# Logic Confusion on Modern Art (Bronze USACO 2017 US Open p.3)

## Problem Info

USACO 2017 US Open Bronze Problem 3 Modern Art Problem Link

## My Work

``````# Read in grid as 2D array
with open("art.in", 'r') as fin:
grid = [[int(i) for i in fin.readline().strip()] for _ in range(n)]
print(grid)

# Get all possible colors, which is everything visible excluding zero
possible = set()
for row in grid:
for p in row:
if 0 in possible:
possible.remove(0)
print(possible)

# Recursive search function that gets the maximum x of the triangle and maximum y of the triangle, which will be used further down the road to calculate whether or not it is a valid rectangle
def search(grid, i, j, v):
global max_x, max_y, searched, area
if i < 0 or i >= n or j < 0 or j >= n or grid[i][j] != v or (i, j) in searched:
max_x = max(max_x, j)
max_y = max(max_y, i)
return
searched.append((i, j))
area += 1
search(grid, i+1, j, v)
search(grid, i-1, j, v)
search(grid, i, j+1, v)
search(grid, i, j-1, v)

# Use the search, and check if there is a possibility of the rectangle being covered. It it is covered, eliminate the rectangle that covers it from the list of possibilities.
searched = []
for i, row in enumerate(grid):
for j, p in enumerate(row):
if (i, j) in searched or not p:
continue
max_x = 0
max_y = 0
# The area variable is uneeded. Using it for debugging
area = 0
search(grid, i, j, p)
print(area, (max_x-j) * (max_y-i))
print()

for k in range(i, max_y):
for l in range(j, max_x):
if grid[k][l] != p and grid[k][l] in possible:
possible.remove(grid[k][l])

# Write the answer to the output file
with open('art.out', 'w') as fout:
fout.write(str(len(possible)))
``````

## Problem

My logic is pretty clear from the code, and I can get 6 out of 10 test cases, but when I try an input like:

``````4
1234
1234
1234
1334
``````

My program outputs 4 instead of 3, which is the correct answer. Therein lies my problem. I have no idea why it is 3 and not 4

## What I’ve Tried

I’ve read over the problem multiple times, and I still don’t get it.

If anyone could help explain it, that would be great.

It is impossible that 2 was the first color painted. Can you see why?

Yes! Thank you