0840

0801-0900/0840_magic_squares_in_grid.rb

@@ -0,0 +1,100 @@
+# brute-force
+# @param {Integer[][]} grid
+# @return {Integer}
+def num_magic_squares_inside(grid)
+ check_magic_square = lambda { |r, c|
+ appear = {}
+ rows = Array.new(3, 0) 
+ cols = Array.new(3, 0)
+ cross = Array.new(2, 0) 
+ (0...3).each { |i|
+ (0...3).each { |j|
+ num = grid[r + i][c + j]
+ return false if num < 1 || num > 9
+ return false if appear.has_key?(num)
+
+ appear[num] = true
+ rows[i] += num
+ cols[j] += num
+ cross[0] += num if i == j
+ cross[1] += num if i == 2 - j
+ }
+ }
+
+ return rows[0] == rows[1] && rows[1] == rows[2] &&
+ rows[0] == cols[0] && cols[0] == cols[1] && cols[1] == cols[2] &&
+ rows[0] == cross[0] && cross[0] == cross[1]
+ }
+
+ rows_size = grid.length
+ cols_size = grid[0].length
+ count = 0
+ (0...rows_size-2).each { |r|
+ (0...cols_size-2).each { |c|
+ count += 1 if check_magic_square.call(r, c)
+ }
+ }
+
+ count
+end
+
+# optimize
+def num_magic_squares_inside(grid)
+ # There are 8 ways of having 3 distinct numbers from 1-9 to sum up to 15
+ # 9+5+1
+ # 8+5+2
+ # 7+5+3
+ # 6+5+4
+ # 9+4+2
+ # 8+6+1
+ # 8+4+3
+ # 7+6+2
+ #
+ # Note that there're 4 sums with 5, 
+ # that are sum of the 1-th row, 1-th col and 2 diagonals
+ # That mean, 5 is the center cell.
+ # there's 2 sums with 1/3/5/7(each), 
+ # that are sum of the 1-th row and 1-th col
+ # so 1/3/5/7 on the side
+ # there's 3 sums with 2/4/6/8(each), 
+ # that are sum of the row and col has the same corner and the diagonal from that corner
+ # so 24/6/8 on the corner
+
+ # so there're only below solutions
+ # 4 3 8 | 8 3 4
+ # 9 5 1 | 1 5 9
+ # 2 7 6 | 6 7 2
+ # and their's variants by rotating 4 edges around the 5 
+ # if you concat 4 egdes, then rotating, for example, the solution above,
+ # the solution must in: '4381672943816729'
+
+ rows_size = grid.length
+ cols_size = grid[0].length
+ round_edges = [[0,0], [0,1], [0,2], [1,2], [2,2], [2,1], [2,0], [1,0]].freeze
+ rotating = [
+ '4381672943816729'.freeze,
+ '8349276183492761'.freeze
+ ]
+
+ count = 0
+ (0...rows_size-2).each { |r|
+ (0...cols_size-2).each { |c|
+ # check center is 5 and corner is even (2/4/6/8)
+ if grid[r][c].even? && grid[r+1][c+1] == 5
+ round_str = ''
+ round_edges.each { |i, j|
+ num = grid[r+i][c+j]
+ break if num < 1 && num > 9
+ round_str << num.to_s
+ }
+
+ if round_str.length == 8
+ && rotating.any? { |r| r.include?(round_str) }
+ count += 1
+ end
+ end
+ }
+ }
+
+ count
+end