1+ /**
2+ * Solution to Magical Cows (https://open.kattis.com/problems/magicalcows)
3+ *
4+ * <p>Problem author: Graeme Zinck
5+ *
6+ * <p>Solution by: William Fiset
7+ *
8+ * <p>The main thing to realize with magical cows is that the total number of cows allowed on each
9+ * farm is bounded by C which is less than or equal to 1000, so you can keep track of all cows in a
10+ * frequency table for each farm size.
11+ *
12+ * <p>NOTE: You can ignore taking the floor/ceiling of the number of cows on a split since when you
13+ * double the number of cows you always get an even number.
14+ */
15+ import java .io .*;
16+ import java .util .*;
17+ 18+ public class MagicalCows {
19+ 20+ static BufferedReader br = new BufferedReader (new InputStreamReader (System .in ));
21+ 22+ // The maximum number of days.
23+ static final int MAX_DAYS = 50 ;
24+ 25+ public static void main (String [] args ) throws IOException {
26+ String [] line = br .readLine ().split (" " );
27+ 28+ // The maximum number of cows on a farm
29+ final int C = Integer .parseInt (line [0 ]);
30+ 31+ // The initial number of farms
32+ final int N = Integer .parseInt (line [1 ]);
33+ 34+ // The number of queries
35+ final int M = Integer .parseInt (line [2 ]);
36+ 37+ // The dp table.
38+ long [][] dp = new long [MAX_DAYS + 1 ][C + 1 ];
39+ 40+ // Count the initial frequency of farms of different sizes
41+ for (int i = 0 ; i < N ; i ++) {
42+ int cows = Integer .parseInt (br .readLine ());
43+ dp [0 ][cows ]++;
44+ }
45+ 46+ for (int day = 0 ; day < MAX_DAYS ; day ++) {
47+ // For all farm sizes between 1 and `C`, double the number of cows.
48+ for (int i = 1 ; i <= C ; i ++) {
49+ if (i <= C / 2 ) {
50+ // Cow count on farm with size `i` doubled, but the number of farms did not.
51+ dp [day + 1 ][i * 2 ] += dp [day ][i ];
52+ } else {
53+ // The number of cows per farm on the farm with size `i` exceeds the
54+ // permitted limit, so double the number of farms.
55+ dp [day + 1 ][i ] += 2 * dp [day ][i ];
56+ }
57+ }
58+ }
59+ 60+ // Answer each query
61+ for (int i = 0 ; i < M ; i ++) {
62+ int day = Integer .parseInt (br .readLine ());
63+ System .out .println (query (dp , day ));
64+ }
65+ }
66+ 67+ // Find the number of farms on a particular day by summing all farms
68+ // of every frequency for that day.
69+ private static long query (long [][] dp , int day ) {
70+ long farms = 0 ;
71+ long [] frequencies = dp [day ];
72+ for (int i = 0 ; i < frequencies .length ; i ++) {
73+ farms += frequencies [i ];
74+ }
75+ return farms ;
76+ }
77+ }
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