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There is one more dimension to this problem. It is the number of tries you are allowed.
- DE2.0 February 23, 2014There are three variables here -
1. No. of eggs - k
2. No. of floors - n
3. No. of tries allowed - q
This problem will then have an optimal substructure property and the recurrence will be the following -
MR is the function calculating the same -
MR(q,k)={1for k=0∨q=0
MR(q−1,k−1)+MR(q−1,k) for k>0∧q>0
MR(q,k) is the maximum number of floors 0..n−1 we can have ,if we have q tries and k eggs to break.
Note that MR(q,q+1)=MR(q,q) because the additional jar cannot be used.MR(q,q)=2^q.