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How to implement classic sorting algorithms in modern C++?

The std::sort algorithm (and its cousins std::partial_sort and std::nth_element ) from the C++ Standard Library is in most implementations a complicated and hybrid amalgamation of more elementary sorting algorithms , such as selection sort, insertion sort, quick sort, merge sort, or heap sort....
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Time complexity of Euclid's Algorithm

...ow what happens over two iterations: a', b' := a % b, b % (a % b) Now a and b will both decrease, instead of only one, which makes the analysis easier. You can divide it into cases: Tiny A: 2a <= b Tiny B: 2b <= a Small A: 2a > b but a < b Small B: 2b > a but b < a Equal: a ==...
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Counting inversions in an array

... find all inversion pairs such that A[i] > A[j] . I'm using merge sort and copying array A to array B and then comparing the two arrays, but I'm having a difficult time seeing how I can use this to find the number of inversions. Any hints or help would be greatly appreciated. ...
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Unique (non-repeating) random numbers in O(1)?

I'd like to generate unique random numbers between 0 and 1000 that never repeat (i.e. 6 doesn't show up twice), but that doesn't resort to something like an O(N) search of previous values to do it. Is this possible? ...
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Evenly distributing n points on a sphere

...le code node[k] is just the kth node. You are generating an array N points and node[k] is the kth (from 0 to N-1). If that is all that is confusing you, hopefully you can use that now. (in other words, k is an array of size N that is defined before the code fragment starts, and which contains a lis...
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What is the easiest way to remove the first character from a string?

... p asdf # >> "12,23,987,43" I'm always looking for the fastest and most readable way of doing things: require 'benchmark' N = 1_000_000 puts RUBY_VERSION STR = "[12,23,987,43" Benchmark.bm(7) do |b| b.report('[0]') { N.times { "[12,23,987,43"[0] = '' } } b.report('sub') { N.time...
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Split list into multiple lists with fixed number of elements

...rate question. Scala has a mysterious gnome that chooses a data structure, and it chose a Stream for you. If you want a List, you should request a List, but you can also just trust the gnome's judgment. – Ion Freeman Jun 21 '17 at 21:09 ...
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Set every cell in matrix to 0 if that row or column contains a 0

Given a NxN matrix with 0s and 1s. Set every row that contains a 0 to all 0 s and set every column that contains a 0 to all 0 s. ...
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Why doesn't 'ref' and 'out' support polymorphism?

... UPDATE: I used this answer as the basis for this blog entry: Why do ref and out parameters not allow type variation? See the blog page for more commentary on this issue. Thanks for the great question. ============= Let's suppose you have classes Animal, Mammal, Reptile, Giraffe, Turtle and Ti...
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Efficient way to rotate a list in python

... A collections.deque is optimized for pulling and pushing on both ends. They even have a dedicated rotate() method. from collections import deque items = deque([1, 2]) items.append(3) # deque == [1, 2, 3] items.rotate(1) # The deque is now: [3, 1, 2] item...