arjunsanjeev7's blog

Search (binary/ternary) in a step function
By arjunsanjeev7, history, 8 years ago, In English

I have a step function 'V', over a domain 't' in [0,10^7]. It has shape as shown below.

V(t) = 0 for t in [0,a),
...... = 1 for t in (a,b), and
...... = 0 for t in (b,10^7]
for some 0 <= a < b <= 10^7.

What is the best way to find a and b (i.e., the starting and ending points of V(t)=1)? Can binary/ternary search be applied in this case?

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8 years ago, # |
  Vote: I like it +35 Vote: I do not like it

if you can find a point x. such that V(x) = 1, then you can apply binary search in [0, x) and (x, 10^7] to find a and b. otherwise I don't think you can

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    8 years ago, # ^ |
      Vote: I like it +14 Vote: I do not like it

    If there is constraint: b=a+1, then this becomes unordered search, you won't find a in less then O(107) queries for arbitrary V.

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