Add solution to MagicalCows

Author: William Fiset

src/main/java/com/williamfiset/algorithms/dp/examples/HouseRobber.java renamed to src/main/java/com/williamfiset/algorithms/dp/examples/houserobber/HouseRobber.java

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src/main/java/com/williamfiset/algorithms/dp/examples/magicalcows/01.ans

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src/main/java/com/williamfiset/algorithms/dp/examples/magicalcows/01.in

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src/main/java/com/williamfiset/algorithms/dp/examples/magicalcows/02.ans

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src/main/java/com/williamfiset/algorithms/dp/examples/magicalcows/02.in

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+/**
+ * Solution to Magical Cows (https://open.kattis.com/problems/magicalcows)
+ * Problem author: Graeme Zinck
+ * Solution by: William Fiset
+ *
+ * The main thing to realize with magical cows is that the total number of cows 
+ * allowed on each farm is bounded by C which is less than or equal to 1000, so
+ * you can keep track of all cows in a frequency table for each farm size.
+ * 
+ * NOTE: You can ignore taking the floor/ceiling of the number of cows on a
+ * split since when you double the number of cows you always get an even number.
+ */
+
+import java.io.*;
+import java.util.*;
+
+public class MagicalCows {
+
+  static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
+
+  // The maximum number of days.
+  static final int MAX_DAYS = 50;
+
+  public static void main(String[] args) throws IOException {
+    String[] line = br.readLine().split(" ");
+
+    // The maximum number of cows on a farm
+    final int C = Integer.parseInt(line[0]);
+
+    // The initial number of farms
+    final int N = Integer.parseInt(line[1]);
+
+    // The number of queries
+    final int M = Integer.parseInt(line[2]);
+
+    // The dp table. 
+    long[][] dp = new long[MAX_DAYS+1][C+1];
+
+    // Count the initial frequency of farms of different sizes
+    for (int i = 0; i < N; i++) {
+      int cows = Integer.parseInt(br.readLine());
+      dp[0][cows]++;
+    }
+
+    for (int day = 1; day <= MAX_DAYS; day++) {
+      // For all farm sizes between 1 and `C`, double the number of cows.
+      for (int i = 1; i <= C; i++) {
+        if (2 * i <= C) {
+          // Cow count on farm with size `i` doubled, but the number of farms did not.
+          dp[day][2*i] += dp[day-1][i];
+        } else {
+          // The number of cows per farm on the farm with size `i` exceeds the
+          // permitted limit, so double the number of farms.
+          dp[day][i] += 2 * dp[day-1][i];
+        }
+      }
+    }
+
+    // Answer each query
+    for (int i = 0; i < M; i++) {
+      int day = Integer.parseInt(br.readLine());
+      System.out.println(query(dp, day));
+    }
+  }
+
+  // Find the number of farms on a particular day by summing all farms
+  // of every frequency for that day.
+  private static long query(long[][] dp, int day) {
+    long farms = 0;
+    long[] frequencies = dp[day];
+    for (int i = 0; i < frequencies.length; i++) {
+      farms += frequencies[i];
+    }
+    return farms;
+  }
+
+}
+
+