algorithm - Average Case Time Complexity Analysis of Binary Counter Increment -

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i attempting find average case time complexity, not amortized analysis, of binary counter. not entirely confident in time complexity analyzing skills, confirm average case analysis of pseudocode provided below correct.

let k length of array.

increment(array)     = 0     while < k , array[i] == 1         array[i] = o         = + 1     if < k         array[i] = 1

in order find average time taken, find average amount of bits flipped per run. result, found o(2+k/(2^k)), equals o(1) large k.

is correct average case running time? if not, how begin approach problem?

i assuming each input has same probability occur

this means each bit independently on or off probability 1/2.

the geometric distribution relevant distribution complexity: flip coins, , end experiment on first tail outcome (there nothing further carry).

the mean of geometric distribution here 2 (see above link, or derive basic principles), average complexity indeed o(1).


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