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[Hacker Rank] Interview Preparation Kit: Arrays: Array Manipulation. ... #115

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sir-gon merged 1 commit into main from feature/crush
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Original file line number Diff line number Diff line change
@@ -0,0 +1,46 @@
/**
* Crush (Brute Force).
*
* @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]]
*/

namespace algorithm_exercises_csharp.hackerrank.interview_preparation_kit;

using System.Diagnostics.CodeAnalysis;

public class CrushBruteForce
{
[ExcludeFromCodeCoverage]
protected CrushBruteForce() { }

private const int INITIALIZER = 0;

public static long arrayManipulation(int n, List<List<int>> queries)
{
// why adding 1?
// first slot to adjust 1-based index and
int[] result = new int[n + 1];
Array.Fill(result, INITIALIZER);
int maximum = INITIALIZER;

foreach (List<int> query in queries)
{
int start = query[0];
int end = query[1];
int value = query[2];

for (int i = start; i < end + 1; i++)
{
result[i] += value;
}

foreach (int current in result)
{
maximum = Math.Max(current, maximum);
}
}

return maximum;
}
}
Original file line number Diff line number Diff line change
@@ -0,0 +1,49 @@
/**
* 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]]
*/

namespace algorithm_exercises_csharp.hackerrank.interview_preparation_kit;

using System.Diagnostics.CodeAnalysis;

public class CrushOptimized
{
[ExcludeFromCodeCoverage]
private CrushOptimized() { }

/**
* arrayManipulation.
*/
public static long arrayManipulation(int n, List<List<int>> queries)
{
// why adding 2?
// first slot to adjust 1-based index and
// last slot for storing accumSum result
int[] result = new int[n + 2];
Array.Fill(result, 0);
int maximum = 0;

foreach (List<int> query in queries)
{
int a = query[0];
int b = query[1];
int k = query[2];

// Prefix
result[a] += k;
result[b + 1] -= k;

int accumSum = 0;
foreach (int value in result)
{
accumSum += value;
maximum = Math.Max(maximum, accumSum);
}
}

return maximum;
}
}
Original file line number Diff line number Diff line change
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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
}
]
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Original file line number Diff line number Diff line change
Expand Up @@ -60,6 +60,7 @@

<ItemGroup>
<EmbeddedResource Include="Resources/hackerrank/interview_preparation_kit/arrays/ctci_array_left_rotation.testcases.json" />
<EmbeddedResource Include="Resources/hackerrank/interview_preparation_kit/arrays/crush.testcases.json" />
<EmbeddedResource Include="Resources/hackerrank/interview_preparation_kit/dictionaries_and_hashmaps/ctci_ransom_note.testcases.json" />
<EmbeddedResource Include="Resources/hackerrank/interview_preparation_kit/dictionaries_and_hashmaps/two_strings.testcases.json" />
<EmbeddedResource Include="Resources/hackerrank/interview_preparation_kit/greedy_algorithms/luck_balance.testcases.json" />
Expand Down
Original file line number Diff line number Diff line change
@@ -0,0 +1,36 @@
namespace algorithm_exercises_csharp.hackerrank.interview_preparation_kit;

[TestClass]
public class CrushBruteForceTest
{
public class CrushBruteForceTestCase
{
public string title { get; set; } = default!;
public List<List<int>> queries { get; set; } = default!;
public int n { get; set; } = default!;
public long expected { get; set; } = default!;
}

private List<CrushBruteForceTestCase> testCases { get; set; } = default!;

[TestInitialize]
public void testInitialize()
{
testCases = JsonLoader.resourceLoad<List<CrushBruteForceTestCase>>(
"hackerrank/interview_preparation_kit/arrays/crush.testcases.json"
) ?? [];
}

[TestMethod]
public void testArrayManipulation()
{
long result;

foreach (CrushBruteForceTestCase test in testCases)
{
result = CrushBruteForce.arrayManipulation(test.n, test.queries);
Assert.AreEqual(test.expected, result);
}
}
}

Original file line number Diff line number Diff line change
@@ -0,0 +1,36 @@
namespace algorithm_exercises_csharp.hackerrank.interview_preparation_kit;

[TestClass]
public class CrushOptimizedTest
{
public class CrushOptimizedTestCase
{
public string title { get; set; } = default!;
public List<List<int>> queries { get; set; } = default!;
public int n { get; set; } = default!;
public long expected { get; set; } = default!;
}

private List<CrushOptimizedTestCase> testCases { get; set; } = default!;

[TestInitialize]
public void testInitialize()
{
testCases = JsonLoader.resourceLoad<List<CrushOptimizedTestCase>>(
"hackerrank/interview_preparation_kit/arrays/crush.testcases.json"
) ?? [];
}

[TestMethod]
public void testArrayManipulation()
{
long result;

foreach (CrushOptimizedTestCase test in testCases)
{
result = CrushOptimized.arrayManipulation(test.n, test.queries);
Assert.AreEqual(test.expected, result);
}
}
}

85 changes: 85 additions & 0 deletions 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`.
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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)

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