[20250306] BOJ / P3 / 미스테리 싸인 / 권혁준

khj20006/202503/06 BOJ P3 미스테리 싸인.md

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+```java
+
+import java.util.*;
+import java.io.*;
+
+class Point{
+	long x,y;
+	Point(long x, long y){
+		this.x = x;
+		this.y = y;
+	}
+	/*
+	 * 1  : 반시계
+	 * -1 : 시계
+	 * 0  : 직선 
+	 */
+	int ccw(Point p, Point q) {
+		long res = p.x * q.y + q.x * this.y + this.x * p.y - (q.x * p.y + this.x * q.y + p.x * this.y);
+		if(res > 0) return 1;
+		if(res < 0) return -1;
+		return 0;
+	}
+}
+
+class Main {
+
+	// IO field
+	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
+	static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
+	static StringTokenizer st;
+
+	static void nextLine() throws Exception {st = new StringTokenizer(br.readLine());}
+	static int nextInt() {return Integer.parseInt(st.nextToken());}
+	static long nextLong() {return Long.parseLong(st.nextToken());}
+	static void bwEnd() throws Exception {bw.flush();bw.close();}
+
+	// Additional field
+
+	static int N, M, K;
+	static Point[] A, B, L;
+	static List<Point> lowerA;
+	static List<Point> upperA;
+	static List<Point> lowerB;
+	static List<Point> upperB;
+
+	public static void main(String[] args) throws Exception {
+
+		ready();
+		solve();
+
+		bwEnd();
+
+	}
+
+	static void ready() throws Exception{
+
+		nextLine();
+		N = nextInt();
+		M = nextInt();
+		K = nextInt();
+		A = new Point[N];
+		B = new Point[M];
+		L = new Point[K];
+
+		nextLine();
+		for(int i=0;i<N;i++) A[i] = new Point(nextInt(), nextInt());
+
+		nextLine();
+		for(int i=0;i<M;i++) B[i] = new Point(nextInt(), nextInt());
+
+		nextLine();
+		for(int i=0;i<K;i++) L[i] = new Point(nextInt(), nextInt());
+
+	}
+
+	static void solve() throws Exception{
+
+		List<Point>[] resA = splitConvexHull(A);
+		lowerA = resA[0];
+		upperA = resA[1];
+
+		List<Point>[] resB = splitConvexHull(B);
+		lowerB = resB[0];
+		upperB = resB[1];
+
+//		bw.write("A's Lower Hull ===========\n");
+//		for(Point temp:lowerA) bw.write("(" + temp.x + "," + temp.y + ") -> ");
+//		bw.write("\n");
+//		bw.write("A's Upper Hull ===========\n");
+//		for(Point temp:upperA) bw.write("(" + temp.x + "," + temp.y + ") -> ");
+//		bw.write("\n");
+//		bw.write("B's Lower Hull ===========\n");
+//		for(Point temp:lowerB) bw.write("(" + temp.x + "," + temp.y + ") -> ");
+//		bw.write("\n");
+//		bw.write("B's Upper Hull ===========\n");
+//		for(Point temp:upperB) bw.write("(" + temp.x + "," + temp.y + ") -> ");
+//		bw.write("\n");
+
+
+		int cntA = 0, cntB = 0;
+		for(Point now:L) {
+
+			boolean isInsideA = false;
+			boolean isInsideB = false;
+
+			// A의 내부에 있는지
+			long minX = lowerA.get(0).x, maxX = lowerA.get(lowerA.size()-1).x;
+			if(minX < now.x && now.x < maxX) {
+				isInsideA = true;
+				int idx1 = findLowerBound(lowerA, now.x);
+
+				if(idx1-1 >= 0 && idx1 < lowerA.size()) isInsideA &= (now.ccw(lowerA.get(idx1-1), lowerA.get(idx1)) == 1);
+				if(idx1 >= 0 && idx1+1 < lowerA.size()) isInsideA &= (now.ccw(lowerA.get(idx1), lowerA.get(idx1+1)) == 1);
+				if(idx1+1 >= 0 && idx1+2 < lowerA.size()) isInsideA &= (now.ccw(lowerA.get(idx1+1), lowerA.get(idx1+2)) == 1);
+
+				int idx2 = findLowerBound(upperA, now.x);
+
+
+				if(idx2+1 < upperA.size()) isInsideA &= (now.ccw(upperA.get(idx2+1), upperA.get(idx2)) == 1);
+				if(idx2-1 >= 0 && idx2 < upperA.size()) isInsideA &= (now.ccw(upperA.get(idx2), upperA.get(idx2-1)) == 1);
+				if(idx2-2 >= 0 && idx2-1 < upperA.size()) isInsideA &= (now.ccw(upperA.get(idx2-1), upperA.get(idx2-2)) == 1);
+
+				if(isInsideA) cntA++;
+			}
+
+			// B의 내부에 있는지
+			minX = lowerB.get(0).x;
+			maxX = lowerB.get(lowerB.size()-1).x;
+			if(minX < now.x && now.x < maxX) {
+				isInsideB = true;
+				int idx1 = findLowerBound(lowerB, now.x);
+
+				if(idx1 < lowerB.size() && idx1-1 >= 0) isInsideB &= (now.ccw(lowerB.get(idx1-1), lowerB.get(idx1)) == 1);
+				if(idx1 >= 0 && idx1+1 < lowerB.size()) isInsideB &= (now.ccw(lowerB.get(idx1), lowerB.get(idx1+1)) == 1);
+				if(idx1+2 < lowerB.size()) isInsideB &= (now.ccw(lowerB.get(idx1+1), lowerB.get(idx1+2)) == 1);
+
+				int idx2 = findLowerBound(upperB, now.x);
+
+				if(idx2+1 < upperB.size()) isInsideB &= (now.ccw(upperB.get(idx2+1), upperB.get(idx2)) == 1);
+				if(idx2-1 >= 0 && idx2 < upperB.size()) isInsideB &= (now.ccw(upperB.get(idx2), upperB.get(idx2-1)) == 1);
+				if(idx2-2 >= 0 && idx2-1 < upperB.size()) isInsideB &= (now.ccw(upperB.get(idx2-1), upperB.get(idx2-2)) == 1);
+
+				if(isInsideB) cntB++;
+			}
+
+//			bw.write("(" + now.x + "," + now.y + ") is " + (isInsideA ? "inside of A\n" : "not inside of A\n"));
+//			bw.write("(" + now.x + "," + now.y + ") is " + (isInsideB ? "inside of B\n" : "not inside of B\n"));
+
+		}
+
+
+		int ans = K-cntA+cntB;
+		if(ans == 0) bw.write("YES\n");
+		else bw.write(ans + "\n");
+
+	}
+
+	static List<Point>[] splitConvexHull(Point[] P) {
+		List<Point> lower = new ArrayList<>();
+		List<Point> upper = new ArrayList<>();
+
+		long minX = (long)2e9, maxX = -(long)2e9;
+		int idxLower = -1, idxUpper = -1;
+		for(int i=0;i<P.length;i++) {
+			if(P[i].x <= minX) {
+				minX = P[i].x;
+				idxLower = i;
+			}
+			if(P[i].x >= maxX) {
+				maxX = P[i].x;
+				idxUpper = i;
+			}
+		}
+
+		if(idxUpper < idxLower) idxUpper += P.length;
+		for(int i=idxLower;i<=idxUpper;i++) lower.add(P[i%P.length]);
+		for(int i=idxLower+P.length;i>=idxUpper;i--) upper.add(P[i%P.length]);
+
+		return new List[] {lower,upper};
+	}
+
+	static int findLowerBound(List<Point> list, long x) {
+
+		int s = 0, e = list.size(), m = (s+e)>>1;
+		while(s<e) {
+			long temp = list.get(m).x;
+			if(temp < x) s = m+1;
+			else e = m;
+			m = (s+e)>>1;
+		}
+		return m;
+
+	}
+
+}
+
+```