import java.io.*; import java.math.*; import java.util.*; import java.lang.*; class Main{ public static FastReader in = new FastReader(inputStream); new Main().run(); out.close(); } // Pivot[] pivots; Disk[] disks; int numDisks; int numPivots; long width; long[][] centreDistances; long[][] radiiSquares; long[] pivotsX; long[] pivotsY; long[] disksRad; long[] disksCst; int cases = in.nextInt(); for(int i=0; i<cases; i++){ numPivots = in.nextInt(); numDisks = in.nextInt(); width = in.nextLong(); pivotsX = new long[numPivots]; pivotsY = new long[numPivots]; for(int pivot=0; pivot<numPivots; pivot++){ long x = in.nextLong(); long y = in.nextLong(); pivotsX[pivot] = x; pivotsY[pivot] = y; } // System.out.println("taken the pivots"); disks = new Disk[numDisks]; for(int disk=0; disk<numDisks; disk++){ long rad = in.nextLong(); long cost = in.nextLong(); disks[disk] = new Disk(rad, cost); } // System.out.println("taken the disks"); boolean[] cheap = new boolean[numDisks]; long last = disks[numDisks-1].cost; cheap[numDisks-1] = true; int numNice = 1; for(int diskNum=numDisks-2; diskNum>=0; diskNum--){ if(disks[diskNum].cost < last){ cheap[diskNum] = true; last = disks[diskNum].cost; numNice++; } } disksRad = new long[numDisks]; disksCst = new long[numDisks]; int index = 0; for(int disk=0; disk<disks.length; disk++){ if(!cheap[disk]){ continue; } disksRad[index] = disks[disk].radius; disksCst[index] = disks[disk].cost; index++; } numDisks = numNice; disks = null; centreDistances = new long[numPivots][numPivots]; for(int from=0; from<numPivots; from++){ for(int to=0; to<numPivots; to++){ long dx = pivotsX[from] - pivotsX[to]; long dy = pivotsY[from] - pivotsY[to]; centreDistances[from][to] = dx*dx + dy*dy; } } radiiSquares = new long[numDisks][numDisks]; for(int disk1=0; disk1<numDisks; disk1++){ for(int disk2=disk1; disk2<numDisks; disk2++){ radiiSquares[disk1][disk2] = radiiSquares[disk2][disk1] = (disksRad[disk1]+disksRad[disk2]) * (disksRad[disk1]+disksRad[disk2]); } } makeGraph(); long cost = dijkstra(source, target); out.println("impossible"); }else{ out.println(cost); } } out.println("time taken " + (end-start)); } void printGraph(){ for(int i=0; i<numVertices; i++){ for(Edge e : graph[i]){ } } } void printDisks(){ for(int disk=0; disk<numDisks; disk++){ } } ArrayList<Edge>[] graph; int numVertices; int source; int target; void makeGraph(){ source = numDisks * numPivots; target = source + 1; numVertices = target+1; for(int i=0; i<numVertices; i++){ graph[i] = new ArrayList<Edge>(); } // Also have to add forward edges that are on same pivot for(int pivot=0; pivot<numPivots; pivot++){ for(int toDisk=1; toDisk<numDisks; toDisk++){ int to = pivot*numDisks + toDisk; int from = to-1; long cost = disksCst[toDisk] - disksCst[toDisk-1]; graph[from].add(new Edge(from, to, cost)); } } // Adding edges from a disk on a pivot to another disk on a // different pivot. for(int fromPivot=0; fromPivot<numPivots; fromPivot++){ O[] distances = new O[numPivots]; for(int toPivot=0; toPivot<numPivots; toPivot++){ distances[toPivot] = new O(centreDistances[fromPivot][toPivot], toPivot); } int mult = fromPivot*numDisks; for(int diskNum=0; diskNum<numDisks; diskNum++){ int fromVertex = mult + diskNum; long centreY = pivotsY[fromPivot]; long radius = disksRad[diskNum]; if(centreY-radius <= 0){ graph[source].add( new Edge(source, fromVertex, disksCst[diskNum])); } if(centreY+radius >= width){ graph[fromVertex].add(new Edge(fromVertex, target, 0)); } int minIndex = 0; for(O o : distances){ int toPivot = o.pivotNum; if(toPivot==fromPivot){ continue; } long centreDistance = o.distance; while(minIndex < numDisks){ if(centreDistance <= radiiSquares[diskNum][minIndex]){ int toVertex = toPivot*numDisks + minIndex; graph[fromVertex].add( new Edge(fromVertex, toVertex, disksCst[minIndex])); break; }else{ minIndex++; } } if(minIndex==numDisks){ break; } } } } } long dijkstra(int root, int target){ TreeSet<Node> pq = new TreeSet<Node>(); long[] distances = new long[numVertices]; pq.add(new Node(root, 0L)); while(!pq.isEmpty()){ Node top = pq.pollFirst(); int v = top.name; long c = top.val; if(v==target){ return c; } if(c > distances[v]){ continue; } distances[v] = c; for(Edge e : graph[v]){ int to = e.b; long x = e.cost; if(distances[to] > c+x){ pq.remove(new Node(to, distances[to])); distances[to] = c+x; pq.add( new Node(to, c+x)); } } } return distances[target]; } class Node implements Comparable<Node>{ long val; int name; public Node(int name, long val){ this.name = name; this.val = val; } public int compareTo(Node that){ if(x!=0){ return x; } } } } class O implements Comparable<O>{ long distance; int pivotNum; public O(long distance, int pivotNum){ this.distance = distance; this.pivotNum = pivotNum; } return distance + " for " + pivotNum; } public int compareTo(O that){ } } class Disk implements Comparable<Disk>{ long radius; long cost; public Disk(long radius, long cost){ this.radius = radius; this.cost = cost; } public int compareTo(Disk that){ if(cmp == 0){ } return cmp; } return "r = " + radius + ", cost = " + cost; } } class Edge implements Comparable<Edge>{ int a; int b; long cost; // a--->b public Edge(int a, int b, long cost){ this.a = a; this.b = b; this.cost = cost; } public int compareTo(Edge that){ } return a + " " + b + " -> " + cost; } public int other(int v){ if(v==a)return b; return a; } } class FastReader{ private boolean finished = false; private byte[] buf = new byte[1024]; private int curChar; private int numChars; private SpaceCharFilter filter; this.stream = stream; } public int read(){ if (numChars == -1){ throw new InputMismatchException (); } if (curChar >= numChars){ curChar = 0; try{ numChars = stream.read (buf); throw new InputMismatchException (); } if (numChars <= 0){ return -1; } } return buf[curChar++]; } public int peek(){ if (numChars == -1){ return -1; } if (curChar >= numChars){ curChar = 0; try{ numChars = stream.read (buf); return -1; } if (numChars <= 0){ return -1; } } return buf[curChar]; } public int nextInt(){ int c = read (); while (isSpaceChar (c)) c = read (); int sgn = 1; if (c == '-'){ sgn = -1; c = read (); } int res = 0; do{ if (c < '0' || c > '9'){ throw new InputMismatchException (); } res *= 10; res += c - '0'; c = read (); } while (!isSpaceChar (c)); return res * sgn; } public long nextLong(){ int c = read (); while (isSpaceChar (c)) c = read (); int sgn = 1; if (c == '-'){ sgn = -1; c = read (); } long res = 0; do{ if (c < '0' || c > '9'){ throw new InputMismatchException (); } res *= 10; res += c - '0'; c = read (); } while (!isSpaceChar (c)); return res * sgn; } int c = read (); while (isSpaceChar (c)) c = read (); StringBuilder res = new StringBuilder (); do{ res.appendCodePoint (c); c = read (); } while (!isSpaceChar (c)); return res.toString (); } public boolean isSpaceChar(int c){ if (filter != null){ return filter.isSpaceChar (c); } return isWhitespace (c); } public static boolean isWhitespace(int c){ return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } StringBuilder buf = new StringBuilder (); int c = read (); while (c != '\n' && c != -1){ if (c != '\r'){ buf.appendCodePoint (c); } c = read (); } return buf.toString (); } while (s.trim ().length () == 0) s = readLine0 (); return s; } if (ignoreEmptyLines){ return nextLine (); }else{ return readLine0 (); } } try{ throw new InputMismatchException (); } } public char nextCharacter(){ int c = read (); while (isSpaceChar (c)) c = read (); return (char) c; } public double nextDouble(){ int c = read (); while (isSpaceChar (c)) c = read (); int sgn = 1; if (c == '-'){ sgn = -1; c = read (); } double res = 0; while (!isSpaceChar (c) && c != '.'){ if (c == 'e' || c == 'E'){ } if (c < '0' || c > '9'){ throw new InputMismatchException (); } res *= 10; res += c - '0'; c = read (); } if (c == '.'){ c = read (); double m = 1; while (!isSpaceChar (c)){ if (c == 'e' || c == 'E'){ } if (c < '0' || c > '9'){ throw new InputMismatchException (); } m /= 10; res += (c - '0') * m; c = read (); } } return res * sgn; } public boolean isExhausted(){ int value; while (isSpaceChar (value = peek ()) && value != -1) read (); return value == -1; } return nextString (); } public SpaceCharFilter getFilter(){ return filter; } public void setFilter(SpaceCharFilter filter){ this.filter = filter; } public interface SpaceCharFilter{ public boolean isSpaceChar(int ch); } } class RabinKarp{ private long patHash; private int M; // pattern length private long Q; // Modulus private int R; // Radix private long RM; // R ^ (M-1) % Q M = pat.length(); R = 256; this.pat = pat; Q = longRandomPrime(); RM = 1; for(int i=1; i<=M-1; i++){ RM = (R * RM) % Q; } patHash = hash(pat, M); } long h = 0; for(int j=0; j<M; j++){ h = (R*h + key.charAt(j)) % Q; } return h; } // check for exact match int N = txt.length(); if(N<M){ return N; } long txtHash = hash(txt, M); // check for match at offset 0 if(patHash == txtHash && check(txt, 0)){ return 0; } // check for hash match; if hashmatch, check for exact match for(int i=M; i<N; i++){ // Remove leading digit, add trailing digit, check for match txtHash = (txtHash + Q - RM*txt.charAt(i-M) % Q) % Q; txtHash = (txtHash*R + txt.charAt(i)) % Q; // match int offset = i - M + 1; if(patHash==txtHash && check(txt, offset)){ return offset; } } // no match return N; } // Las Vegas version: does pat[] match txt[i...i-M+1] ? for(int j=0; j<M; j++){ if(pat.charAt(j) != txt.charAt(i+j)){ return false; } } return true; } // a random 31-bit prime private static long longRandomPrime(){ return prime.longValue(); } }
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