[Python题解] CodeForces 1804 D. Accommodation

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Title

CodeForces 1804 D. Accommodation

Time Limit

2 seconds

Memory Limit

512 megabytes

Problem Description

Annie is an amateur photographer. She likes to take pictures of giant residential buildings at night. She just took a picture of a huge rectangular building that can be seen as a table of $n\times m$ windows. That means that the building has $n$ floors and each floor has exactly $m$ windows. Each window is either dark or bright, meaning there is light turned on in the room behind it.

Annies knows that each apartment in this building is either one-bedroom or two-bedroom. Each one-bedroom apartment has exactly one window representing it on the picture, and each two-bedroom apartment has exactly two consecutive windows on the same floor. Moreover, the value of $m$ is guaranteed to be divisible by $4$ and it is known that each floor has exactly $\frac{m}{4}$ two-bedroom apartments and exactly $\frac{m}{2}$ one-bedroom apartments. The actual layout of apartments is unknown and can be different for each floor.

Annie considers an apartment to be occupied if at least one of its windows is bright. She now wonders, what are the minimum and maximum possible number of occupied apartments if judged by the given picture?

Formally, for each of the floors, she comes up with some particular apartments layout with exactly $\frac{m}{4}$ two-bedroom apartments (two consecutive windows) and $\frac{m}{2}$ one-bedroom apartments (single window). She then counts the total number of apartments that have at least one bright window. What is the minimum and maximum possible number she can get?

Input

The first line of the input contains two positive integers $n$ and $m$ ($1\le n\cdot m\le 5\cdot 10^5$) — the number of floors in the building and the number of windows per floor, respectively. It is guaranteed that $m$ is divisible by $4$.

Then follow $n$ lines containing $m$ characters each. The $j$-th character of the $i$-th line is “0” if the $j$-th window on the $i$-th floor is dark, and is “1” if this window is bright.

Output

Print two integers, the minimum possible number of occupied apartments and the maximum possible number of occupied apartments, assuming each floor can have an individual layout of $\frac{m}{4}$ two-bedroom and $\frac{m}{2}$ one-bedroom apartments.

Sample Input

5 4
0100
1100
0110
1010
1011

Sample Onput

7 10

Note

In the first example, each floor consists of one two-bedroom apartment and two one-bedroom apartments.

The following apartment layout achieves the minimum possible number of occupied apartments equal to $7$.

|0 1|0|0|
|1 1|0|0|
|0|1 1|0|
|1|0 1|0|
|1|0|1 1|

The following apartment layout achieves the maximum possible number of occupied apartments equal to $10$.

|0 1|0|0|
|1|1 0|0|
|0 1|1|0|
|1|0 1|0|
|1 0|1|1|

Source

CodeForces 1804 D. Accommodation

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Solution

n, m = map(int, input().split())
smin = smax = 0for i in range(n):s = input()two = j = 0# 将连续两盏灯都先视为两居室while j < m - 1:if s[j] == '1' and s[j + 1] == '1':j += 1two += 1j += 1two = min(two, m // 4)  # 两居室的数量不能超过总窗户数的四分之一smin += s.count('1') - twotwo = j = 0# 统计可能的不开灯的两居室和只开一盏灯的两居室数量while j < m - 1:if s[j] != '1' or s[j + 1] != '1':j += 1two += 1j += 1two = min(two, m // 4)  # 两居室的数量不能超过总窗户数的四分之一smax += s.count('1') - (m // 4 - two)  # (m // 4 - two) 为开两盏灯的两居室数量
print(smin, smax)