Please type your question here: There are N islands in the sea, enumerated from
ID: 674554 • Letter: P
Question
Please type your question here:
There are N islands in the sea, enumerated from 1 to N. Each of them is so small that we can consider them as points on a plane. You are given the Cartesian coordinates of all islands. X-axis is directed towards East and Y-axis is directed towards North.
You need to illuminate all the islands. To do this, you can place lighthouses on some of the islands. You can't place more than one lighthouse on any single island. Each lighthouse can light only one of the 4 quadrants: North-Western, North-Eastern, South-Western or South-Eastern. If some island is located on the border of an illuminated quadrant, it is considered to be illuminated as well. Note that this means that a lighthouse always illuminates it's own island as well.
Find the smallest possible number of lighthouses required to illuminate all the islands (say L). Describe their configurations — positions and quadrants illuminated — as well.
Input
The first line of input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a single integer N denoting the number of islands.
The ith of the following N lines contains two integers Xi and Yi denoting the coordinates of the ith island.
Output
For each test case, first line of output must contain minimum number of lighthouses required to illuminate all islands, L.
Following L lines must describe configuration of the lighthouses, one configuration per line. Description of a lighthouse configuration consists of the number of the island where the lighthouse is placed, and the direction of the quadrant (NW for North-Western, NE for North-Eastern, SW for South-Western, SE for South-Eastern) illuminated by it, separated by a single space.
If there are many possible placements, output any one of them.
Constraints
• 1 T 1000
• 1 N 105
• The sum of N over all test cases doesn't exceed 5*105
• Absolute value of each coordinate doesn't exceed 109
• No two given islands coincide.
Subtasks
Subtask 1: (15 points)
• 1 N 8
• Absolute value of each coordinate doesn't exceed 50
Subtask 2: (85 points)
• Original constraints
Example
Input:
2
5
0 0
1 0
2 0
0 -1
0 -2
4
5 0
-5 0
0 5
0 -5
Output:
1
3 SW
2
4 NE
2 NE
Explanation / Answer
.There will be atmost 2 lighthouse is needed to illuminate all island...justbreak this question in two parts.. first part when 1 light house is needed & 2nd part when two light house is needed.. for the first part jus find any one out of four location that is topleft,topright,bottomleft,bootomright if any such cordnate exist one light house should be place there to illumintae all other island
if there exist no such cordinate then 2 cordinate is needed jus find a cordinate with minimum x and maximum x find if cordinate with maximum x is above than cordinate with minimum x the first light house should be place on cordinate with minimum x & second will be place at cordinate at maximum x (direction of lighthouse of xordinate with min x will be NE & for max x SW) similarly if cordinate with max x is below than than cordinate with min x then first light house should be place on cordinate with min x direction SE & 2nd will be place on cordinate with max x direction NW