1+ /**
2+ * Here I show how you can generate all the combinations of a sequence of size r which are repeated
3+ * at most k times.
4+ *
5+ * <p>Time Complexity: O(n+r-1 choose r) = O((n+r-1)!/(r!(n-1)!))
6+ *
7+ * @author William Fiset, william.alexandre.fiset@gmail.com
8+ */
9+ package com .williamfiset .algorithms .other ;
10+ 11+ public class CombinationsWithRepetition {
12+ 13+ /**
14+ * Computes all combinations of elements of 'r' elements which can be repeated at most 'k' times
15+ * each.
16+ *
17+ * @param sequence - The sequence containing all the elements we wish to take combinations from
18+ * @param usedCount - Tracks how many of each element we currently have selected
19+ * @param at - The current position we're at in the sequence
20+ * @param r - The number of elements we're choosing
21+ * @param k - The maximum number of times each element is allowed to be picked
22+ */
23+ private static void combinationsWithRepetition (
24+ int [] sequence , int [] usedCount , int at , int r , int k ) {
25+ 26+ final int N = sequence .length ;
27+ 28+ // We reached the end
29+ if (at == N ) {
30+ 31+ // We selected 'r' elements in total
32+ if (r == 0 ) {
33+ 34+ // Print combination
35+ System .out .print ("{ " );
36+ for (int i = 0 ; i < N ; i ++)
37+ for (int j = 0 ; j < usedCount [i ]; j ++) System .out .print (sequence [i ] + " " );
38+ System .out .println ("}" );
39+ }
40+ 41+ } else {
42+ 43+ // For this particular time at position 'at' try including it each of [0, k] times
44+ for (int itemCount = 0 ; itemCount <= k ; itemCount ++) {
45+ 46+ // Try including this element itemCount number of times (this is possibly more than once)
47+ usedCount [at ] = itemCount ;
48+ 49+ combinationsWithRepetition (sequence , usedCount , at + 1 , r - itemCount , k );
50+ }
51+ }
52+ }
53+ 54+ // Given a sequence this method prints all the combinations of size
55+ // 'r' in a given sequence which has each element repeated at most 'k' times
56+ public static void printCombinationsWithRepetition (int [] sequence , int r , int k ) {
57+ 58+ if (sequence == null ) return ;
59+ final int n = sequence .length ;
60+ if (r > n ) throw new IllegalArgumentException ("r must be <= n" );
61+ if (k > r ) throw new IllegalArgumentException ("k must be <= r" );
62+ 63+ int [] usedCount = new int [sequence .length ];
64+ combinationsWithRepetition (sequence , usedCount , 0 , r , k );
65+ }
66+ 67+ public static void main (String [] args ) {
68+ 69+ // Prints all combinations of size 3 where
70+ // each element is repeated at most twice
71+ int [] seq = {1 , 2 , 3 , 4 };
72+ printCombinationsWithRepetition (seq , 3 , 2 );
73+ // prints:
74+ // { 3 4 4 }
75+ // { 3 3 4 }
76+ // { 2 4 4 }
77+ // { 2 3 4 }
78+ // { 2 3 3 }
79+ // { 2 2 4 }
80+ // { 2 2 3 }
81+ // { 1 4 4 }
82+ // { 1 3 4 }
83+ // { 1 3 3 }
84+ // { 1 2 4 }
85+ // { 1 2 3 }
86+ // { 1 2 2 }
87+ // { 1 1 4 }
88+ // { 1 1 3 }
89+ // { 1 1 2 }
90+ 91+ }
92+ }
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