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

Author: Gonzalo Diaz

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`
+
+## 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`
+
+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.

src/hackerrank/interview_preparation_kit/dynamic_programming/max_array_sum.js

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+/**
+ * @link Problem definition [[docs/hackerrank/interview_preparation_kit/dynamic_programming/max_array_sum.md]]
+ * @see Solution Notes: [[docs/hackerrank/interview_preparation_kit/dynamic_programming/max_array_sum-solution-notes.md]]
+ */
+
+const bigIntMax = (...args) =>
+  args.reduce((m, e) => (e > m ? e : m), BigInt(0));
+
+export function maxSubsetSum(arr) {
+  const arrCopy = arr.map((x) => BigInt(x));
+
+  if (arrCopy.length === 0) {
+    return 0;
+  }
+
+  const total = arrCopy.length;
+
+  if (total === 1) {
+    return Number(arrCopy[0]);
+  }
+
+  let tMax = bigIntMax(arrCopy[0], arrCopy[1]);
+  arrCopy[1] = tMax;
+
+  for (let i = 2; i < total; i++) {
+    tMax = bigIntMax(arrCopy[i - 2] + arrCopy[i], tMax);
+    tMax = bigIntMax(arrCopy[i], tMax);
+    arrCopy[i] = tMax;
+  }
+
+  return Number(tMax);
+}
+
+export default { maxSubsetSum };

src/hackerrank/interview_preparation_kit/dynamic_programming/max_array_sum.test.js

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+import { describe, expect, it } from '@jest/globals';
+import { logger as console } from '../../../logger.js';
+
+import { maxSubsetSum } from './max_array_sum.js';
+
+import TEST_CASES from './max_array_sum.testcases.json';
+import TEST_CASE3 from './max_array_sum.testcase3.json';
+
+const ALL_TEST_CASES = [...TEST_CASES, TEST_CASE3];
+
+const DECIMAL_RADIX = 10;
+
+describe('max_array_sum', () => {
+  it('maxSubsetSum test cases', () => {
+    expect.assertions(4);
+
+    ALL_TEST_CASES.forEach((test) => {
+      const answer = maxSubsetSum(test.input).toString(DECIMAL_RADIX);
+
+      console.debug(`maxSubsetSum(${test.input}) solution found: ${answer}`);
+
+      expect(answer).toStrictEqual(test.expected);
+    });
+  });
+
+  it('maxSubsetSum edge case zero', () => {
+    expect.assertions(1);
+
+    const input = [];
+    const expected = 0;
+
+    const answer = maxSubsetSum(input);
+
+    console.debug(`maxSubsetSum(${input}) solution found: ${answer}`);
+
+    expect(answer).toStrictEqual(expected);
+  });
+
+  it('maxSubsetSum edge case one', () => {
+    expect.assertions(1);
+
+    const input = [1];
+    const expected = 1;
+
+    const answer = maxSubsetSum(input);
+
+    console.debug(`maxSubsetSum(${input}) solution found: ${answer}`);
+
+    expect(answer).toStrictEqual(expected);
+  });
+});

src/hackerrank/interview_preparation_kit/dynamic_programming/max_array_sum.testcase3.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"
+  }
+]