#!/usr/bin/perl
# https://theweeklychallenge.org/blog/perl-weekly-challenge-251/#TASK2
#
# Task 2: Lucky Numbers
# =====================
#
# You are given a m x n matrix of distinct numbers.
#
# Write a script to return the lucky number, if there is one, or -1 if not.
#
## A lucky number is an element of the matrix such that it is
## the minimum element in its row and maximum in its column.
#
## Example 1
##
## Input: $matrix = [ [ 3,  7,  8],
##                    [ 9, 11, 13],
##                    [15, 16, 17] ];
## Output: 15
##
## 15 is the only lucky number since it is the minimum in its row
## and the maximum in its column.
#
## Example 2
##
## Input: $matrix = [ [ 1, 10,  4,  2],
##                    [ 9,  3,  8,  7],
##                    [15, 16, 17, 12] ];
## Output: 12
#
## Example 3
##
## Input: $matrix = [ [7 ,8],
##                    [1 ,2] ];
## Output: 7
#
############################################################
##
## discussion
##
############################################################
#
# For a lucky number, we know:
# Since the minimum in a row is at the same time the maximum in
# a column, there is no number bigger in that column, so in all
# other rows, there is a number that is smaller than the current
# number, so the minimum in that other row has to be smaller or
# equal to this number; being smaller, it can't be bigger than any
# of the numbers in the original row, so it's can't be a lucky number
# as well.
# So we know we have at most one lucky number.
# Finding it is simple: In each row, find the minimum number, then
# check whether it is as well the maximum number in its column.

def lucky_numbers(matrix: list) -> None:
    print("Input: [");
    for row in matrix:
        print("        [", ", ".join([str(x) for x in row]), "],")
    print("       ];")
    rows = len(matrix)
    columns = len(matrix[0])
    row_min = []
    column_max = []
    for column in range(columns):
        column_elements = []
        for row in range(rows):
            column_elements.append(matrix[row][column])
        column_max.append(max(column_elements))
    for i in range(rows):
        row_min.append(min(matrix[i]))
        for j in range(columns):
            elem = matrix[i][j]
            if elem == row_min[i] and elem == column_max[j]:
                print(f"Output: {elem}")
                return
    print("Output: -1")

lucky_numbers([ [ 3,  7,  8], [ 9, 11, 13], [15, 16, 17] ])
lucky_numbers([ [ 1, 10,  4,  2], [ 9,  3,  8,  7], [15, 16, 17, 12] ])
lucky_numbers([ [7 ,8], [1 ,2] ])
lucky_numbers([ [7 ,8], [10 ,2] ])