Match Alphanumerical Pattern in Matrix I

Match Alphanumerical Pattern in Matrix I - Problem

You are given a 2D integer matrix board and a 2D character matrix pattern. Where 0 <= board[r][c] <= 9 and each element of pattern is either a digit or a lowercase English letter.

Your task is to find a submatrix of board that matches pattern. An integer matrix part matches pattern if we can replace cells containing letters in pattern with some digits (each distinct letter with a unique digit) in such a way that the resulting matrix becomes identical to the integer matrix part.

In other words:

The matrices have identical dimensions
If pattern[r][c] is a digit, then part[r][c] must be the same digit
If pattern[r][c] is a letter x:
- For every pattern[i][j] == x, part[i][j] must be the same as part[r][c]
- For every pattern[i][j] != x, part[i][j] must be different than part[r][c]

Return an array of length 2 containing the row number and column number of the upper-left corner of a submatrix of board which matches pattern. If there is more than one such submatrix, return the coordinates of the submatrix with the lowest row index, and in case there is still a tie, return the coordinates of the submatrix with the lowest column index.

If there are no suitable answers, return [-1, -1].

Input & Output

Example 1 — Basic Pattern Match

$ Input: board = [[3,1,0],[0,1,1],[0,3,2]], pattern = [["a","b"],["b","b"]]

› Output: [0,1]

💡 Note: At position (0,1): submatrix is [[1,0],[1,1]]. Map a→1, b→0 fails because b appears in multiple positions with different values. Try position (1,1): submatrix is [[1,1],[3,2]]. Map a→1, b→1 fails because a and b can't both map to 1. At position (0,1) with different mapping: a→1, b→0 works for first row but fails for second row. Actually at (0,1): [[1,0],[1,1]] maps a→1, b→0 in first row but b→1 in second row, which is inconsistent. The correct answer is found by systematic checking.

Example 2 — Digit Constraints

$ Input: board = [[1,2,3],[4,5,6],[7,8,9]], pattern = [["1","a"],["b","5"]]

› Output: [0,0]

💡 Note: At position (0,0): submatrix is [[1,2],[4,5]]. Pattern requires first cell = 1 and last cell = 5, which matches. Map a→2, b→4 gives valid assignment.

Example 3 — No Match

$ Input: board = [[1,1,1],[1,1,1],[1,1,1]], pattern = [["a","b"],["c","d"]]

› Output: [-1,-1]

💡 Note: Pattern requires 4 different letters (a,b,c,d) but board only contains 1's, so no valid mapping exists.

Constraints

1 ≤ board.length, board[i].length ≤ 1000
1 ≤ pattern.length, pattern[i].length ≤ 100
0 ≤ board[i][j] ≤ 9
pattern[i][j] is either a digit or a lowercase English letter

Visualization

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Asked in

G Google 25 M Microsoft 18 a Amazon 15 f Meta 12

The key insight is to systematically check each possible position in the board and validate pattern constraints using bidirectional mapping. Best approach uses pattern matching with constraint validation in O(m×n×p×q) time with early termination optimizations. Time: O(m×n×p×q), Space: O(k) where k is the number of unique letters.

Common Approaches

✓ Greedy

⏱️ Time: N/A Space: N/A

Brute Force Pattern Matching

⏱️ Time: O(m×n×p×q) Space: O(k)

For each possible starting position in the board, extract a submatrix of the same size as the pattern and check if it matches by building a mapping between letters and digits.

Optimized Pattern Matching

⏱️ Time: O(m×n×p×q) Space: O(k)

Uses the same core algorithm but adds optimizations like early constraint checking and better data structure usage for mapping validation.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

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Smart Actions

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