f438.
855 - Lunch in Grid City

Content

在二維座標中找與所有點的曼哈頓距離總和最小的點

Grid city is a city carefully planned. Its street-map very much resembles that of downtown Manhattan in New York. Streets and avenues are orderly setup like a grid.

A group of friends living in Grid city decide to meet for lunch. Given that the group is dynamic, that is, its size may grow or shrink from time to time, they follow a written rule to determine the meeting point. It states that the meeting point is the one that minimizes the total distance the all group has to walk from their homes upto that point. If there is more than one candidate point, the rule imposes that the meeting point is the one corresponding to the smaller number for street and avenue. For large groups, this rule naturally avoids the usual long discussions that take place before aggreeing on a possible meeting point. For simplicity, consider that each person lives at a corner formed by a street and an avenue. You can also assume that the distance between two corners along one street or avenue is always one unit.

Your task is to suggest to the group their best meeting point (corner between a street and an avenue).

As an example, the following figure illustrates one such Crid city and the location of 11 friends. For this scenario, the best meeting point is street 3 and avenue 4. You can assume that streets and avenues are set and ordered as illustrated in this figure.

Please note that if we add another friend located at, say street 3 and avenue 5, making a total of 12 friends, then we would have two candidate meeting points, pairs (3,4) and (3,5). The rule clearly efines that street 3 and avenue 4 is the meeting point.

Given the size of a grid representing the Grid city and the locations of each person of the group of friends, your task is to determine the best meeting point following the rule of the group, as stated above.

Input

第一行有一個T代表測資數

每筆測資的第一行有S,A,F(S ≤ 1000 and A ≤ 1000)(0 < F ≤ 50000)(S,A)為二維座標的右上角共有F個點

接下來有F行 每行有個在二維座標上的點

The first line of the input contains the number T of test cases, followed by T input blocks.

The first line of each test case consists of three positive numbers, the number of streets S, the number of avenues A (where S ≤ 1000 and A ≤ 1000), and the number of friends F (where 0 < F ≤ 50000). The following F input lines indicate the locations of the friends. A location is defined by two numbers,a street and an avenue, in this order.

Output

輸出與所有點的曼哈頓距離總和最小的點座標 如果有多組解X,Y越小越好(輸出格式請參考範例)

The output for each test case must list the best meeting point formatted as follows:(Street: 3, Avenue: 4) Each test case must be on a separate line.

Sample Input
#1

2 2 2 2 1 1 2 2 7 7 11 1 2 1 7 2 2 2 3 2 5 3 4 4 2 4 5 4 6 5 3 6 5

Sample Output
#1

(Street: 1, Avenue: 1) (Street: 3, Avenue: 4)

測資資訊：

記憶體限制：
512
MB

公開 測資點#0 (20%): 1.0s , <10M

公開 測資點#1 (20%): 1.0s , <10M

公開 測資點#2 (20%): 1.0s , <10M

公開 測資點#3 (20%): 1.0s , <10M

公開 測資點#4 (20%): 1.0s , <10M

公開 測資點#0 (20%): 1.0s , <10M

公開 測資點#1 (20%): 1.0s , <10M

公開 測資點#2 (20%): 1.0s , <10M

公開 測資點#3 (20%): 1.0s , <10M

公開 測資點#4 (20%): 1.0s , <10M

計程車幾何(Taxicab geometry)或曼哈頓距離(Manhattan distance or Manhattan length)或方格線距離是由十九世紀的赫爾曼·閔可夫斯基所創辭彙，為歐幾里得幾何度量空間的幾何學之用語，用以標明兩個點上在標準坐標系上的絕對軸距之總和。

以上出自維基百科

2020 6月CPE第四題

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