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Task/Sorting-algorithms-Counting-sort/00-TASK.txt

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+{{Sorting Algorithm}}
+{{Wikipedia|Counting sort}}
+
+
+;Task:
+Implement the [[wp:Counting sort|Counting sort]].   This is a way of sorting integers when the minimum and maximum value are known.
+
+
+;Pseudocode:
+ '''function''' ''countingSort''(array, min, max):
+     count: '''array of''' (max - min + 1) '''elements'''
+     '''initialize''' count '''with''' 0
+     '''for each''' number '''in''' array '''do'''
+         count[number - min] := count[number - min] + 1
+     '''done'''
+     z := 0
+     '''for''' i '''from''' min '''to''' max '''do'''
+         '''while''' ( count[i - min] > 0 ) '''do'''
+             array[z] := i
+             z := z+1
+             count[i - min] := count[i - min] - 1
+         '''done'''
+     '''done'''
+
+The ''min'' and ''max'' can be computed apart, or be known ''a priori''.
+
+
+'''Note''': &nbsp; we know that, given an array of integers, &nbsp; its maximum and minimum values can be always found; &nbsp; but if we imagine the worst case for an array that can hold up to 32 bit integers, &nbsp; we see that in order to hold the counts, &nbsp; an array of up to '''2<sup>32</sup>''' elements may be needed. &nbsp; I.E.: &nbsp; we need to hold a count value up to '''2<sup>32</sup>-1''', &nbsp; which is a little over 4.2 Gbytes. &nbsp; So the counting sort is more practical when the range is (very) limited, &nbsp; and minimum and maximum values are known &nbsp; ''a priori''. &nbsp; &nbsp; (However, as a counterexample, &nbsp; the use of &nbsp; ''sparse arrays'' &nbsp; minimizes the impact of the memory usage, &nbsp; as well as removing the need of having to know the minimum and maximum values &nbsp; ''a priori''.)
+<br><br>
+