Partitioning Logic

Partitioning logic refers to algorithms that divide a problem or data structure into smaller partitions to enable parallel or more efficient processing.

Some examples include:

  • Divide and conquer algorithms
  • Hash partitioning in distributed systems
  • Partitioning for parallel map-reduce
  • Database sharding and partitioning

Java - Array quicksort partitioning:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12

int partition(int[] arr, int low, int high) {
  int pivot = arr[high];
  int i = low;
  for (int j = low; j < high; j++) {
    if (arr[j] < pivot) {
      swap(arr, i, j);
      i++;
    }
  }
  swap(arr, i, high);
  return i;
}

C++ - Graph partitioning for distribution:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12

void partitionGraph(Graph graph, int npartitions) {

  vector<vector<Node>> partitions(npartitions);
  
  // Clustering logic
  // Assign nodes to partitions

  for (int i = 0; i < npartitions; i++) {
    assignPartition(partitions[i]); 
  }

}

Python - Database sharding:

1
2
3
4
5
6
7
8
9

def shard_database(db):

  # Partition DB into N shards
  shards = partition_db(db, N) 

  for shard in shards:
    distribute_shard(shard)

  # Routing logic to route queries

Partitioning decomposes problems into independently solvable chunks, enabling parallelism. Useful across domains.

Quick Select and Quick Sort algorithms use a partitioning logic where an element is placed at its correct position in the sorted array, and all elements smaller than it are placed to its left, and all larger elements to its right. This is done through a partition function.

Here are some LeetCode problems that can be solved using this partitioning logic:

  1. Find the kth largest (or smallest) element in an unsorted array:

    • Kth Largest Element in an Array. This problem can be solved using Quick Select algorithm, which is an efficient in-place variation of Quick Sort that is used to select the kth largest element.

  2. Sort an array:

    • Sort an Array. This is a basic application of the Quick Sort algorithm.

  3. Color Sort:

    • Sort Colors. This problem is a variation of the Dutch national flag problem, which can be solved using a three-way partitioning algorithm, a variant of Quick Sort partitioning.

  4. Find the kth smallest element in a sorted matrix:

  5. Wiggle Sort:

    • Wiggle Sort II. This problem can be solved using a variant of Quick Select to find the median and then partition the array.

While these problems can be solved using partitioning logic, there may be other efficient algorithms and approaches to solve them depending on the constraints and requirements of the problem.

Code

Here’s a simple example of the partitioning logic of Quick Select / Quick Sort in Python:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12

def partition(arr, low, high):
    pivot = arr[high]     # Choose pivot as the last element
    i = low - 1           # Index of smaller element
  
    for j in range(low, high):
        # If current element is smaller than or equal to pivot
        if arr[j] <= pivot:
            i = i + 1
            arr[i], arr[j] = arr[j], arr[i]  # Swap elements
  
    arr[i + 1], arr[high] = arr[high], arr[i + 1]  # Swap pivot into place
    return i + 1  # Return pivot index

The partition function takes an array arr and two indexes low and high, and rearranges the array such that all elements less than arr[high] (the pivot) are to the left of it, and all elements greater than arr[high] are to the right. It then returns the index of the pivot element.

This is a simple, in-place implementation of the partitioning logic. You could use it as a building block for more complex problems that require partitioning, such as the LeetCode problems mentioned in the previous response.

In Quick Select or Quick Sort, you would typically follow up this partitioning step with recursive calls to process the two partitions.