Tontti

import math
from array import array

# Parse input
line = input().split()
height = int(line[0])
width = int(line[1])
desired_trees = int(line[2])

field = []
for y in range(height):
    line = input()
    field.extend([x == '*' for x in line])

# Create index
index = []
for i in range(width*height):
    this = 0
    y, x = divmod(i, width)
    if field[i]:
        this = 1
    if y > 0:
        this += index[i-width]
    if x > 0:
        this += index[i-1]
    if y > 0 and x > 0:
        this -= index[i-width-1]
    index.append(this)
index = array('I', index) # use array instead of list for sake of speed

# Calculate
def trees_in(x1, y1, size):
    x2 = x1 + size - 1
    y2 = y1 + size - 1
    if x1 == 0 and y1 == 0:
        return index[y2*width + x2]
    elif x1 == 0:
        return index[y2*width + x2] - index[(y1-1)*width + x2]
    elif y1 == 0:
        return index[y2*width + x2] - index[y2*width + (x1-1)]
    else:
        return (index[y2*width + x2] - index[(y1-1)*width + x2] -
                index[y2*width + (x1-1)] + index[(y1-1)*width + (x1-1)])

options = 0
min_size = math.ceil(math.sqrt(desired_trees))
for y in range(height):
    for x in range(width):
        max_size = min(height-y, width-x)
        for size in range(min_size, max_size+1):
            trees = trees_in(x, y, size)
            if trees == desired_trees:
                options += 1
            elif trees > desired_trees:
                # bigger area can't have less trees
                break

print(options)

Test 1

Group: 1

Verdict: ACCEPTED

Test 2

Group: 1

Verdict: ACCEPTED

Test 3

Group: 1

Verdict: ACCEPTED

Test 4

Group: 1

Verdict: ACCEPTED

Test 5

Group: 1

Verdict: ACCEPTED

Test 6

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 7

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 8

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 9

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 10

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 11

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 12

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 13

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 14

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 15

Group: 3

Verdict: TIME LIMIT EXCEEDED