Here is a near O(1) solution for a Fibonacci sequence term. Admittedly, O(log n) depending on the system Math.pow() implementation, but it is Fibonacci w/o a visible loop, if your interviewer is looking for that. The ceil() was due to rounding precision on larger values returning .9 repeating. Example in JS: function fib (n) { … Read more
list The Average Case assumes parameters generated uniformly at random. Internally, a list is represented as an array; the largest costs come from growing beyond the current allocation size (because everything must move), or from inserting or deleting somewhere near the beginning (because everything after that must move). If you need to add/remove at both … Read more
In the draft C++11 standard N3337 the answer can be found in ยง 24.2.1 paragraph 8: All the categories of iterators require only those functions that are realizable for a given category in constant time (amortized). Since each operation on an iterator must be constant time, iterating through n elements must be O(n).
You would use a min-max-median heap to find the min, max and median in constant time (and take linear time to build the heap). You can use order-statistics trees to find the kth smallest/largest value. Both of these data structures are described in this paper on min-max heaps [PDF]. Min-max heaps are binary heaps that … Read more
O(max(input)+n) The complexity just appears awkward to express because most sorting algorithms are data agnostic. Their time scales with the amount of data, not the data itself. FWIW, as pointed out here, this is not a reliable algorithm for sorting data.
Get largest sub-array having size 3k+1 Apply cycle leader algorithm to the parts of this sub-array, starting from positions 1, 3, 9, … 3k-1: move element to its proper position in sub-array (even-indexed elements to the left of sub-array, odd-indexed – to the right), the replaced element should be also moved to its proper position, … Read more
There are many ways to do this shorter. For example, you can use the Counter class (in Python 2.7 or later): import collections s = “helloworld” print(collections.Counter(s).most_common(1)[0]) If you don’t have that, you can do the tally manually (2.5 or later has defaultdict): d = collections.defaultdict(int) for c in s: d[c] += 1 print(sorted(d.items(), key=lambda … Read more
@Blindy talks about possible approaches that Java could take in implementing pow. First of all, the general case cannot be repeated multiplication. It won’t work for the general case where the exponent is not an integer. (The signature for pow is Math.pow(double, double)!) In the OpenJDK 8 codebase, the native code implementation for pow can … Read more
Dig into the CPython source code and visit Objects/listobject.c, you will find the source code for the count() method in there. It looks like this: static PyObject * list_count(PyListObject *self, PyObject *value) { Py_ssize_t count = 0; Py_ssize_t i; for (i = 0; i < Py_SIZE(self); i++) { int cmp = PyObject_RichCompareBool(self->ob_item[i], value, Py_EQ); if … Read more
I think it would be constant since it seems that property is set automatically on all arrays and you’re just looking it up? Right. It’s a property which is stored (not calculated) and automatically updated as necessary. The specification is explicit about that here and here amongst other places. In theory, a JavaScript engine would … Read more