3044 - Most Frequent Prime.

Medium

You are given a m x n 0-indexed 2D matrix mat. From every cell, you can create numbers in the following way:

• There could be at most 8 paths from the cells namely: east, south-east, south, south-west, west, north-west, north, and north-east.

• Select a path from them and append digits in this path to the number being formed by traveling in this direction.

• Note that numbers are generated at every step, for example, if the digits along the path are 1, 9, 1, then there will be three numbers generated along the way: 1, 19, 191.

Return the most frequent prime number greater than 10 out of all the numbers created by traversing the matrix or -1 if no such prime number exists. If there are multiple prime numbers with the highest frequency, then return the largest among them.

Note: It is invalid to change the direction during the move.

Example 1:

Input: mat = \[\[1,1],9,9,1,1]

Output: 19

Explanation:

From cell (0,0) there are 3 possible directions and the numbers greater than 10 which can be created in those directions are:

East: 11, South-East: 19, South: 19,191.

Numbers greater than 10 created from the cell (0,1) in all possible directions are: 19,191,19,11.

Numbers greater than 10 created from the cell (1,0) in all possible directions are: 99,91,91,91,91.

Numbers greater than 10 created from the cell (1,1) in all possible directions are: 91,91,99,91,91.

Numbers greater than 10 created from the cell (2,0) in all possible directions are: 11,19,191,19.

Numbers greater than 10 created from the cell (2,1) in all possible directions are: 11,19,19,191.

The most frequent prime number among all the created numbers is 19.

Example 2:

Input: mat = \[\[7]]

Output: -1

Explanation: The only number which can be formed is 7. It is a prime number however it is not greater than 10, so return -1.

Example 3:

Input: mat = \[\[9,7,8],4,6,5,2,8,6]

Output: 97

Explanation:

Numbers greater than 10 created from the cell (0,0) in all possible directions are: 97,978,96,966,94,942.

Numbers greater than 10 created from the cell (0,1) in all possible directions are: 78,75,76,768,74,79.

Numbers greater than 10 created from the cell (0,2) in all possible directions are: 85,856,86,862,87,879.

Numbers greater than 10 created from the cell (1,0) in all possible directions are: 46,465,48,42,49,47.

Numbers greater than 10 created from the cell (1,1) in all possible directions are: 65,66,68,62,64,69,67,68.

Numbers greater than 10 created from the cell (1,2) in all possible directions are: 56,58,56,564,57,58.

Numbers greater than 10 created from the cell (2,0) in all possible directions are: 28,286,24,249,26,268.

Numbers greater than 10 created from the cell (2,1) in all possible directions are: 86,82,84,86,867,85.

Numbers greater than 10 created from the cell (2,2) in all possible directions are: 68,682,66,669,65,658.

The most frequent prime number among all the created numbers is 97.

Constraints:

• m == mat.length

• n == mat[i].length

• 1 <= m, n <= 6

• 1 <= mat[i][j] <= 9