POJ 1696 Space Ant

 

Space Ant

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 834		Accepted: 542

Description

The most exciting space discovery occurred at the end of the 20th century. In 1999, scientists traced down an ant-like creature in the planet Y1999 and called it M11. It has only one eye on the left side of its head and just three feet all on the right side of its body and suffers from three walking limitations:

1. It can not turn right due to its special body structure.
2. It leaves a red path while walking.
3. It hates to pass over a previously red colored path, and never does that.

The pictures transmitted by the Discovery space ship depicts that plants in the Y1999 grow in special points on the planet. Analysis of several thousands of the pictures have resulted in discovering a magic coordinate system governing the grow points of the plants. In this coordinate system with x and y axes, no two plants share the same x or y.
An M11 needs to eat exactly one plant in each day to stay alive. When it eats one plant, it remains there for the rest of the day with no move. Next day, it looks for another plant to go there and eat it. If it can not reach any other plant it dies by the end of the day. Notice that it can reach a plant in any distance.
The problem is to find a path for an M11 to let it live longest.
Input is a set of (x, y) coordinates of plants. Suppose A with the coordinates (xA, yA) is the plant with the least y-coordinate. M11 starts from point (0,yA) heading towards plant A. Notice that the solution path should not cross itself and all of the turns should be counter-clockwise. Also note that the solution may visit more than two plants located on a same straight line.

Input

The first line of the input is M, the number of test cases to be solved (1 <= M <= 10). For each test case, the first line is N, the number of plants in that test case (1 <= N <= 50), followed by N lines for each plant data. Each plant data consists of three integers: the first number is the unique plant index (1..N), followed by two positive integers x and y representing the coordinates of the plant. Plants are sorted by the increasing order on their indices in the input file. Suppose that the values of coordinates are at most 100.

Output

Output should have one separate line for the solution of each test case. A solution is the number of plants on the solution path, followed by the indices of visiting plants in the path in the order of their visits.

Sample Input

2
10
1 4 5
2 9 8
3 5 9
4 1 7
5 3 2
6 6 3
7 10 10
8 8 1
9 2 4
10 7 6
14
1 6 11
2 11 9
3 8 7
4 12 8
5 9 20
6 3 2
7 1 6
8 2 13
9 15 1
10 14 17
11 13 19
12 5 18
13 7 3
14 10 16

Sample Output

10 8 7 3 4 9 5 6 2 1 10
14 9 10 11 5 12 8 7 6 13 4 14 1 3 2

Source

Tehran 1999

 

 /* 寻找逆时针圈 (1)首先对所有点按y坐标升序排列 (2)然后循环n次 每次循环取首点,然后对剩下的点按照策略1排序;每次循环后首点位置往前移动一位 策略1:按照剩下点与首点的相对偏移角度排序,偏移角度小的排在前面,相同偏移角度的离首点 位置近的排在前面. 这样可以取尽所有点 */ #include <iostream> #include <algorithm> #define MAX_N 50 using namespace std; struct point { int id, x, y; }points[MAX_N + 1]; int n, countv; point *res[MAX_N + 1]; int xPro(int x1, int y1, int x2, int y2, int x3, int y3) { return (x3 - x1) * (y2 - y1) - (x2 - x1) * (y3 - y1); } int distPow2(int x1, int y1, int x2, int y2) { return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1); } //按照y坐标值排序 bool compare1(const point &p1, const point &p2) { if(p1.y < p2.y) return true; else return false; } point *first; //按照相对于first点的偏移角度进行排序 bool compare2(const point &p1, const point &p2) { int xp = xPro(first->x, first->y, p1.x, p1.y, p2.x, p2.y); if(xp < 0) return true; else if(xp > 0) return false; else { int d1 = distPow2(first->x, first->y, p1.x, p1.y); int d2 = distPow2(first->x, first->y, p2.x, p2.y); if(d1 <= d2) return true; else return false; } } int main() { int caseNum, i; scanf("%d", &caseNum); while(caseNum--) { scanf("%d", &n); for(i = 0; i < n; i++) scanf("%d%d%d", &points[i].id, &points[i].x, &points[i].y); countv = 0; sort(points, points + n, compare1); int curP = 0; while(curP < n) { res[countv++] = &points[curP]; first = &points[curP]; curP++; sort(points + curP, points + n, compare2); } printf("%d", countv); for(i = 0; i < countv; i++) printf(" %d", res[i]->id); printf("/n"); } return 0; }