15 files changed, 734 insertions, 0 deletions
diff --git a/algorithms/__init__.py b/algorithms/__init__.py
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/algorithms/__init__.py
diff --git a/algorithms/algorithm.py b/algorithms/algorithm.py
new file mode 100644
index 0000000..66f8724
--- /dev/null
+++ b/algorithms/algorithm.py
@@ -0,0 +1,23 @@
+# Copyright (c) 2016 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+from . import input_kind
+
+
+class Algorithm:
+    def __init__(self, codename, display_name, f):
+        self.codename = codename
+        self.display_name = display_name
+        self.function = f
+
+    @staticmethod
+    def gen_input(n, case=input_kind.InputKind.AVERAGE):
+        #raise NotImplementedError('input generation is not defined for a generic algorithm')
+        return input_kind.gen_input_for_sorting(n, case)
+
+
+class SortingAlgorithm(Algorithm):
+    def gen_input(self, n, case=input_kind.InputKind.AVERAGE):
+        return input_kind.gen_input_for_sorting(n, case)
diff --git a/algorithms/impl/__init__.py b/algorithms/impl/__init__.py
new file mode 100644
index 0000000..84bd702
--- /dev/null
+++ b/algorithms/impl/__init__.py
@@ -0,0 +1,30 @@
+# Copyright (c) 2016 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+from importlib import import_module
+import os.path
+from pkgutil import iter_modules
+
+from .. import algorithm
+
+
+_ALGORITHMS_NAME = '_ALGORITHMS'
+
+
+def refresh_algorithms():
+    all_algorithms = {}
+
+    for _, module_name, is_pkg in iter_modules([os.path.dirname(__file__)]):
+        if is_pkg:
+            continue
+        module = import_module('.' + module_name, __package__)
+        if hasattr(module, _ALGORITHMS_NAME):
+            module_algorithms = getattr(module, _ALGORITHMS_NAME)
+            for descr in module_algorithms:
+                assert isinstance(descr, algorithm.Algorithm)
+                assert descr.codename not in all_algorithms
+                all_algorithms[descr.codename] = descr
+
+    return all_algorithms
diff --git a/algorithms/impl/bubble_sort.py b/algorithms/impl/bubble_sort.py
new file mode 100644
index 0000000..0ea66bb
--- /dev/null
+++ b/algorithms/impl/bubble_sort.py
@@ -0,0 +1,56 @@
+# Copyright (c) 2015 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+import sys
+
+from ..algorithm import SortingAlgorithm
+
+
+def bubble_sort(xs):
+    while True:
+        swapped = False
+        for i in range(1, len(xs)):
+            if xs[i - 1] > xs[i]:
+                xs[i], xs[i - 1] = xs[i - 1], xs[i]
+                swapped = True
+        if not swapped:
+            break
+    return xs
+
+
+def bubble_sort_optimized(xs):
+    n = len(xs)
+    while True:
+        new_n = 0
+        for i in range(1, n):
+            if xs[i - 1] > xs[i]:
+                xs[i], xs[i - 1] = xs[i - 1], xs[i]
+                new_n = i
+        n = new_n
+        if not n:
+            break
+    return xs
+
+
+_ALGORITHMS = [
+    SortingAlgorithm('bubble_sort', 'Bubble sort', bubble_sort),
+    SortingAlgorithm('bubble_sort_optimized', 'Bubble sort (optimized)', bubble_sort_optimized),
+]
+
+
+def _parse_args(args=None):
+    if args is None:
+        args = sys.argv[1:]
+    return list(map(int, args))
+
+
+def main(args=None):
+    xs = _parse_args(args)
+    print(bubble_sort(list(xs)))
+    print(bubble_sort_optimized(list(xs)))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/algorithms/impl/heapsort.py b/algorithms/impl/heapsort.py
new file mode 100644
index 0000000..81bea20
--- /dev/null
+++ b/algorithms/impl/heapsort.py
@@ -0,0 +1,82 @@
+# Copyright (c) 2015 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+import sys
+
+from ..algorithm import SortingAlgorithm
+
+# Disclaimer: implemented in the most literate way.
+
+
+def heapsort(xs):
+    _heapify(xs)
+    first, last = 0, len(xs) - 1
+    for end in range(last, first, -1):
+        xs[end], xs[first] = xs[first], xs[end]
+        _siftdown(xs, first, end - 1)
+    return xs
+
+
+# In a heap stored in a zero-based array,
+# left_child = node * 2 + 1
+# right_child = node * 2 + 2
+# parent = (node - 1) // 2
+
+
+def _get_parent(node):
+    return (node - 1) // 2
+
+
+def _get_left_child(node):
+    return node * 2 + 1
+
+
+def _get_right_child(node):
+    return node * 2 + 2
+
+
+def _heapify(xs):
+    last = len(xs) - 1
+    first_parent, last_parent = 0, _get_parent(last)
+    for parent in range(last_parent, first_parent - 1, -1):
+        _siftdown(xs, parent, last)
+
+
+def _siftdown(xs, start, end):
+    root = start
+    while True:
+        # We swap if there is at least one child
+        child = _get_left_child(root)
+        if child > end:
+            break
+        # If there are two children, select the minimum
+        right_child = _get_right_child(root)
+        if right_child <= end and xs[child] < xs[right_child]:
+            child = right_child
+        if xs[root] < xs[child]:
+            xs[root], xs[child] = xs[child], xs[root]
+            root = child
+        else:
+            break
+
+
+_ALGORITHMS = [
+    SortingAlgorithm('heapsort', 'Heapsort', heapsort),
+]
+
+
+def _parse_args(args=None):
+    if args is None:
+        args = sys.argv[1:]
+    return list(map(int, args))
+
+
+def main(args=None):
+    xs = _parse_args(args)
+    print(heapsort(list(xs)))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/algorithms/impl/insertion_sort.py b/algorithms/impl/insertion_sort.py
new file mode 100644
index 0000000..13f16a0
--- /dev/null
+++ b/algorithms/impl/insertion_sort.py
@@ -0,0 +1,37 @@
+# Copyright (c) 2015 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+import sys
+
+from ..algorithm import SortingAlgorithm
+
+
+def insertion_sort(xs):
+    for i in range(1, len(xs)):
+        j = i
+        while j > 0 and xs[j - 1] > xs[j]:
+            xs[j], xs[j - 1] = xs[j - 1], xs[j]
+            j -= 1
+    return xs
+
+
+_ALGORITHMS = [
+    SortingAlgorithm('insertion_sort', 'Insertion sort', insertion_sort),
+]
+
+
+def _parse_args(args=None):
+    if args is None:
+        args = sys.argv[1:]
+    return list(map(int, args))
+
+
+def main(args=None):
+    xs = _parse_args(args)
+    print(insertion_sort(list(xs)))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/algorithms/impl/median.py b/algorithms/impl/median.py
new file mode 100644
index 0000000..a754cdb
--- /dev/null
+++ b/algorithms/impl/median.py
@@ -0,0 +1,67 @@
+# Copyright (c) 2016 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+from heapq import heappush, heappop
+import sys
+
+from ..algorithm import Algorithm
+from .quicksort import quicksort_random
+
+
+def calc_median_heaps(xs):
+    cur_median = 0.0
+    min_heap, max_heap = [], []
+    for x in xs:
+        if x < cur_median:
+            heappush(max_heap, -x)
+        elif x > cur_median or len(max_heap) > len(min_heap):
+            heappush(min_heap, x)
+        else:
+            heappush(max_heap, -x)
+
+        if len(max_heap) > len(min_heap) + 1:
+            heappush(min_heap, -heappop(max_heap))
+        elif len(min_heap) > len(max_heap) + 1:
+            heappush(max_heap, -heappop(min_heap))
+
+        if len(max_heap) > len(min_heap):
+            cur_median = -max_heap[0]
+        elif len(max_heap) == len(min_heap):
+            cur_median = -max_heap[0] / 2 + min_heap[0] / 2
+        else:
+            cur_median = min_heap[0]
+    return cur_median
+
+
+def calc_median_sorting(xs):
+    if not xs:
+        return 0.0
+    quicksort_random(xs)
+    if len(xs) % 2:
+        return xs[len(xs) // 2]
+    else:
+        return xs[len(xs) // 2 - 1] / 2 + xs[len(xs) // 2] / 2
+
+
+_ALGORITHMS = [
+    Algorithm('median_sorting', 'Median value (using explicit sorting)', calc_median_sorting),
+    Algorithm('median_heaps', 'Median value (using heaps)', calc_median_heaps),
+]
+
+
+def _parse_args(args=None):
+    if args is None:
+        args = sys.argv[1:]
+    return list(map(int, args))
+
+
+def main(args=None):
+    xs = _parse_args(args)
+    print(calc_median_sorting(list(xs)))
+    print(calc_median_heaps(list(xs)))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/algorithms/impl/merge_sort.py b/algorithms/impl/merge_sort.py
new file mode 100644
index 0000000..fecdf78
--- /dev/null
+++ b/algorithms/impl/merge_sort.py
@@ -0,0 +1,52 @@
+# Copyright (c) 2015 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+import sys
+
+from ..algorithm import SortingAlgorithm
+
+
+def merge(left, right):
+    result = []
+    l, r = 0, 0
+    while l < len(left) and r < len(right):
+        if left[l] <= right[r]:
+            result.append(left[l])
+            l += 1
+        else:
+            result.append(right[r])
+            r += 1
+    if left:
+        result.extend(left[l:])
+    if right:
+        result.extend(right[r:])
+    return result
+
+
+def merge_sort(xs):
+    if len(xs) < 2:
+        return xs
+    mid = len(xs) // 2
+    return merge(merge_sort(xs[:mid]), merge_sort(xs[mid:]))
+
+
+_ALGORITHMS = [
+    SortingAlgorithm('merge_sort', 'Merge sort', merge_sort),
+]
+
+
+def _parse_args(args=None):
+    if args is None:
+        args = sys.argv[1:]
+    return list(map(int, args))
+
+
+def main(args=None):
+    xs = _parse_args(args)
+    print(merge_sort(list(xs)))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/algorithms/impl/quicksort.py b/algorithms/impl/quicksort.py
new file mode 100644
index 0000000..dd0c92b
--- /dev/null
+++ b/algorithms/impl/quicksort.py
@@ -0,0 +1,103 @@
+# Copyright (c) 2015 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+from random import randrange, seed
+import sys
+
+from ..algorithm import SortingAlgorithm
+
+
+seed()
+
+
+def _partition(xs, beg, end, select_pivot):
+    pivot = select_pivot(xs, beg, end)
+    xs[pivot], xs[end] = xs[end], xs[pivot]
+    for i in range(beg, end):
+        if xs[i] <= xs[end]:
+            xs[i], xs[beg] = xs[beg], xs[i]
+            beg += 1
+    xs[beg], xs[end] = xs[end], xs[beg]
+    return beg
+
+
+def _quicksort(xs, beg, end, select_pivot):
+    if beg < end:
+        pivot = _partition(xs, beg, end, select_pivot)
+        _quicksort(xs, beg, pivot - 1, select_pivot)
+        _quicksort(xs, pivot + 1, end, select_pivot)
+
+
+def _select_first(xs, beg, end):
+    return beg
+
+
+def _select_second(xs, beg, end):
+    return beg + 1
+
+
+def _select_middle(xs, beg, end):
+    return (beg + end) // 2
+
+
+def _select_last(xs, beg, end):
+    return end
+
+
+def _select_random(xs, beg, end):
+    return randrange(beg, end + 1)
+
+
+def quicksort_first(xs):
+    _quicksort(xs, 0, len(xs) - 1, _select_first)
+    return xs
+
+
+def quicksort_second(xs):
+    _quicksort(xs, 0, len(xs) - 1, _select_second)
+    return xs
+
+
+def quicksort_middle(xs):
+    _quicksort(xs, 0, len(xs) - 1, _select_middle)
+    return xs
+
+
+def quicksort_last(xs):
+    _quicksort(xs, 0, len(xs) - 1, _select_last)
+    return xs
+
+
+def quicksort_random(xs):
+    _quicksort(xs, 0, len(xs) - 1, _select_random)
+    return xs
+
+
+_ALGORITHMS = [
+    SortingAlgorithm('quicksort_first', 'Quicksort (first element as pivot)', quicksort_first),
+    SortingAlgorithm('quicksort_second', 'Quicksort (second element as pivot)', quicksort_second),
+    SortingAlgorithm('quicksort_middle', 'Quicksort (middle element as pivot)', quicksort_middle),
+    SortingAlgorithm('quicksort_last', 'Quicksort (last element as pivot)', quicksort_last),
+    SortingAlgorithm('quicksort_random', 'Quicksort (random element as pivot)', quicksort_random),
+]
+
+
+def _parse_args(args=None):
+    if args is None:
+        args = sys.argv[1:]
+    return list(map(int, args))
+
+
+def main(args=None):
+    xs = _parse_args(args)
+    print(quicksort_first(list(xs)))
+    print(quicksort_second(list(xs)))
+    print(quicksort_middle(list(xs)))
+    print(quicksort_last(list(xs)))
+    print(quicksort_random(list(xs)))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/algorithms/impl/selection_sort.py b/algorithms/impl/selection_sort.py
new file mode 100644
index 0000000..e9a5a09
--- /dev/null
+++ b/algorithms/impl/selection_sort.py
@@ -0,0 +1,39 @@
+# Copyright (c) 2015 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+import sys
+
+from ..algorithm import SortingAlgorithm
+
+
+def selection_sort(xs):
+    for i in range(len(xs) - 1):
+        min_i = i
+        for j in range(i + 1, len(xs)):
+            if xs[j] < xs[min_i]:
+                min_i = j
+        if min_i != i:
+            xs[i], xs[min_i] = xs[min_i], xs[i]
+    return xs
+
+
+_ALGORITHMS = [
+    SortingAlgorithm('selection_sort', 'Selection sort', selection_sort),
+]
+
+
+def _parse_args(args=None):
+    if args is None:
+        args = sys.argv[1:]
+    return list(map(int, args))
+
+
+def main(args=None):
+    xs = _parse_args(args)
+    print(selection_sort(list(xs)))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/algorithms/input_kind.py b/algorithms/input_kind.py
new file mode 100644
index 0000000..08e1c9e
--- /dev/null
+++ b/algorithms/input_kind.py
@@ -0,0 +1,34 @@
+# Copyright (c) 2016 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+from array import array
+from enum import Enum
+from random import seed, sample
+
+
+seed()
+
+
+class InputKind(Enum):
+    BEST, AVERAGE, WORST = 'best', 'average', 'worst'
+
+    def __str__(self):
+        return self.value
+
+
+def _gen_input_from(xs):
+    return array('l', xs)
+
+
+def gen_input_for_sorting(n, case=InputKind.AVERAGE):
+    if n < 0:
+        raise ValueError('input length cannot be less than zero')
+    if case is InputKind.BEST:
+        return _gen_input_from(range(n))
+    if case is InputKind.AVERAGE:
+        return _gen_input_from(sample(range(n), n))
+    if case is InputKind.WORST:
+        return _gen_input_from(range(n - 1, -1, -1))
+    raise NotImplementedError('invalid input kind: ' + str(case))
diff --git a/algorithms/params.py b/algorithms/params.py
new file mode 100644
index 0000000..486cb0e
--- /dev/null
+++ b/algorithms/params.py
@@ -0,0 +1,142 @@
+# Copyright (c) 2016 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+from enum import Enum
+from numbers import Integral
+
+from .input_kind import InputKind
+from .plotter import PlotBuilder
+from . import registry
+from .timer import Timer
+
+
+class TimeUnits(Enum):
+    SECONDS = 'seconds'
+    MILLISECONDS = 'milliseconds'
+    MICROSECONDS = 'microseconds'
+
+    def get_factor(self):
+        if self is TimeUnits.SECONDS:
+            return 1.
+        if self is TimeUnits.MILLISECONDS:
+            return 1000.
+        if self is TimeUnits.MICROSECONDS:
+            return 1000000.
+        raise NotImplementedError('invalid time units: ' + str(self))
+
+    def __str__(self):
+        return self.value
+
+
+class AlgorithmParameters:
+    def __init__(self, algorithm, min_len, max_len,
+                 input_kind=InputKind.AVERAGE, iterations=1):
+
+        if isinstance(algorithm, str):
+            algorithm = registry.get(algorithm)
+        self.algorithm = algorithm
+
+        self.input_kind = input_kind
+
+        self._min_len = None
+        self._max_len = None
+        self.min_len = min_len
+        self.max_len = max_len
+
+        self._iterations = None
+        self.iterations = iterations
+
+    @property
+    def min_len(self):
+        return self._min_len
+
+    @min_len.setter
+    def min_len(self, val):
+        if not isinstance(val, Integral):
+            raise TypeError('must be an integral value')
+        val = int(val)
+        if val < 0:
+            raise ValueError('must be non-negative')
+        if self.max_len is not None and self.max_len < val:
+            raise ValueError('must not be greater than the maximum length')
+        self._min_len = val
+
+    @property
+    def max_len(self):
+        return self._max_len
+
+    @max_len.setter
+    def max_len(self, val):
+        if not isinstance(val, Integral):
+            raise TypeError('must be an integral value')
+        val = int(val)
+        if val < 0:
+            raise ValueError('must be non-negative')
+        if self.min_len is not None and self.min_len > val:
+            raise ValueError('must not be lesser than the minimum length')
+        self._max_len = val
+
+    @property
+    def iterations(self):
+        return self._iterations
+
+    @iterations.setter
+    def iterations(self, val):
+        if not isinstance(val, Integral):
+            raise TypeError('must be an integral value')
+        val = int(val)
+        if val < 1:
+            raise ValueError('must be positive')
+        self._iterations = val
+
+    def measure_running_time(self):
+        input_len_range = list(range(self.min_len, self.max_len + 1))
+        running_time = []
+        for input_len in input_len_range:
+            input_sample = self.algorithm.gen_input(input_len, self.input_kind)
+            input_copies = [list(input_sample) for _ in range(self.iterations)]
+            with Timer(running_time, self.iterations):
+                for i in range(self.iterations):
+                    self.algorithm.function(input_copies[i])
+        return input_len_range, running_time
+
+    @staticmethod
+    def _format_plot_xlabel():
+        return 'Input length'
+
+    @staticmethod
+    def _format_plot_ylabel(units):
+        return 'Running time ({})'.format(units)
+
+    def _format_plot_title(self):
+        return '{}, {} case'.format(
+            self.algorithm.display_name, self.input_kind)
+
+    def _format_plot_suptitle(self):
+        return self.algorithm.display_name
+
+    @staticmethod
+    def _derive_time_units(ys):
+        max_y = max(ys)
+        if max_y > 0.1:
+            return TimeUnits.SECONDS
+        if max_y > 0.0001:
+            return TimeUnits.MILLISECONDS
+        return TimeUnits.MICROSECONDS
+
+    def plot_running_time(self, output_path=None):
+        xs, ys = self.measure_running_time()
+        units = self._derive_time_units(ys)
+        ys = [y * units.get_factor() for y in ys]
+
+        plot_builder = PlotBuilder()
+        title = self._format_plot_title()
+        xlabel = self._format_plot_xlabel()
+        ylabel = self._format_plot_ylabel(units)
+        plot_builder.plot(title, xlabel, ylabel, xs, ys)
+        if output_path is None:
+            plot_builder.show()
+        else:
+            plot_builder.save(output_path)
diff --git a/algorithms/plotter.py b/algorithms/plotter.py
new file mode 100644
index 0000000..d3e4ee4
--- /dev/null
+++ b/algorithms/plotter.py
@@ -0,0 +1,25 @@
+# Copyright (c) 2016 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+import matplotlib.pyplot as plt
+
+
+class PlotBuilder:
+    def __init__(self):
+        self._fig, self._ax = plt.subplots(figsize=(8, 6), dpi=200)
+        self._ax.grid(alpha=0.8, linestyle=':')
+
+    def plot(self, title, xlabel, ylabel, xs, ys):
+        self._ax.set_title(title)
+        self._ax.set_xlabel(xlabel)
+        self._ax.set_ylabel(ylabel)
+        self._ax.plot(xs, ys)
+
+    @staticmethod
+    def show():
+        plt.show()
+
+    def save(self, output_path):
+        self._fig.savefig(output_path)
diff --git a/algorithms/registry.py b/algorithms/registry.py
new file mode 100644
index 0000000..3bc6495
--- /dev/null
+++ b/algorithms/registry.py
@@ -0,0 +1,17 @@
+# Copyright (c) 2016 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+from . import impl
+
+
+_ALL_ALGORITHMS = impl.refresh_algorithms()
+
+
+def get_codenames():
+    return _ALL_ALGORITHMS.keys()
+
+
+def get(codename):
+    return _ALL_ALGORITHMS[codename]
diff --git a/algorithms/timer.py b/algorithms/timer.py
new file mode 100644
index 0000000..c567a3f
--- /dev/null
+++ b/algorithms/timer.py
@@ -0,0 +1,27 @@
+# Copyright (c) 2016 Egor Tensin <Egor.Tensin@gmail.com>
+# This file is part of the "Sorting algorithms" project.
+# For details, see https://github.com/egor-tensin/sorting-algorithms.
+# Distributed under the MIT License.
+
+import gc
+import time
+
+
+def get_timestamp():
+    return time.perf_counter()
+
+
+class Timer:
+    def __init__(self, dest, iterations=1):
+        self._dest = dest
+        self._iterations = iterations
+
+    def __enter__(self):
+        gc.disable()
+        self._start = get_timestamp()
+        return self
+
+    def __exit__(self, *args):
+        end = get_timestamp()
+        gc.enable()
+        self._dest.append((end - self._start) / self._iterations)