Soluție HackerRank pentru Circle City, subdomeniul Geometry, în C++14. Include cerința formatată, exemple, explicația pașilor și cod sursă.
- Problemă: Circle City
- Domeniu: Geometry
- Limbaj: C++14
Challenge: Circle City
Scor cont: 30.0 / 30
Submission status: Accepted
Submission score: 1.0
Submission ID: 464734298
Limbaj: cpp14
Link challenge: https://www.hackerrank.com/challenges/circle-city/problem
Cerință
Roy lives in a city that is circular in shape on a 2D plane that has radius r. The city center is located at origin (0,0) and it has suburbs lying on the lattice points (points with integer coordinates). The city Police Department Headquarters can only protect those suburbs which are located strictly inside the city. The suburbs located on the border of the city are still unprotected. So the police department decides to build at most k additional police stations at some suburbs. Each of these police stations can protect the suburb it is located in.
Given the *square of radius*, d (=r^2), of the city, Roy has to determine if it is possible to protect all the suburbs.
Input Format
The first line of input contains integer t; t test cases follow.
Each of the next t lines contains two space-separated integers: d, *the square of the radius* of the city, and k, the maximum number of police stations the headquarters is willing to build.
Constraints
1 ≤ t ≤ 10^3
1 ≤ d ≤ 2 × 10^9
0 ≤ k ≤ 2×10^9
Output Format
For each test case, print in a new line `possible` if it is possible to protect all the suburbs;, otherwise, print `impossible`.
Sample Input
5
1 3
1 4
4 4
25 11
25 12
Sample Output
impossible
possible
possible
impossible
possible
Explanation
- For d = 1, there are 4 points on circumference - _[(0,1), (0,-1), (1,0), (-1,0)]_.
- For d = 4, there are 4 points on circumference - _[(0,2), (0,-2), (2,0),(-2,0)]_.
- For d = 25, there are 12 points on circumference - _[(0,5), (0,-5), (3,4), (-3,4), (3,-4), (-3,-4), (4,3), (-4,3), (4,-3), (-4,-3), (5,0), (-5,0)]_.
*Test Case #01:* There are 4 suburbs on the border, while we are allowed to construct max k = 3 police stations.
*Test Case #02:* We can cover all the 4 suburbs as exactly 4 stations are allowed.
*Test Case #03:* We can cover all the 4 suburbs as exactly 4 stations are allowed.
*Test Case #04:* It is impossible to cover 12 suburbs, on the border, with 11 police stations.
*Test Case #05:* We can to cover all 12 suburbs, on the border, with 12 police stations.
Timelimits
Timelimits for this challenge are given [here](https://hr-assets.s3.amazonaws.com/7bb46cae_challenge_assets/checker_limits/3926/limits.json)
Cod sursă
// ==================================================
// Problem : Circle City
// Score : 30 /30
// Language : C++14
// ==================================================
#include <cstdio>
#include <cmath>
using namespace std;
int main()
{
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
int t;
scanf("%d", &t);
while (t--) {
int d, k;
scanf("%d %d", &d, &k);
int r = sqrt(d);
int latticePointCount = 0;
for (int x = 0; x <= r; ++x) {
int y = sqrt(d - x * x);
if (x * x + y * y == d) {
++latticePointCount;
}
}
latticePointCount *= 4; // 4 quadrants
if (r * r == d) {
// Points on X-axis and Y-axis already taken twice
latticePointCount -= 4;
}
printf(k < latticePointCount ? "impossible\n" : "possible\n");
}
return 0;
}