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Sorting lists: 1. Slow Sort

Sorting lists: 1. Slow Sort. inorder ( []). inorder ([_]). inorder ([A,B|T]) :- A < B, inorder ([B|T]). % slow_sort (L, S): Sorts list L, returning S. % Keep permuting L until it becomes sorted. slowsort (L, S) :- permutation(L, S), inorder (S). permutation([ ], [ ]).

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Sorting lists: 1. Slow Sort

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  1. Sorting lists: 1. Slow Sort inorder( []). inorder([_]). inorder([A,B|T]) :- A < B, inorder([B|T]). COSC 2P93 : More examples % slow_sort(L, S): Sorts list L, returning S. % Keep permuting L until it becomes sorted. slowsort(L, S) :- permutation(L, S), inorder(S). permutation([ ], [ ]). permutation(L, [H|T]) :- append(V, [H|U], L), append(V, U, W), permutation(W, T).

  2. 2. Bubble sort COSC 2P93 : More examples bubblesort(L, S) :- append(X, [A,B|Y], L), B < A, append(X, [B,A|Y], L2), bubblesort(L2, S). bubblesort(L, L).

  3. 3. Insertion sort COSC 2P93 : More examples insort([ ], [ ]). insort([X|L], M) :- insort(L, N), insortx(X, N, M). insortx(X, [ ], [X]). insortx(X, [A|L], [A|M]) :- A < X, insortx(X, L, M). insortx(X, [A|L], [X,A|L]) :- A >= X.

  4. 4. Quick sort COSC 2P93 : More examples qsort([], []). qsort([H|T], S) :- split(H, T, A, B), qsort(A, AS), qsort(B, BS), append(AS, [H|BS], S).

  5. Quick sort (cont) COSC 2P93 : More examples % split(H, L, Less, Greater): % All items in L that are less in value than H are put in Less (in order). % The rest are put in Greater (in order). split(_, [], [], []). split(H, [A|X], [A|Y], Z) :- A < H, split(H, X, Y, Z). split(H, [A|X], Y, [A|Z]) :- A >= H, split(H, X, Y, Z).

  6. Lotto 6/49 simulator COSC 2P93 : More examples % Lotto 6/49 generator: generate 6 random numbers (no duplicates!) ?- use_module(library(random)). %  include random number library (Sicstus) lotto649(Numbers) :- make_intlist(1, 49, All), % see previous overheads! select_random(6, All, Numbers). % select_random(N, A, L): selects N numbers from A, putting them in L select_random(N, _, [ ]) :- N =< 0. select_random(N, All, [Number | Rest]) :- N > 0, size(All, Size), % see “count” from assignment generate_random_int(1, Size, R), remove_nth(R, All, Number, Leftover), M is N - 1, select_random(M, Leftover, Rest).

  7. Lotto 6/49 (cont) COSC 2P93 : More examples % generate random value between Low and High, incl. % random/1 returns random float between [0.0, 1.0). (ie. never 1.0) generate_random_int(Low, High, R) :- Range is High - Low + 1, random(X), % Sicstusbuiltin R is integer(X * Range) + Low. % remove_nth(R, All, Item, Rest) removes the Rth entry Item from All, % leaving Rest. R is between 1 and the size of All. remove_nth(1, [Item|Rest], Item, Rest). remove_nth(N, [X|All], Item, [X|Rest]) :- M is N - 1, remove_nth(M, All, Item, Rest).

  8. Another Lotto 6/49 program COSC 2P93 : More examples This version accepts an integer seed to scramble random numbers (could do this in previous program as well!) ?- use_module(library(random)). lotto649(Seed, Numbers) :- make_intlist(1, 49, All), setrand(Seed), random_permutation(All, [A,B,C,D,E,F| _ ]), % Sicstus built-in sort([A,B,C,D,E,F], Numbers).

  9. Integer puzzle solver COSC 2P93 : More examples • problem: given a list of integers between 1 and N, generate lists of unique integers from this list that add up to a given integer value % int_puzzle(H, N, L) solves the problem in L for integers ranging from 1 to H, adding to value N int_puzzle(High, Number, List) :- make_intlist(1, High, All), find_soln(Number, All, List). find_soln(0, _, [ ]). find_soln(Tot, All, [Num|List]) :- Tot > 0, remove(Num, All, Rest), NewTot is Tot-Num, find_soln(NewTot, Rest, List).

  10. int_puzzle(cont) COSC 2P93 : More examples % remove(N, L, R) removes item N from list L, resulting in R. % Will fail if N is not found in L. remove(N, [N|L], L). remove(N, [A|R], [A|L]) :- remove(N, R, L). • One problem with int_puzzle: returns permutations of solutions • Later, will modify to keep track of unique solutions, and filter duplicated ones

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