right-arrows and Y up-arrows. That's C(X+Y,X) or equivalently C(X+Y,Y).

Now, there is a building that covers (A,B) to (A+N,B+M). Let f(X,Y) be the number of combinations can be made with X right-arrows and Y up-arrows. That is, f(X,Y) = C(X+Y,X) = C(X+Y,Y).

Then the number of pathes is as follows:

f(X,Y) — f(A+1,B+1)f(M-2,N-2)f(X-A-N+1,Y-B-M+1)

can you explain last equation in detail?

In fact it's wrong. I'm finding a new formula. But the idea was:

1

6 6

4 4 1 1

answer is 74. your solution is wrong.

A path should contain exactly one of arrows in the picture. (there are A up-arrows and B right-arrows)

So, the answer is: