Orig Description
Convenience Store
To expand its business, the convenience store Seven-Eleven is considering opening its first store in Wakamatsu City. Since there are already many other convenience stores in Wakamatsu City, the location of the new store is likely to be the key to success. Under the premise of "customers will use the convenience store closest to their home area," Seven-Eleven plans to open a store at a location where "many customers are likely to use it."
Seven-Eleven divided the map of Wakamatsu City into congruent regular hexagons ("blocks") to understand the range covered by each existing convenience store. At this time, the city was divided into blocks so that at most one existing convenience store could be included in each block. Based on the number of blocks that need to be traversed to reach a convenience store from each block, the distance between the convenience store and each block is determined. Each block is considered to be covered by the convenience store that covers it with the shortest distance. The problem is to find the "blocks for which there are no existing convenience stores that cover as many blocks as possible" based on this map.
You are a programmer at Seven-Eleven, and you have been tasked with developing a program to calculate the maximum number of blocks that can be covered from all candidate locations based on the map divided into blocks and information about the candidate location of the new store.
The map divided into blocks of m × n is represented as shown in Figure 1. Blocks of hexagons are arranged horizontally in m rows and vertically in n columns, each represented by a coordinate (x, y). The left edge of odd-numbered rows is located just below the left edge of the row above it, and the left edge of even-numbered rows is located just below the left edge of the row above it. For example, coordinate (1, 1) represents the top-left block in Figure 1. Coordinate (1, 2) is located just below coordinate (1, 1), and coordinate (1, 3) is located just below coordinate (1, 2).
Figure 2 shows an example where there are six existing convenience stores, divided into a 6 × 6 map. Each convenience store is numbered in order from 1. When the blocks covered by each convenience store are colored by number, they are divided as shown in Figure 3. Blocks that are not colored, such as block (1, 4) and (2, 5), have two or more convenience stores that are closest, and cannot be determined which convenience store covers the block. For example, in the case of block (1, 4), the distance to convenience stores 4 and 5 is equal, and it is assumed that there is no convenience store that covers this block. The number of blocks covered by convenience store 4 is 5.
Suppose Seven-Eleven is considering locations (1, 3) and (5, 3) as candidate locations for the new store. If a store is located at (1, 3), it can cover three blocks (Figure 4). On the other hand, if a store is located at (5, 3), it can cover four blocks (Figure 5). Therefore, the maximum number of blocks that can be covered is 4.
The input consists of multiple datasets. The end of the input is indicated by
Extracted Specification
Canonicalized Input Description:
An integer M (1 ≤ M ≤ 100), representing some quantity or size.
An integer N (1 ≤ N ≤ 100), representing some quantity or size.
A list of tuples containing two integers, each tuple representing a coordinate (x, y) with 1 ≤ x ≤ M and 1 ≤ y ≤ N.
A list of tuples containing two integers, each tuple representing a coordinate (x, y) with 1 ≤ x ≤ M and 1 ≤ y ≤ N.
### Example Input:
```
6
6
1 1
1 2
1 3
2 1
2 2
2 3
4 4
5 5
6 6
1 3
5 3
```
### Function Signature:
Write a function f(M, N, existing_store_coordinates, candidate_coordinates) that takes in the input.
```python
def f(M: int, N: int, existing_store_coordinates: List[Tuple[int, int]], candidate_coordinates: List[Tuple[int, int]]):
'''
M: an integer
N: an integer
existing_store_coordinates: a list of tuples, each containing two integers
candidate_coordinates: a list of tuples, each containing two integers
'''
```
Test Case Generator
To generate test cases for the given problem statement about the convenience store placement, we need to take into account the constraints and the structure of the input and output. The map is divided into hexagonal blocks arranged in a grid, and the goal is to calculate the maximum number of blocks that can be covered from all candidate locations based on the map and the existing convenience stores.
First, let's outline the structure of the input and output based on the problem statement:
**Input:**
1. First line: Two integers \(m\) and \(n\) (1 ≤ \(m, n\) ≤ 100), representing the number of rows and columns of the map.
2. Next \(m\) lines: Each line contains \(n\) integers, where each integer represents whether there is an existing convenience store in that block (1 if there is a store, 0 if there is not).
3. Next line: An integer \(k\) (1 ≤ \(k\) ≤ 100), representing the number of candidate locations for new stores.
4. Next \(k\) lines: Each line contains two integers \(x\) and \(y\) (1 ≤ \(x\) ≤ \(m\), 1 ≤ \(y\) ≤ \(n\)), representing the coordinates of the candidate locations.
**Output:**
- A single integer representing the maximum number of blocks that can be covered by a new store placed in one of the candidate locations.
Here is the test case generator for the problem:
```python
import random
def generate_test_case():
m = random.randint(1, 100)
n = random.randint(1, 100)
# Generate the map with existing convenience stores
map_grid = [[random.choice([0, 1]) for _ in range(n)] for _ in range(m)]
k = random.randint(1, 100)
# Generate candidate locations
candidate_locations = [(random.randint(1, m), random.randint(1, n)) for _ in range(k)]
# Construct the input
input_data = f"{m} {n}\n"
for row in map_grid:
input_data += " ".join(map(str, row)) + "\n"
input_data += f"{k}\n"
for loc in candidate_locations:
input_data += f"{loc[0]} {loc[1]}\n"
return input_data
# Example usage:
print(generate_test_case())
```
**Explanation:**
1. **Map dimensions (m, n):** Randomly chosen within the given constraints (1 ≤ m, n ≤ 100).
2. **Map grid:** A \(m \times n\) list of lists where each element is either 0 or 1, representing the absence or presence of a convenience store.
3. **Number of candidate locations (k):** Randomly chosen within the given constraints (1 ≤ k ≤ 100).
4. **Candidate locations:** A list of \(k\) tuples, each representing the coordinates of a candidate location.
The generated test case follows the input format specified in the problem statement. You can use the `generate_test_case` function to create various test cases for your competitive programming problem.
Feel free to modify the constraints and randomization as needed for more specific scenarios or additional testing.
Extract Arguments
def extract_arguments(fh):
datasets = []
while True:
# Read dimensions m and n
line = fh.readline().strip()
if line == '':
break
m, n = map(int, line.split())
# Read the map
city_map = []
for _ in range(m):
row = list(map(int, fh.readline().strip().split()))
city_map.append(row)
# Read the number of candidate locations
num_candidates = int(fh.readline().strip())
# Read candidate locations
candidates = []
for _ in range(num_candidates):
x, y = map(int, fh.readline().strip().split())
candidates.append((x, y))
datasets.append((m, n, city_map, candidates))
return datasets