# Python Program for Pigeonhole Sort

Pigeonhole sorting is a sorting algorithm that is suitable for sorting lists of elements where the number of elements and the number of possible key values are approximately the same.
It requires O(n + Range) time where n is number of elements in input array and \’Range\’ is number of possible values in array.

Working of Algorithm :

1. Find minimum and maximum values in array. Let the minimum and maximum values be \’min\’ and \’max\’ respectively. Also find range as \’max-min-1\’.
2. Set up an array of initially empty “pigeonholes” the same size as of the range.
3. Visit each element of the array and then put each element in its pigeonhole. An element arr[i] is put in hole at index arr[i] – min.
4. Start the loop all over the pigeonhole array in order and put the elements from non- empty holes back into the original array.

 `# Python program to implement Pigeonhole Sort */ ` ` `  `# source code : "https://en.wikibooks.org/wiki/ ` `#   Algorithm_Implementation/Sorting/Pigeonhole_sort" ` `def` `pigeonhole_sort(a): ` `    ``# size of range of values in the list  ` `    ``# (ie, number of pigeonholes we need) ` `    ``my_min ``=` `min``(a) ` `    ``my_max ``=` `max``(a) ` `    ``size ``=` `my_max ``-` `my_min ``+` `1` ` `  `    ``# our list of pigeonholes ` `    ``holes ``=` `[``0``] ``*` `size ` ` `  `    ``# Populate the pigeonholes. ` `    ``for` `x ``in` `a: ` `        ``assert` `type``(x) ``is` `int``, ``"integers only please"` `        ``holes[x ``-` `my_min] ``+``=` `1` ` `  `    ``# Put the elements back into the array in order. ` `    ``i ``=` `0` `    ``for` `count ``in` `range``(size): ` `        ``while` `holes[count] > ``0``: ` `            ``holes[count] ``-``=` `1` `            ``a[i] ``=` `count ``+` `my_min ` `            ``i ``+``=` `1` `             `  ` `  `a ``=` `[``8``, ``3``, ``2``, ``7``, ``4``, ``6``, ``8``] ` `print``(``"Sorted order is : "``, end ``=``" "``) ` ` `  `pigeonhole_sort(a) ` `         `  `for` `i ``in` `range``(``0``, ``len``(a)): ` `    ``print``(a[i], end ``=``" "``) ` `    `

Output:

`Sorted order is : 2 3 4 6 7 8 8 `

Please refer complete article on Pigeonhole Sort for more details!

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