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("%d\n", lo);
return 0;
}
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