2352. Equal Row and Column Pairs

Description of Problem

Given a 0-indexed n x n integer matrix grid, return the number of pairs (ri, cj) such that row ri and column cj are equal.

A row and column pair is considered equal if they contain the same elements in the same order (i.e., an equal array).

Example 1:

Input: grid = [[3,2,1],[1,7,6],[2,7,7]]
Output: 1
Explanation: There is 1 equal row and column pair:
- (Row 2, Column 1): [2,7,7]

Example 2:

Input: grid = [[3,1,2,2],[1,4,4,5],[2,4,2,2],[2,4,2,2]]
Output: 3
Explanation: There are 3 equal row and column pairs:
- (Row 0, Column 0): [3,1,2,2]
- (Row 2, Column 2): [2,4,2,2]
- (Row 3, Column 2): [2,4,2,2]

Constraints:

• n == grid.length == grid[i].length
• 1 <= n <= 200
• 1 <= grid[i][j] <= 10^5

Solution

Code (Rust)

impl Solution {
    pub fn equal_pairs(grid: Vec<Vec<i32>>) -> i32 {
        use std::collections::HashMap;
        let n = grid.len();
       
        let mut map = HashMap::new();
        for j in 0..n{
            let mut v = Vec::new();
            for k in 0..n{
                v.push(grid[k][j]);
            }

            if let Some(c) = map.get_mut(&v){
                *c +=1;
            }else{
                map.insert(v, 1);
            }
        }

        let mut count = 0;
        for row in grid.iter() {
            if let Some(&c) = map.get(row){
                count+=c;
            }
        }

        return count;
    }
}

Complexity

• Assume hash query costs constant time

Time Complexity

• \(T(n) = \Theta(n)\)

Auxiliary Space

• \(S(n) = O(1)\)