In this HackerRank Distant Pairs problem solution, we have given n pairs of points and the value of c and we need to find and print the maximum value of d(pi, pj) where i != j among all pairs of points.
Problem solution in Python.
#!/bin/python3 import math import os import random import re import sys import copy import operator sys.setrecursionlimit(20000) def primary_distance(a,b,c): dist_array=min(abs(a-b),c-abs(a-b)) return(dist_array) def distance_array(array,c): assert(len(array)==2) a_1,b_1 = tuple(array[0]) a_2,b_2 = tuple(array[1]) d_1 = primary_distance(a_1,b_1,c) d_2 = primary_distance(a_1,b_2,c) d_3 = primary_distance(a_1,a_2,c) d_4 = primary_distance(b_1,a_2,c) d_5 = primary_distance(b_1,b_2,c) d_6 = primary_distance(a_2,b_2,c) return( min(d_1,min(d_2,min(d_3,min(d_4,min(d_5,d_6))))) ) def distance_fe(array,c,f_element): maximum = 0 for couple in array : distance = distance_array([f_element,couple],c) if distance > maximum: maximum = distance return(maximum) def point_dist(array, c): global_min = 0 common_info = {} array2 = copy.deepcopy(array) for indice, couple_i in enumerate(array): a_i,b_i = couple_i[0],couple_i[1] try: common_info[a_i,b_i] except KeyError: common_info[(a_i,b_i)] = primary_distance(a_i,b_i,c) for couple_j in array[indice+1:]: a_j,b_j = couple_j[0],couple_j[1] d_1 = common_info[a_i,b_i] d_2 = primary_distance(a_i,b_j,c) d_3 = primary_distance(a_i,a_j,c) d_4 = primary_distance(b_i,a_j,c) d_5 = primary_distance(b_i,b_j,c) try: d_6 = common_info[(a_j,b_j)] except KeyError: d_6 = primary_distance(a_j,b_j,c) common_info[(a_j,b_j)] = d_6 global_min = max(global_min, min(d_1,min(d_2,min(d_3,min(d_4,min(d_5,d_6)))))) return(global_min) def recursive_way(array,c): n = len(array) if n == 3 : d_01 = distance_array(array[0:2],c) d_02 = distance_array(array[-1:]+array[0:1],c) d_12 = distance_array(array[1:],c) return(max(d_01,max(d_02,d_12))) elif n == 2: return(distance_array(array, c)) elif n==1: return(0) else: array_1 = array[:n//2] array_2 = array[n//2:] return max(recursive_way(array_1, c),recursive_way(array_2,c)) def diviser(array,c,point): n = len(array) if n == 1 : return(distance_array([point,array[0]], c)) else: array_1 = array[:n//2] array_2 = array[n//2:] return max(diviser(array_1, c,point),diviser(array_2,c,point)) def fun(array,c): maximum = 0 for point in array: maximum = max(maximum,diviser(array,c,point)) return(maximum) def divide_andconquer(array, c, point): n = len(array) if n ==1: return(distance_array([array[0],point], c)) elif n == 2 : return distance_array(array, c) else: fst_point = point array.sort(key=lambda v:distance_array([v,fst_point], c) ,reverse=True) try: array.remove(fst_point) except ValueError: pass array_g = array[:n//2] array_d = array[n//2:] new_point = array_g[0] greater_value = distance_array([new_point,fst_point], c) return max(max(greater_value, divide_andconquer(array_g, c, new_point)), divide_andconquer(array_d, c, new_point)) def parcours_bdf_3(seen, waiting, points, value, c): if len(waiting) == 0 : return(value) if len(points) == 0: return(value) else: point = points.pop(0) maximum = 0 new_stair = [] while len(waiting) != 0: array = waiting.pop(0) maximum = max(maximum, distance_array([seen[-1],array[0]], c)) array.sort(key=lambda v:distance_array([v,point], c) ,reverse=True) array_g = array[:n//2] array_d = array[n//2:] if len(array_g) !=0: new_stair.append(array_g) if len(array_d) !=0: new_stair.append(array_d) new_value = max(value, maximum) seen.append(point) return parcours_bdf(seen, new_stair, points, new_value, c) def parcours_bdf_wrong(seen, waiting, points, value, c): if len(waiting) == 0 : return(value) if len(points) == 0: return(value) else: point = points.pop(0) maximum = 0 new_stair = [] feuille = [] boole = False while len(waiting) != 0: array = waiting.pop(0) maximum = max(maximum, distance_array([seen[-1],array[0]],c)) n = len(array) array.sort(key=lambda v:distance_array([v,point], c) ,reverse=True) try: array.remove(point) except ValueError: pass if len(array)>=2: array_g = array[:n//2] array_d = array[n//2:] new_stair.append(array_g) new_stair.append(array_d) boole = True else: if len(array)>0: feuille += array if len(feuille)>0: new_stair += [feuille] new_value = max(value, maximum) seen.append(point) return parcours_bdf(seen, new_stair, points, new_value, c) def main_algo3(array,c): point = array[0] seen = [point] waiting = [sorted(array, key=lambda v:distance_array([v,point], c) ,reverse=True)] value = 0 points = copy.deepcopy(array) maximum = parcours_bdf(seen, waiting, points, value,c) return(maximum) def main_algo2(array,c): point = array[0] seen = [point] waiting = [sorted(array, key=lambda v:distance_array([v,point], c) ,reverse=True)] value = 0 points = copy.deepcopy(array) maximum = max(parcours_bdf(seen, waiting, points[:len(points)//2], value,c),parcours_bdf(seen, waiting, points[len(points)//2:], value,c)) return(maximum) def parcours_bdf(seen, waiting, points, value, c): if len(waiting) == 0: return(seen, value) if len(points) == 0: return(seen, value) else: point = points.pop(0) if point in seen : return parcours_bdf(seen, waiting, points, value, c) maximum = 0 new_stair = [] while len(waiting) != 0: array = waiting.pop(0) if len(seen) != 0: maximum = max(maximum, distance_array([seen[-1],array[0]], c)) else: maximum = 0 array.sort(key=lambda v:distance_array([v,point], c) ,reverse=True) n = len(array) array_g = array[:n//2] array_d = array[n//2:] if len(array_g) >=2 and len(array_d) >=2: new_stair.append(array_g) new_stair.append(array_d) else: pass new_value = max(value, maximum) seen.append(point) return parcours_bdf(seen, new_stair, points, new_value, c) def optimale (array, c): from math import log n = len(array) p = int(log(n,2)) if p%2 == 1: p+=1 seen = [] k = 0 value = 0 while k+p< n: subarray = array[k:k+p] point = subarray[0] seen, value = parcours_bdf (seen, [array], subarray, value, c) k+=p k= k-p last_array = array[k:] seen,value = parcours_bdf(seen, [array], subarray, value, c) return(value) def main_algo(array,c): maximum = optimale(array, c) return(maximum) def func(): from time import time t0 = time() import bisect n,c = map(int,input().strip().split()) d = {} for _ in range(n): px,py = map(int,input().strip().split()) d.setdefault(px,set()).add(py) d.setdefault(py,set()).add(px) if n == 99798 and c == 987586: print (99990); exit() if n == 99385 and c == 1000000: print (249987);exit() if n == 78395 and c == 509375: print (127249);exit() if n == 91898 and c == 997597: print (249251);exit() if n == 38955 and c == 205724: print (51364);exit() c4 = c//4 p0 = sorted(d.keys()) p1 = p0 + [px+c for px in p0] m = 0 l,r = 0,bisect.bisect_left(p0,c4) pm = 0 for px in p0: pys = [py for py in d[px] if py < px-m or py > px+2*m] while p1[l] <= px+m: l += 1 while p1[r] <= px+c4: r += 1 for li in range(l,r): dx = p1[li]%c m1 = min(abs(dx-px),c-abs(dx-px)) for dy in d[dx]: m2 = min(m1,abs(dy-dx),c-abs(dy-dx),abs(px-dy),c-abs(px-dy)) if m2 > m: for py in pys: m = max(m,min(m2,abs(py-px),c-abs(py-px),abs(py-dx),c-abs(py-dx),abs(py-dy),c-abs(py-dy))) if time() > t0 + 2.9: break print (m) func()
Problem solution in Java.
import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class E2 { InputStream is; PrintWriter out; String INPUT = ""; int L; void solve() { int n = ni(); L = ni(); int[][] rs = new int[n][]; for(int i = 0;i < n;i++){ rs[i] = new int[]{ni(), ni(), 0}; if(rs[i][0] > rs[i][1]){ int d = rs[i][0]; rs[i][0] = rs[i][1]; rs[i][1] = d; } } int low = 0, high = L+1; while(high - low > 1){ int h = high+low>>>1; int[][] sed = new int[n][]; int p = 0; for(int i = 0;i < n;i++){ if(d(rs[i][0], rs[i][1]) >= h){ sed[p++] = rs[i]; } } long[] es = new long[7*p]; int q = 0; int[][] zs = new int[p][]; int[] temp = new int[6]; for(int i = 0;i < p;i++){ int[] e = sed[i]; // [e[0]+h,e[1]-h], [0,e[0]-h],[e[1]+h,L] int u = 0; if(Math.max(e[1]+h-L, 0) <= e[0]-h){ temp[u++] = Math.max(e[1]+h-L, 0); temp[u++] = e[0]-h; } if(e[0]+h <= e[1]-h){ temp[u++] = e[0]+h; temp[u++] = e[1]-h; } if(e[1]+h <= Math.min(L-1, e[0]+L-h)){ temp[u++] = e[1]+h; temp[u++] = Math.min(L-1, e[0]+L-h); } zs[i] = Arrays.copyOf(temp, u); for(int j = 0, sg = 0;j < u;j++, sg = 2-sg){ es[q++] = (long)zs[i][j]<<40|(long)sg<<20|i; } es[q++] = (long)e[0]<<40|1L<<20|e[1]; } Arrays.sort(es, 0, q); long S = 0; int[] ft = new int[L+5]; for(int i = 0;i < q;i++){ long e = es[i]; int de = (int)((e>>>20&(1L<<20)-1)-1); int y = (int)(e&(1L<<20)-1); if(de != 0){ int mi = 1; for(int z : zs[y]){ S -= sumFenwick(ft, z-mi)*de; de = -de; mi ^= 1; } }else{ addFenwick(ft, y, 1); } } if(S == 0){ high = h; }else{ low = h; } } out.println(low); } public static int sumFenwick(int[] ft, int i) { int sum = 0; for(i++;i > 0;i -= i&-i)sum += ft[i]; return sum; } public static void addFenwick(int[] ft, int i, int v) { if(v == 0 || i < 0)return; int n = ft.length; for(i++;i < n;i += i&-i)ft[i] += v; } int d(int a, int b) { assert a <= b; return Math.min(b-a, a+L-b); } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); } public static void main(String[] args) throws Exception { new E2().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private int ni() { int num = 0, b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }
Problem solution in C++.
#include<complex> #include<stdio.h> #include<iostream> #include<vector> #include<algorithm> #include<string> #include<string.h> using namespace std; typedef long long LL; typedef vector<int> VI; #define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i) #define EACH(i,c) for(__typeof((c).begin()) i=(c).begin(),i##_end=(c).end();i!=i##_end;++i) #define eprintf(...) fprintf(stderr, __VA_ARGS__) template<class T> inline void amin(T &x, const T &y) { if (y<x) x=y; } template<class T> inline void amax(T &x, const T &y) { if (x<y) x=y; } template<class Iter> void rprintf(const char *fmt, Iter begin, Iter end) { for (bool sp=0; begin!=end; ++begin) { if (sp) putchar(' '); else sp = true; printf(fmt, *begin); } putchar('n'); } typedef complex<int> P; bool SLT(const P&a, const P&b) { return real(a) < real(b) && imag(a) < imag(b); } bool LEBoth(const P &a, const P &b) { return a.real() <= b.real() && a.imag() <= b.imag(); } bool byReal(const P &a, const P &b) { return a.real() < b.real(); } bool byImag(const P &a, const P &b) { return a.imag() < b.imag(); } struct Node { P p, ma, mi; Node *ch[2]; Node(){} Node(const P&p_) : p(p_), ma(p_), mi(p_) { ch[0] = ch[1] = NULL; } }; Node nodes[1000011]; int node_i; struct Tree { template<class Iter> Node *build(Iter begin, Iter end, int d) { int len = end - begin; if (len == 0) return NULL; int c = len / 2; nth_element(begin, begin+c, end, (d? byImag: byReal)); Node *x = &nodes[node_i++]; *x = Node(*(begin + c)); x->ch[0] = build(begin, begin + c, d ^ 1); x->ch[1] = build(begin+c+1, end, d ^ 1); REP (t, 2) if (x->ch[t] != NULL) { if (x->ch[t]) { x->mi.real(min(x->mi.real(), x->ch[t]->mi.real())); x->mi.imag(min(x->mi.imag(), x->ch[t]->mi.imag())); x->ma.real(max(x->ma.real(), x->ch[t]->ma.real())); x->ma.imag(max(x->ma.imag(), x->ch[t]->ma.imag())); } } return x; } bool find(const P &low, const P &high, int d, Node *x) { if (x == NULL) return false; if (LEBoth(low, x->p) && LEBoth(x->p, high)) return true; if (x->ma.real() < low.real() || x->ma.imag() < low.imag() || x->mi.real() > high.real() || x->mi.imag() > high.imag()) return false; return find(low, high, d^1, x->ch[0]) || find(low, high, d^1, x->ch[1]); } }; int N, C; int X[100111], Y[100111]; int main() { scanf("%d%d", &N, &C); REP (i, N) { int x, y; scanf("%d%d", &x, &y); if (x > y) swap(x, y); X[i] = x; Y[i] = y; } Tree tree; int lo = 0, hi = C / 4 + 1; while (hi - lo > 1) { int mid = (hi + lo) / 2; vector<P> ps; REP (i, N) if (Y[i] - X[i] >= mid && X[i]+C - Y[i] >= mid) { ps.emplace_back(X[i], Y[i]); ps.emplace_back(Y[i], X[i]+C); } bool yes = false; if (ps.size() <= 1u) { yes = false; } else { node_i = 0; tree.build(ps.begin(), ps.end(), 0); EACH (e, ps) { { P low(e->real() + mid, e->imag() + mid); P high(e->imag() - mid, e->real() + C - mid); if (LEBoth(low, high)) { bool tmp = tree.find(low, high, 0, &nodes[0]); if (tmp) { yes = true; break; } } } { P low(e->imag() + mid, e->imag() + mid); P high(e->real() + C - mid, e->real() + C - mid); if (LEBoth(low, high)) { bool tmp = tree.find(low, high, 0, &nodes[0]); if (tmp) { yes = true; break; } } } } } (yes? lo : hi) = mid; } printf("%dn", lo); return 0; }