[Hacker Rank] Interview Preparation Kit: Dynamic Programming: Max Array Sum. Solved ✓.

Author: Gonzalo Diaz

algorithm-exercises-java/src/main/java/ae/hackerrank/interview_preparation_kit/dynamic_programming/MaxArraySum.java

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+// @link Problem definition
+// [[docs/hackerrank/interview_preparation_kit/dynamic_programming/max_array_sum.md]]
+
+package ae.hackerrank.interview_preparation_kit.dynamic_programming;
+
+import java.util.List;
+
+public class MaxArraySum {
+  private MaxArraySum() {}
+
+  public static int maxSubsetSum(List<Integer> arr) {
+    int total = arr.size();
+
+    if (total == 0) { // Edge case
+        return 0;
+    }
+
+    if (total == 1) { // Edge case
+        return arr.get(0);
+    }
+
+    // Base case start from index 0 and 1
+    int tMax = Math.max(arr.get(0), arr.get(1));
+    arr.set(1, tMax);
+
+    for (int i = 2; i < total; i++) {
+        tMax = Math.max(arr.get(i - 2) + arr.get(i), tMax); // Max uptill now
+        tMax = Math.max(arr.get(i), tMax); // Max in special case where
+        // arr[i] + previous max is still less than arr[i]
+        // update our inplace array with max for future calculations
+        arr.set(i, tMax);
+    }
+
+    return tMax;
+  }
+}

algorithm-exercises-java/src/test/java/ae/hackerrank/interview_preparation_kit/dynamic_programming/MaxArraySumTest.java

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+package ae.hackerrank.interview_preparation_kit.dynamic_programming;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import java.io.IOException;
+import java.util.ArrayList;
+import java.util.List;
+import org.junit.jupiter.api.BeforeAll;
+import org.junit.jupiter.api.Test;
+import org.junit.jupiter.api.TestInstance;
+import org.junit.jupiter.api.TestInstance.Lifecycle;
+import util.JsonLoader;
+
+/** MaxArraySumTest. */
+@TestInstance(Lifecycle.PER_CLASS)
+class MaxArraySumTest {
+  public static class MaxArraySumTestCase {
+    public String title;
+    public List<Integer> input;
+    public Integer expected;
+  }
+
+  private final List<MaxArraySumTestCase> testCases = new ArrayList<>();
+
+  @BeforeAll
+  void setup() throws IOException {
+    String path =
+        String.join(
+            "/",
+            "hackerrank",
+            "interview_preparation_kit",
+            "dynamic_programming",
+            "max_array_sum.testcases.json");
+
+    this.testCases.clear();
+    this.testCases.addAll(JsonLoader.loadJson(path, MaxArraySumTestCase.class));
+  }
+
+  @Test
+  void testMaxArraySum() {
+    for (MaxArraySumTestCase test : testCases) {
+      int solutionFound = MaxArraySum.maxSubsetSum(test.input);
+
+      assertEquals(
+          test.expected,
+          solutionFound,
+          "%s(%s) answer must be: %d"
+              .formatted("MaxArraySum.maxSubsetSum", test.input.toString(), test.expected));
+    }
+  }
+}

algorithm-exercises-java/src/test/resources/hackerrank/interview_preparation_kit/dynamic_programming/max_array_sum.testcases.json

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+[
+  {
+    "title": "Sample Test case 0",
+    "input": [3, 7, 4, 6, 5],
+    "expected": 13
+  },
+  {
+    "title": "Sample Test case 1",
+    "input": [2, 1, 5, 8, 4],
+    "expected": 11
+  },
+  {
+    "title": "Sample Test case 2",
+    "input": [3, 5, -7, 8, 10],
+    "expected": 15
+  }
+]

docs/hackerrank/interview_preparation_kit/dynamic_programming/max_array_sum-solution-notes.md

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+# [Dynamic Programming: Max Array Sum](https://www.hackerrank.com/challenges/max-array-sum)
+
+- Difficulty:  `#medium`
+- Category: `#ProblemSolvingIntermediate` `#dynamicprogramming`
+
+## Sources
+
+- [Max Array Sum — HackerRank Medium Using Inplace Dynamic Programming](https://iawale.medium.com/max-array-sum-hackerrank-medium-using-inplace-dynamic-programming-215a620d7705)

docs/hackerrank/interview_preparation_kit/dynamic_programming/max_array_sum.md

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+# [Dynamic Programming: Max Array Sum](https://www.hackerrank.com/challenges/max-array-sum)
+
+- Difficulty:  `#medium`
+- Category: `#ProblemSolvingIntermediate` `#dynamicprogramming`
+
+Given an array of integers, find the subset of
+non-adjacent elements with the maximum sum.
+Calculate the sum of that subset.
+It is possible that the maximum sum is `0`, the case when all elements are negative.
+
+## Example
+
+`arr = [-2, 1, 3, -4, 5]`
+
+The following subsets with more than  element exist.
+These exclude the empty subset and single element subsets which are also valid.
+
+```text
+Subset      Sum
+[-2, 3, 5]   6
+[-2, 3]      1
+[-2, -4]    -6
+[-2, 5]      3
+[1, -4]     -3
+[1, 5]       6
+[3, 5]       8
+```
+
+The maximum subset sum is . Note that any individual element is a subset as well.
+
+`arr = [-2, -3, -1]`
+
+In this case, it is best to choose no element: return `0`.
+
+## Function Description
+
+Complete the `maxSubsetSum` function in the editor below.
+
+maxSubsetSum has the following parameter(s):
+
+- `int arr[n]`: an array of integers
+
+## Returns
+
+- `int`: the maximum subset sum
+
+## Input Format
+
+The first line contains an integer, `n`.
+The second line contains `n` space-separated integers `arr[i]`.
+
+## Constraints
+
+- $ 1 \leq n \leq 10^5 $
+- $ -10^4 \leq arr[i] \leq 10^4 $
+
+## Sample Input 0
+
+```text
+5
+3 7 4 6 5
+```
+
+## Sample Output 0
+
+```text
+13
+```
+
+## Explanation 0
+
+Our possible subsets are `[3, 4, 5]`. `[3, 4]`, `[3, 6]`, `[3, 5]`, `[7, 6]`,
+`[7, 5]` and `[4, 5]`.
+The largest subset sum is `13` from subset `[7, 6]`
+
+## Sample Input 1
+
+```text
+5
+2 1 5 8 4
+```
+
+## Sample Output 1
+
+```text
+11
+```
+
+## Explanation 1
+
+Our subsets are `[2, 5, 4]`, `[2, 5]`, `[2, 8]`, `[2, 4]`, `[1, 8]`,
+`[1, 4]` and `[5, 4]`.
+The maximum subset sum is `11` from the first subset listed.
+
+## Sample Input 2
+
+```text
+5
+3 5 -7 8 10
+```
+
+## Sample Output 2
+
+```text
+15
+```
+
+## Explanation 2
+
+Our subsets are `[3, -7, 10]`, `[3, 8]`, `[3,10]`, `[5, 8]`,
+`[5, 10]` and `[-7, 10]`.
+
+The maximum subset sum is `15` from the fifth subset listed.