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quiz_6/quiz_6_Interesting_Method_Not_Recommended.py

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+# Randomly generates a grid with 0s and 1s, whose 10ension is controlled by user input,
+# as well as the density of 1s in the grid, and determines the size of the largest
+# isosceles triangle, consisting of nothing but 1s and whose base can be either
+# vertical or horizontal, pointing either left or right or up or down.
+#
+# Written by *** and Eric Martin for COMP9021
+
+
+from random import seed, randint
+import sys
+
+
+def display_grid():
+    for i in range(len(grid)):
+        print('   ', ' '.join(str(int(grid[i][j] != 0)) for j in range(len(grid))))
+
+
+
+# interesting method with optimization
+# actually, this is 'Dynamic Programming'
+# However, it's not necessary to understand what the 'Dynamic Programming' is.
+# 
+# time complexity: O(n^2)
+
+
+def size_of_largest_isosceles_triangle():
+	# initialize length and size, and make a copy/clone of grid
+	length, size, new_grid = len(grid), 0, [row[:] for row in grid]
+
+	# rotate new_grid for 4 times
+	for _ in range(4):
+		# rotate this new_grid which is two-dimensional array
+		new_grid = list(list(x)[::-1] for x in zip(*new_grid))
+		# initialize/reset matrix every time
+		# the boundary conditions can be neglected while column(matrix) >= 2 and rows(matrix) >= 1
+		matrix = [[0 for _ in range(length + 2)] for _ in range(length + 1)]
+		# traverse new_grid
+		for i in range(length):
+			for j in range(length):
+				# find the position where new_grid[i][j] != 0
+				if new_grid[i][j]:
+					# 'Dynamic Programming':
+					# choose the one direction: up
+					#  * * * * *
+					#    * * *
+					#      *
+					matrix[i+1][j+1] = 1 + min(matrix[i][j], matrix[i][j+1], matrix[i][j+2])
+		size = max(size, max(element for line in matrix for element in line))
+
+	return size
+
+
+
+try:
+    arg_for_seed, density = (abs(int(x)) for x in input('Enter two integers: ').split())
+except ValueError:
+    print('Incorrect input, giving up.')
+    sys.exit()
+seed(arg_for_seed)
+grid = [[randint(0, density) for _ in range(10)] for _ in range(10)]
+print('Here is the grid that has been generated:')
+display_grid()
+print('The largest isosceles triangle has a size of',
+      size_of_largest_isosceles_triangle()
+     )