By Lin Quan
This ebook is written for aiding humans arrange for Google Coding Interview. It includes best 10 programming difficulties commonly asked @Google with special worked-out recommendations either in pseudo-code and C++(and C++11).
Read or Download Top 10 coding interview problems asked in Google with solutions: Algorithmic Approach PDF
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Extra info for Top 10 coding interview problems asked in Google with solutions: Algorithmic Approach
Example text
The tree will be a ternary tree, since every comparison has three possible outcomes: less than, equal, or greater than The height of such a tree corresponds to the worst-case number of comparisons made by the algorithm it represents, which in turn is a lower bound on the running time of that algorithm. We therefore want a lower bound of Ω(nlog n) on the height, H, of any decision tree that solves nuts n bolts problem mentioned in earlier section. To begin with, note that the number of leaves L in any ternary tree must satisfy L ≤ 3H.
Randomized algorithms, on the other hand, base their behavior not only on the input but also on several random choices. The same randomized algorithm, given the same input multiple times, may perform different computations in each invocation. This means, among other things, that the running time of a randomized algorithm on a given input is no longer fixed, but is itself a random variable. When we analyze randomized algorithms, we are typically interested in the worst-case expected running time.
Worst case partition(for example in case of sorted sequence as input) will result into two subsequences of lengths n - 1 and 0 respectively. T(n) = T(n - 1) + T(0) + Θ(n) = T(n - 1) + Θ(n) = Θ(n2) Best case partition will result into almost equal size subsequences every time. T(n) = 2T(n∕2) + Θ(n) = Θ(nlog n) quicksort’s average case is closer to the best case than to the worst case. 4 Randomized Quicksort So far we have assumed that all input permutations are equally likely which is true always, hence we add randomization to quicksort.