[Hacker Rank] Interview Preparation Kit: Arrays: Array Manipulation. Solved ✅.

Author: Gonzalo Diaz

algorithm-exercises-java/src/main/java/ae/hackerrank/interview_preparation_kit/arrays/CrushOptimized.java

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+package ae.hackerrank.interview_preparation_kit.arrays;
+
+import java.util.Arrays;
+import java.util.List;
+
+
+/**
+ * Crush (Optimized).
+ *
+ * @link Problem definition [[docs/hackerrank/interview_preparation_kit/arrays/crush.md]]
+ * @link Solution notes [[docs/hackerrank/interview_preparation_kit/arrays/crush_optimized-solution-notes.md]]
+ */
+public class CrushOptimized {
+
+  private CrushOptimized() {
+  }
+
+  static java.util.logging.Logger logger = util.CustomLogger.getLogger();
+
+  /**
+   * arrayManipulation.
+   */
+  public static long arrayManipulation(int n, List<List<Integer>> queries) {
+    // why adding 2?
+    //   first slot to adjust 1-based index and
+    //   last slot for storing accumSum result
+    int[] result = new int[n + 2];
+    Arrays.fill(result, 0);
+    int maximum = 0;
+
+    for (List<Integer> query : queries) {
+      int a = query.get(0);
+      int b = query.get(1);
+      int k = query.get(2);
+
+      // Prefix
+      result[a] += k;
+      result[b + 1] -= k;
+
+      int accumSum = 0;
+      for (int value : result) {
+        accumSum += value;
+        maximum = Math.max(maximum, accumSum);
+      }
+    }
+
+    return maximum;
+  }
+}

algorithm-exercises-java/src/test/java/ae/hackerrank/interview_preparation_kit/arrays/CrushTest.java

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+package ae.hackerrank.interview_preparation_kit.arrays;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import com.fasterxml.jackson.databind.ObjectMapper;
+import java.io.File;
+import java.io.IOException;
+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;
+
+
+@TestInstance(Lifecycle.PER_CLASS)
+class CrushTest {
+
+  public static class CrushTestCase {
+    public String title;
+    public Integer n;
+    public List<List<Integer>> queries;
+    public long expected;
+  }
+
+  List<CrushTestCase> testCases;
+
+  @BeforeAll
+  public void setup() throws IOException {
+    ObjectMapper objectMapper = new ObjectMapper();
+
+    String path = String.join("/", "hackerrank",
+        "interview_preparation_kit",
+        "arrays",
+        "crush.testcases.json");
+    File file = new File(
+        this.getClass()
+        .getClassLoader()
+        .getResource(path)
+        .getFile()
+    );
+
+    ObjectMapper mapper = new ObjectMapper();
+    this.testCases  = mapper.readerForListOf(CrushTestCase.class)
+        .readValue(objectMapper.readTree(file));
+  }
+
+  @Test void testArrayManipulation() {
+    for (CrushTestCase testCase : testCases) {
+      long solutionFound = CrushOptimized
+          .arrayManipulation(testCase.n, testCase.queries);
+
+      assertEquals(testCase.expected, solutionFound,
+          String.format("%s(%d, %s) answer must be: %s",
+            "CrushOptimized.arrayManipulation",
+            testCase.n,
+            testCase.queries.toString(),
+            testCase.expected
+          )
+      );
+    }
+  }
+}

algorithm-exercises-java/src/test/resources/hackerrank/interview_preparation_kit/arrays/crush.testcases.json

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+[
+    {
+        "title": "Sample Test Case 0",
+        "n": 5,
+        "queries": [[1, 2, 100],
+                    [2, 5, 100],
+                    [3, 4, 100]],
+        "expected": 200
+    },
+    {
+        "title": "Sample Test Case 1",
+        "n": 10,
+        "queries": [[1, 5, 3],
+                    [4, 8, 7],
+                    [6, 9, 1]],
+        "expected": 10
+    },
+    {
+        "title": "Sample Test Case 3",
+        "n": 10,
+        "queries": [[2, 6, 8],
+                    [3, 5, 7],
+                    [1, 8, 1],
+                    [5, 9, 15]],
+        "expected": 31
+    }
+]

docs/hackerrank/interview_preparation_kit/arrays/crush.md

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+# [Arrays: Array Manipulation](https://www.hackerrank.com/challenges/crush)
+
+Perform m operations on an array and print the maximum of the values.
+
+- Difficulty:  `#hard`
+- Category: `#ProblemSolvingIntermediate` `#arrays`
+
+Starting with a 1-indexed array of zeros and a list of operations, for each
+operation add a value to each the array element between two given indices,
+inclusive. Once all operations have been performed, return the maximum
+value in the array.
+
+## Example
+
+Queries are interpreted as follows:
+
+```text
+    a b k
+    1 5 3
+    4 8 7
+    6 9 1
+```
+
+Add the values of  between the indices  and  inclusive:
+
+```text
+index->  1 2 3  4  5 6 7 8 9 10
+        [0,0,0, 0, 0,0,0,0,0, 0]
+        [3,3,3, 3, 3,0,0,0,0, 0]
+        [3,3,3,10,10,7,7,7,0, 0]
+        [3,3,3,10,10,8,8,8,1, 0]
+```
+
+The largest value is `10` after all operations are performed.
+
+## Function Description
+
+Complete the function arrayManipulation in the editor below.
+
+arrayManipulation has the following parameters:
+
+- `int n` - the number of elements in the array
+- `int queries[q][3]` - a two dimensional array of queries where
+each `queries[i]` contains three integers, `a`, `b`, and `k`.
+
+## Returns
+
+- int - the maximum value in the resultant array
+
+## Input Format
+
+The first line contains two space-separated integers `n` and `m`, the size of
+the array and the number of operations.
+Each of the next `m` lines contains three space-separated integers
+`a`, `b` and `k`, the left index, right index and summand.
+
+## Constraints
+
+- $ 3 \leq n \leq 10^7 $
+- $ 1 \leq m \leq 2*10^5 $
+- $ 1 \leq a \leq b \leq n $
+- $ 0 \leq k \leq 10^9 $
+
+## Sample Input
+
+```text
+5 3
+1 2 100
+2 5 100
+3 4 100
+```
+
+## Sample Output
+
+```text
+200
+````
+
+## Explanation
+
+After the first update the list is `100 100 0 0 0`.
+After the second update list is `100 200 100 100 100`.
+After the third update list is `100 200 200 200 100`.
+
+The maximum value is `200`.

docs/hackerrank/interview_preparation_kit/arrays/crush_optimized-solution-notes.md

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+# [Array Manipulation](https://www.hackerrank.com/challenges/crush)
+
+Perform m operations on an array and print the maximum of the values.
+
+- Difficulty:  `#hard`
+- Category: `#ProblemSolvingIntermediate` `#arrays`
+
+## Solution sources
+
+### Brute force idea
+
+The first solution attempt is based on the idea of going through:
+
+> each row and then,
+> > each sub-set of elements affected by the operation.
+
+With this principle, the algorithm becomes O(N^2)
+
+### Optimized
+
+Reading about posible optimizations,
+I found the possibility of summarizing the interior traversal with
+addition operations for each element in each row of operations,
+in only 2 constant operations, which represents the necessary values so that
+in a single final traversal, the sum values can be obtained "by drag".
+The algorithm is called "prefix sum."
+
+Some sources about "prefix sum"
+
+- <https://hmn.wiki/en/Prefix_sum>
+- <https://en.wikipedia.org/wiki/Prefix_sum>
+- <https://usaco.guide/silver/prefix-sums?lang=py>
+
+Some sources about implementation in:
+
+- [HackerRank Array Manipulation — beat the clock using Prefix Sum (JavaScript)](https://medium.com/@mlgerardvla/hackerrank-array-manipulation-beat-the-clock-using-prefix-sum-92471060035e)
+- [Hackerrank Discussions Forums: Array Manipulation](https://www.hackerrank.com/challenges/one-month-preparation-kit-crush/forum)