Add: Dynamic Programming - Count of Subsets With A Given Difference

Author: alpha037

DynamicProgramming/CountOfSubsetsWithAGivenDifference/Solution.java

@@ -0,0 +1,74 @@
+package DynamicProgramming.CountOfSubsetsWithAGivenDifference;
+
+import java.util.Arrays;
+
+/**
+ * * Count of Subsets With A Given Difference (Variation of 0/1 Knapsack)
+ */
+
+public class Solution {
+  public int countOfSubsets(int[] array, int difference) {
+    int sum = Arrays.stream(array).sum();
+
+    return countOfSubsetsDP(array, sum, difference);
+  }
+
+  /**
+   * * Dynamic Programming Approach
+   * 
+   * * TC: O(ns)
+   * * SC: O(ns)
+   */
+  private int countOfSubsetsDP(int[] array, int sum, int difference) {
+    /**
+     * Equation I: S1 - S2 = difference
+     * Equation II: S1 + S2 = sum(array)
+     * 
+     * Adding I and II,
+     * 
+     * 2S1 = sum(array) + difference
+     * so, S1 = (sum(array) + difference) / 2
+     * 
+     * Now, we need to find the count of
+     * subsets equal to a given sum, which
+     * is S1
+     */
+    int target = (sum + difference) / 2;
+
+    return countOfSubsetsDP(array, target);
+  }
+
+  private int countOfSubsetsDP(int[] array, int sum) {
+    int len = array.length;
+    int[][] dp = new int[len + 1][sum + 1];
+
+    for (int i = 0; i < len + 1; i++) dp[i][0] = 1;
+
+    for (int j = 1; j < sum + 1; j++) dp[0][j] = 0;
+
+    for (int i = 1; i < len + 1; i++) {
+      for (int j = 1; j < sum + 1; j++) {
+        // If the current item is less than
+        // or equal to the current sum, then we
+        // need to consider both the scenarios
+        // where we include this current item and
+        // where we don't include this current item
+        if (array[i - 1] <= j) dp[i][j] = dp[i - 1][j] + dp[i - 1][j - array[i - 1]];
+
+        // If the current item is greater
+        // than our current sum, then there's
+        // only one scenario where we don't
+        // include this current item
+        else dp[i][j] = dp[i - 1][j];
+      }
+    }
+
+    return dp[len][sum];
+  }
+
+  public static void main(String[] args) {
+    Solution solution = new Solution();
+
+    System.out.println(solution.countOfSubsets(new int[] {1, 1, 2, 3}, 1));
+  }
+}