Alternating Lists
February 1, 2019
This is simple enough:
(define (alternate . xss)
(let loop ((xss xss) (zs (list)))
(cond ((null? xss) (reverse zs))
((null? (car xss)) (loop (cdr xss) zs))
(else (loop (append (cdr xss) (list (cdar xss)))
(cons (caar xss) zs))))))
The only trick is the expression (list (cdar xss)), where the list is required to keep the data structure as a list of lists. Here’s the example problem, with added output to show what is happening inside the loop:
> (alternate '(1 2 3 4 5) '(a b c) '(w x y z))
((1 2 3 4 5) (a b c) (w x y z)) ()
((a b c) (w x y z) (2 3 4 5)) (1)
((w x y z) (2 3 4 5) (b c)) (a 1)
((2 3 4 5) (b c) (x y z)) (w a 1)
((b c) (x y z) (3 4 5)) (2 w a 1)
((x y z) (3 4 5) (c)) (b 2 w a 1)
((3 4 5) (c) (y z)) (x b 2 w a 1)
((c) (y z) (4 5)) (3 x b 2 w a 1)
((y z) (4 5) ()) (c 3 x b 2 w a 1)
((4 5) () (z)) (y c 3 x b 2 w a 1)
(() (z) (5)) (4 y c 3 x b 2 w a 1)
((z) (5)) (4 y c 3 x b 2 w a 1)
((5) ()) (z 4 y c 3 x b 2 w a 1)
(() ()) (5 z 4 y c 3 x b 2 w a 1)
(()) (5 z 4 y c 3 x b 2 w a 1)
() (5 z 4 y c 3 x b 2 w a 1)
(1 a w 2 b x 3 c y 4 z 5)
You can run the program at https://ideone.com/qt9FQ7.
Programming Praxis 
In Ruby. Assumes elements are in the lists are not nil.
Mumps version
LISTS(LISTS) ; S MAX=0 F I=1:1:$L(LISTS,"|") S LEN=$L($P(LISTS,"|",I),";"),MAX=$S(LEN>MAX:LEN,1:MAX) S LIST="" F J=1:1:MAX F I=1:1:$L(LISTS,"|") S CHAR=$P($P(LISTS,"|",I),";",J) S:CHAR'="" LIST=LIST_CHAR_" " Q $E(LIST,1,$L(LIST)-1)1 a w 2 b x 3 c y 4 z 5
— Here’s some Haskell, I’ll leave it to enthusiasts to convert to pointfree style.
-- Interleave elements from a list of lists. -- Corecursive so works with infinite lists. interleave s = aux (filter (not . null) s) where aux [] = [] aux s = map head s ++ interleave (map tail s) -- Specialize to Int to avoid problems with [] iinterleave = interleave :: [[Int]] -> [Int] main = print (iinterleave [[],[]]) >> print (iinterleave [[1,2,3],[]]) >> print (iinterleave [[],[1,2,3]]) >> print (iinterleave [[1,2,3],[4,5,6]]) >> print (iinterleave [[1,2,3],[4,5,6],[7,8,9]]) >> print (take 10 (iinterleave [[1,4..],[2,5..],[3,6..]]))In Python.
from itertools import zip_longest sentinel = object() def alt_lists(*lists): return [xi for x in zip_longest(*lists, fillvalue=sentinel) for xi in x if xi is not sentinel] print(alt_lists([1,2,3,4,5], ["a", "b", "c"], ["w", "x", "y", "z"]))I think my solution is a bit simpler:
(define (alternate x . y)
(cond
((null? y) x)
((null? x)
(apply alternate y))
(else
(cons
(car x)
(apply
alternate
(append y (list (cdr x))))))))
Here’s another Haskell solution. (In pointfree style! :-)
{-# OPTIONS_GHC -fno-warn-type-defaults #-} import Data.List (transpose) alternate :: [[a]] -> [a] alternate = concat . transpose main :: IO () main = do -- From the original problem. print $ alternate [['1', '2', '3', '4', '5'], ['a', 'b', 'c'], ['w', 'x', 'y', 'z']] -- From matthew's solution. print $ alternate [[], [] :: [()]] print $ alternate [[1, 2, 3], []] print $ alternate [[], [1, 2, 3]] print $ alternate [[1, 2, 3], [4, 5, 6]] print $ alternate [[1, 2, 3], [4, 5, 6], [7, 8, 9]] print $ take 10 $ alternate [[1, 4..], [2, 5..], [3, 6..]]@Globules: very nice – it would be good to have a pointfree definition of transpose as well!
Here’s another Haskell version, this one is a simplification of a modification of the Haskell library definition of transpose. I’ve not seen that list comprehension with partial matches idiom before:
And here’s a pointfree Haskell solution that doesn’t seem too incomprehensible:
Here’s an simple-minded scheme solution with filter and map:
(define (not-null? x) (not (null? x)))
(define (splice . lists)
(let ((flists (filter not-null? lists)))
(if (not-null? flists)
(append (map car flists)
(apply splice (map cdr flists)))
'())))
Here’s a solution in C that uses linked lists.
#include <ctype.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct node { char* val; struct node* next; } node_t; void print_list(node_t* list) { while (list != NULL) { printf("%s", list->val); if (list->next != NULL) printf("->"); list = list->next; } printf("\n"); } void free_list(node_t* list) { while (list != NULL) { node_t* next = list->next; free(list); list = next; } } void alternate(node_t** lists, int n, node_t** output) { node_t* list = NULL; int done = 0; while (!done) { done = 1; for (int i = 0; i < n; ++i) { if (lists[i] == NULL) continue; done = 0; node_t* node = malloc(sizeof(node_t)); node->val = lists[i]->val; node->next = list; list = node; lists[i] = lists[i]->next; } } node_t* prev = NULL; node_t* node = NULL; node_t* next = list; while (next != NULL) { prev = node; node = next; next = next->next; node->next = prev; } list = node; *output = list; } int main(int argc, char* argv[]) { int n = 0; int capacity = 1; node_t** lists = malloc(sizeof(node_t*) * capacity); node_t* list = NULL; char* sep = argv[1]; for (int i = argc - 1; i >= 1; --i) { char* arg = argv[i]; if (!strcmp(sep, arg)) { if (list == NULL) continue; ++n; if (n > capacity) { capacity *= 2; lists = realloc(lists, sizeof(node_t*) * capacity); } lists[n - 1] = list; list = NULL; continue; } node_t* node = malloc(sizeof(node_t)); node->next = list; node->val = arg; list = node; } for (int i = 0; i < n / 2; ++i) { node_t* tmp = lists[i]; lists[i] = lists[n - i - 1]; lists[n - i - 1] = tmp; } node_t* alternating = NULL; alternate(lists, n, &alternating); print_list(alternating); for (int i = 0; i < n; ++i) { free_list(lists[i]); } free_list(alternating); free(lists); return EXIT_SUCCESS; }Example:
Here’s a more raw, packageless python implementation I thought of:
def alternator(lists):
max_len = 0
if name == “main“:
lists = [[1,2,3,4,5],[‘a’,’b’,’c’],[‘w’,’x’,’y’,’z’]]
alternator(lists)
Here’s a solution in Common Lisp.
(defun alternate (&rest lists) (labels ((rec (result lists) (let ((lists (remove-if #'null lists))) (if (null lists) result (rec (reduce #'(lambda (a b) (cons b a)) (mapcar #'car lists) :initial-value result) (mapcar #'cdr lists)))))) (reverse (rec (list) lists))))Example.
Here’s a solution in C that uses arrays.
#include <stdlib.h> #include <stdio.h> #include <string.h> #define INIT_CAPACITY 1 typedef struct array { int n; char** data; } array_t; void print_array(array_t* array) { printf("["); for (int i = 0; i < array->n; ++i) { if (i > 0) printf(" "); printf("%s", array->data[i]); } printf("]\n"); } void alternate(array_t* arrays, int n, array_t* output) { output->n = 0; for (int i = 0; i < n; ++i) output->n += arrays[i].n; output->data = malloc(sizeof(char*) * output->n); int col = 0; // index in input data (column of jagged array) int idx = 0; // index in output data while (idx < output->n) { for (int i = 0; i < n; ++i) { if (col >= arrays[i].n) continue; output->data[idx++] = arrays[i].data[col]; } ++col; } } int main(int argc, char* argv[]) { char* sep = argv[1]; int n = 0; for (int i = 1; i < argc; ++i) if (!strcmp(sep, argv[i])) ++n; array_t* arrays = malloc(sizeof(array_t) * n); int capacity = INIT_CAPACITY; for (int i = 0; i < n; ++i) { arrays[i].n = 0; arrays[i].data = malloc(sizeof(char*) * capacity); } int pos = 0; for (int i = 2; i < argc; ++i) { if (!strcmp(sep, argv[i])) { ++pos; capacity = INIT_CAPACITY; continue; } ++(arrays[pos].n); if (arrays[pos].n > capacity) { capacity *= 2; arrays[pos].data = realloc(arrays[pos].data, sizeof(char*) * capacity); } arrays[pos].data[arrays[pos].n - 1] = argv[i]; } array_t alternating; alternate(arrays, n, &alternating); print_array(&alternating); for (int i = 0; i < n; ++i) free(arrays[i].data); free(arrays); free(alternating.data); return EXIT_SUCCESS; }Example:
Here’s a solution in Python.
def alternate(l): l = [list(reversed(x)) for x in l] output = [] while l: l = [x for x in l if x] for x in l: output.append(x.pop()) return output l = [[ 1 , 2 , 3 , 4, 5], ['a', 'b', 'c'], ['w', 'x', 'y', 'z']] print(alternate(l))Output:
Klong version (Does not handle empty list for list entry) Code: f::{[r l2]; r::x; l2::[]; {r::r,*x; l2::l2,(,(1_x))}'y; (,r),(,l2)} g2::{[t]; :[0=+/#'y;x;g2((t::f(x;y))@0; t@1)]} g::{g2([]; x)} Output: {.p(x," --> ",g(x))}'[[[1 2 3 4 5] ["a" "b" "c"] ["W" "X" "Y" "Z"]] [[] []] [[1 2 3] []] [[] [1 2 3]] [[1 2 3] [4 5 6]] [[1 2 3] [4 5 6] [7 8 9]] [[1 4 5 6 7 8 9 10 11 12] [2 5 6 7 8 9 10 11 12] [3 6 7 8 9 10 11 12 13 14]]] [[1 2 3 4 5] [a b c] [W X Y Z] --> 1 a W 2 b X 3 c Y 4 Z 5] [[] [] --> ] [[1 2 3] [] --> 1 2 3] [[] [1 2 3] --> 1 2 3] [[1 2 3] [4 5 6] --> 1 4 2 5 3 6] [[1 2 3] [4 5 6] [7 8 9] --> 1 4 7 2 5 8 3 6 9] [[1 4 5 6 7 8 9 10 11 12] [2 5 6 7 8 9 10 11 12] [3 6 7 8 9 10 11 12 13 14] --> 1 2 3 4 5 6 5 6 7 6 7 8 7 8 9 8 9 10 9 10 11 10 11 12 11 12 13 12 14]