Equal Row and Column Pairs

class TrieNode {
    int countElem;
    Map<Integer, TrieNode> childNodes;

    public TrieNode() {
        this.countElem = 0;
        this.childNodes = new HashMap<>();
    }
}

class Trie {
    TrieNode root;

    public Trie() {
        this.root = new TrieNode();
    }

    public void insert(int[] sequence) {
        TrieNode current = this.root;
        for (int num : sequence) {
            if (!current.childNodes.containsKey(num)) {
                current.childNodes.put(num, new TrieNode());
            }
            current = current.childNodes.get(num);
        }
        current.countElem += 1;
    }

    public int find(int[] sequence) {
        TrieNode current = this.root;
        for (int num : sequence) {
            if (current.childNodes.containsKey(num)) {
                current = current.childNodes.get(num);
            } else {
                return 0;
            }
        }
        return current.countElem;
    }
}

class Solution {
    public int equalPairs(int[][] matrix) {
        Trie trieData = new Trie();
        int matchCount = 0, n = matrix.length;
        
        for (int[] row : matrix) {
            trieData.insert(row);
        }
        
        for (int col = 0; col < n; ++col) {
            int[] columnData = new int[n];
            for (int row = 0; row < n; ++row) {
                columnData[row] = matrix[row][col];
            }
            matchCount += trieData.find(columnData);
        }
    
        return matchCount;
    }
}

The provided Java code defines a solution for determining the number of matching rows and columns in a given matrix using a Trie data structure. Here are the core components and functionality:

• TrieNode Class

  • This class represents each node of the Trie which contains:
    • countElem: Counter for the number of times a sequence (row or column of the matrix) ends at this node.
    • childNodes: A map (integer to TrieNode) holding children nodes, essentially, the next number in the sequence and its corresponding TrieNode.

• Trie Class

  • This class encompasses the operations related to the Trie:
    • insert(int[] sequence): Takes an array of integers (sequence) and inserts it into the Trie. If a number in the sequence does not exist as a child of the current node, it creates a new TrieNode for that number.
    • find(int[] sequence): Checks if a sequence exists in the Trie and returns the count of how many times this exact sequence has been added (stored in countElem).

• Solution Class

  • Contains the method equalPairs(int[][] matrix) which calculates how many times rows and columns in the matrix are equal.
    • A Trie named trieData is initialized.
    • Rows of the matrix are inserted into the Trie.
    • Each column of the matrix is then constructed and checked against entries in the Trie using the find method. The total matches are accumulated in matchCount.

The final functionality allows the calculation of equal row and column pairs by leveraging a Trie to efficiently match and count the sequences, giving an optimized approach to solving the problem in question. This method highlights the effective use of Trie for multidimensional array operations, where sequences are key elements of the computation.

class TrieNode:
    def __init__(self):
        self.node_count = 0
        self.children_map = {}

class TrieStructure:
    def __init__(self):
        self.root = TrieNode()

    def insert(self, sequence):
        node = self.root
        for element in sequence:
            if element not in node.children_map:
                node.children_map[element] = TrieNode()
            node = node.children_map[element]
        node.node_count += 1

    def search(self, sequence):
        node = self.root
        for element in sequence:
            if element in node.children_map:
                node = node.children_map[element]
            else:
                return 0
        return node.node_count

class Solution:
    def equalPairs(self, grid: List[List[int]]) -> int:
        trie = TrieStructure()
        pair_count = 0
        grid_size = len(grid)
        
        for row in grid:
            trie.insert(row)
        
        for index in range(grid_size):
            column = [grid[row_index][index] for row_index in range(grid_size)]
            pair_count += trie.search(column)
    
        return pair_count

The given Python program implements a solution to the problem of finding equal row and column pairs in a grid using a Trie data structure. Here’s an overview of how the solution works:

• Define a TrieNode class which contains:

  • node_count: to track the number of sequences that terminate at this node.
  • children_map: a dictionary to store child nodes.

• Define a TrieStructure class which includes:

  • A root TrieNode.
  • insert method: inserts a sequence (array of integers) into the trie. Each element of the sequence becomes a node in the trie if not already present.
  • search method: searches for a sequence in the trie and returns the count of how many times that sequence has been inserted.

• Define a Solution class with a method equalPairs:

  • Initializes a TrieStructure.
  • Loops through each row of the grid and inserts each row into the trie.
  • Constructs each column of the grid iteratively and uses the search method to determine how many times the column appears as a row in the trie. This count is added to pair_count.

The program effectively counts the number of times a row and column in a grid are identical by leveraging the efficient lookup and insert operations of a trie. The final output, pair_count, represents the total number of pairs of identical rows and columns.