add CombinationSum and test

Author: Avaneeshakrishna

src/main/java/com/thealgorithms/backtracking/CombinationSum.java

@@ -0,0 +1,31 @@
+package com.thealgorithms.backtracking;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+/** Backtracking: pick/not-pick with reuse of candidates. */
+public class CombinationSum {
+
+    public static List<List<Integer>> combinationSum(int[] candidates, int target) {
+        Arrays.sort(candidates); // helps pruning
+        List<List<Integer>> res = new ArrayList<>();
+        backtrack(candidates, target, 0, new ArrayList<>(), res);
+        return res;
+        // Note: result order is not guaranteed; compare sorted in tests if needed
+    }
+
+    private static void backtrack(int[] nums, int remain, int start, List<Integer> path, List<List<Integer>> res) {
+        if (remain == 0) {
+            res.add(new ArrayList<>(path));
+            return;
+        }
+        for (int i = start; i < nums.length; i++) {
+            int val = nums[i];
+            if (val > remain) break; // prune
+            path.add(val);
+            backtrack(nums, remain - val, i, path, res); // i (reuse allowed)
+            path.remove(path.size() - 1);
+        }
+    }
+}

src/test/java/com/thealgorithms/backtracking/CombinationSumTest.java

@@ -0,0 +1,31 @@
+package com.thealgorithms.backtracking;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import java.util.ArrayList;
+import java.util.Comparator;
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+class CombinationSumTest {
+
+    private static List<List<Integer>> norm(List<List<Integer>> x) {
+        List<List<Integer>> y = new ArrayList<>();
+        for (var p : x) {
+            var q = new ArrayList<>(p);
+            q.sort(Integer::compare);
+            y.add(q);
+        }
+        y.sort(Comparator.<List<Integer>, Integer>comparing(List::size)
+            .thenComparing(a -> a.toString()));
+        return y;
+    }
+
+    @Test
+    void sample() {
+        int[] candidates = {2,3,6,7};
+        int target = 7;
+        var expected = List.of(List.of(2,2,3), List.of(7));
+        assertEquals(norm(expected), norm(CombinationSum.combinationSum(candidates, target)));
+    }
+}