4386 make constellation
알고리즘(MST)
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1. 모든 별들 사이의 거리를 구한 다음에, 두 별의 위치, 거리를 저장한 구조체 배열을 거리순으로 오름차순 정렬
2. 구조체 배열에서 하나씩 빼가며 크루스칼 시행 -> edge == numOfStar -1 이면 중지 후 출력
코드
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#include <iostream>
#include <vector>
#include <cmath>
#include <cstdio>
#include <algorithm>
#define MAX_STAR 100
using namespace std;
typedef struct Star {
double x;
double y;
} Star;
typedef struct Distance {
int first;
int second;
double distance;
bool operator <(Distance d) {
return distance < d.distance;
}
} Distance;
Star star[MAX_STAR];
Distance dist[(MAX_STAR * (MAX_STAR+1))/2];
int numOfStar, checkStar[MAX_STAR], distIndex;
vector<vector<int>> set;
double getMinDistance();
void generateDistance();
bool unionFind(int a, int b);
int main() {
cin >> numOfStar;
for (int i = 0; i < numOfStar; i++) {
cin >> star[i].x >> star[i].y;
}
for (int i = 0; i < numOfStar; i++)
checkStar[i] = -1;
cout.precision(20);
cout << getMinDistance();
}
double getMinDistance() {
generateDistance();
sort(dist, dist + distIndex);
double value = 0;
int edge = 0;
for (int i = 0; i < distIndex; i++) {
if (unionFind(dist[i].first, dist[i].second)) {
value += dist[i].distance;
edge++;
}
if (edge == numOfStar - 1)
break;
}
return value;
}
void generateDistance() {
for (int i = 0; i < numOfStar; i++) {
for (int j = i + 1; j < numOfStar; j++) {
dist[distIndex].first = i;
dist[distIndex].second = j;
dist[distIndex++].distance = sqrt(((star[i].x - star[j].x) * (star[i].x - star[j].x)) + ((star[i].y - star[j].y) * (star[i].y - star[j].y)));
}
}
}
bool unionFind(int a, int b) {
if (checkStar[a] == -1 && checkStar[b] == -1) {
set.push_back({ a, b });
checkStar[a] = set.size() - 1;
checkStar[b] = set.size() - 1;
}
else if (checkStar[a] == -1) {
set[checkStar[b]].push_back(a);
checkStar[a] = checkStar[b];
}
else if (checkStar[b] == -1) {
set[checkStar[a]].push_back(b);
checkStar[b] = checkStar[a];
}
else if (checkStar[a] != checkStar[b]) {
int temp = checkStar[b];
for (int i = 0; i < set[temp].size(); i++) {
set[checkStar[a]].push_back(set[temp][i]);
checkStar[set[temp][i]] = checkStar[a];
}
set[temp].clear();
}
else
return false;
return true;
}