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Ingy döt Net 2026-02-01 16:33:20 -08:00
parent 5150844a7d
commit 4bb20c9b71
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Task/Sorting-algorithms-Patience-sort/Ada/sorting-algorithms-patience-sort.ada
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----------------------------------------------------------------------
with Ada.Text_IO;
procedure patience_sort_task is
use Ada.Text_IO;
function next_power_of_two
(n : in Natural)
return Positive is
-- This need not be a fast implementation.
pow2 : Positive;
begin
pow2 := 1;
while pow2 < n loop
pow2 := pow2 + pow2;
end loop;
return pow2;
end next_power_of_two;
generic
type t is private;
type t_array is array (Integer range <>) of t;
type sorted_t_indices is array (Integer range <>) of Integer;
procedure patience_sort
(less : access function
(x, y : t)
return Boolean;
ifirst : in Integer;
ilast : in Integer;
arr : in t_array;
sorted : out sorted_t_indices);
procedure patience_sort
(less : access function
(x, y : t)
return Boolean;
ifirst : in Integer;
ilast : in Integer;
arr : in t_array;
sorted : out sorted_t_indices) is
num_piles : Integer;
piles : array (1 .. ilast - ifirst + 1) of Integer :=
(others => 0);
links : array (1 .. ilast - ifirst + 1) of Integer :=
(others => 0);
function find_pile
(q : in Positive)
return Positive is
--
-- Bottenbruch search for the leftmost pile whose top is greater
-- than or equal to some element x. Return an index such that:
--
-- * if x is greater than the top element at the far right, then
-- the index returned will be num-piles.
--
-- * otherwise, x is greater than every top element to the left
-- of index, and less than or equal to the top elements at
-- index and to the right of index.
--
-- References:
--
-- * H. Bottenbruch, "Structure and use of ALGOL 60", Journal of
-- the ACM, Volume 9, Issue 2, April 1962, pp.161-221.
-- https://doi.org/10.1145/321119.321120
--
-- The general algorithm is described on pages 214 and 215.
--
-- * https://en.wikipedia.org/w/index.php?title=Binary_search_algorithm&oldid=1062988272#Alternative_procedure
--
index : Positive;
i, j, k : Natural;
begin
if num_piles = 0 then
index := 1;
else
j := 0;
k := num_piles - 1;
while j /= k loop
i := (j + k) / 2;
if less
(arr (piles (j + 1) + ifirst - 1), arr (q + ifirst - 1))
then
j := i + 1;
else
k := i;
end if;
end loop;
if j = num_piles - 1 then
if less
(arr (piles (j + 1) + ifirst - 1), arr (q + ifirst - 1))
then
-- A new pile is needed.
j := j + 1;
end if;
end if;
index := j + 1;
end if;
return index;
end find_pile;
procedure deal is
i : Positive;
begin
for q in links'range loop
i := find_pile (q);
links (q) := piles (i);
piles (i) := q;
num_piles := Integer'max (num_piles, i);
end loop;
end deal;
procedure k_way_merge is
--
-- k-way merge by tournament tree.
--
-- See Knuth, volume 3, and also
-- https://en.wikipedia.org/w/index.php?title=K-way_merge_algorithm&oldid=1047851465#Tournament_Tree
--
-- However, I store a winners tree instead of the recommended
-- losers tree. If the tree were stored as linked nodes, it
-- would probably be more efficient to store a losers
-- tree. However, I am storing the tree as an array, and one
-- can find an opponent quickly by simply toggling the least
-- significant bit of a competitor's array index.
--
total_external_nodes : Positive;
total_nodes : Positive;
begin
total_external_nodes := next_power_of_two (num_piles);
total_nodes := (2 * total_external_nodes) - 1;
declare
-- In Fortran I had the length-2 dimension come first, to
-- take some small advantage of column-major order. The
-- recommendation for Ada compilers, however, is to use
-- row-major order. So I have reversed the order.
winners : array (1 .. total_nodes, 1 .. 2) of Integer :=
(others => (0, 0));
function find_opponent
(i : Natural)
return Natural is
begin
return (if i rem 2 = 0 then i + 1 else i - 1);
end find_opponent;
function play_game
(i : Positive)
return Positive is
j, iwinner : Positive;
begin
j := find_opponent (i);
if winners (i, 1) = 0 then
iwinner := j;
elsif winners (j, 1) = 0 then
iwinner := i;
elsif less
(arr (winners (j, 1) + ifirst - 1),
arr (winners (i, 1) + ifirst - 1))
then
iwinner := j;
else
iwinner := i;
end if;
return iwinner;
end play_game;
procedure replay_games
(i : Positive) is
j, iwinner : Positive;
begin
j := i;
while j /= 1 loop
iwinner := play_game (j);
j := j / 2;
winners (j, 1) := winners (iwinner, 1);
winners (j, 2) := winners (iwinner, 2);
end loop;
end replay_games;
procedure build_tree is
istart, i, iwinner : Positive;
begin
for i in 1 .. total_external_nodes loop
-- Record which pile a winner will have come from.
winners (total_external_nodes - 1 + i, 2) := i;
end loop;
for i in 1 .. num_piles loop
-- The top of each pile becomes a starting competitor.
winners (total_external_nodes + i - 1, 1) := piles (i);
end loop;
for i in 1 .. num_piles loop
-- Discard the top of each pile
piles (i) := links (piles (i));
end loop;
istart := total_external_nodes;
while istart /= 1 loop
i := istart;
while i <= (2 * istart) - 1 loop
iwinner := play_game (i);
winners (i / 2, 1) := winners (iwinner, 1);
winners (i / 2, 2) := winners (iwinner, 2);
i := i + 2;
end loop;
istart := istart / 2;
end loop;
end build_tree;
isorted, i, next : Integer;
begin
build_tree;
isorted := 0;
while winners (1, 1) /= 0 loop
sorted (sorted'first + isorted) :=
winners (1, 1) + ifirst - 1;
isorted := isorted + 1;
i := winners (1, 2);
next := piles (i); -- The next top of pile i.
if next /= 0 then
piles (i) := links (next); -- Drop that top.
end if;
i := (total_nodes / 2) + i;
winners (i, 1) := next;
replay_games (i);
end loop;
end;
end k_way_merge;
begin
deal;
k_way_merge;
end patience_sort;
begin
-- A demonstration.
declare
type integer_array is array (Integer range <>) of Integer;
procedure integer_patience_sort is new patience_sort
(Integer, integer_array, integer_array);
subtype int25_array is integer_array (1 .. 25);
example_numbers : constant int25_array :=
(22, 15, 98, 82, 22, 4, 58, 70, 80, 38, 49, 48, 46, 54, 93, 8,
54, 2, 72, 84, 86, 76, 53, 37, 90);
sorted_numbers : int25_array := (others => 0);
function less
(x, y : Integer)
return Boolean is
begin
return (x < y);
end less;
begin
integer_patience_sort
(less'access, example_numbers'first, example_numbers'last,
example_numbers, sorted_numbers);
Put ("unsorted ");
for i of example_numbers loop
Put (Integer'image (i));
end loop;
Put_Line ("");
Put ("sorted ");
for i of sorted_numbers loop
Put (Integer'image (example_numbers (i)));
end loop;
Put_Line ("");
end;
end patience_sort_task;
----------------------------------------------------------------------