Equal Row and Column Pairs
Description
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].length1 <= n <= 2001 <= grid[i][j] <= 10^5
Complexity
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- Time:
O(n^3) or O(n^2) with hashing - Space:
O(n^2)
Hints
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- Pattern
- Hash map with tuple/string keys
- Approach
- Convert rows to tuples and store in a Counter. Then for each column, check if it exists in the Counter and add the count.
- Complexity
- Hash each row and column, then count matches
Solutions
Show PY Solution
from collections import defaultdict
def solution(grid: list[list[int]]) -> int:
mr = defaultdict(int)
mc = defaultdict(int)
for r in range(len(grid)):
mr[tuple(grid[r])] += 1
cs = []
for r2 in range(len(grid)):
cs.append(grid[r2][r])
mc[tuple(cs)] += 1
count = 0
for k, v in mr.items():
count += mc[k] * v
# print(mr, mc)
return count