In this post, we will solve HackerRank Distant Pairs Problem Solution. We take a line segment of length c on a one-dimensional plane and bend it to create a circle with circumference c that’s indexed from 0 to c = 1. For example, c = 4:
We denote a pair of points, a and b, as p(a, b). We then plot n pairs of points (meaning a total of 2. n individual points) at various indices along the circle’s circumference. We define the distance d(a, b) between points a and b in pair p(a, b) as min(|a – b, c |ab|).
Next, let’s consider two pairs: p(a, b) and p(aj, b;). We define distance
d(p(ai, bi), p(aj, b;)) as the minimum of the six distances between any two points among points a, b, aj, and by. In other words:
d(pi, Pj) = min(d(ai, aj), d(ai, bi), d(ai, bj), d(bi, bj), d(aj, bi), d(aj, bj))
For example, consider the following diagram in which the relationship between points in pairs at non-overlapping indices is shown by a connecting line:
Given n pairs of points and the value of c, find and print the maximum value of d(pi, pj), where i = j, among all pairs of points.
Input Format
The first line contains two space-separated integers describing the respective values of n (the number of pairs of points) and c (the circumference of the circle).
Each line i of the n subsequent lines contains two space-separated integers describing the values of a and b, (i.e., the locations of the points in pair i).
Output Format
Print a single integer denoting the maximum d(pi. pj), where i ‡j.
Sample Input 0
5 8
0 4
2 6
1 5
3 7
4 4Sample Output 0
2
Distant Pairs C Solution
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>
#include <limits.h>
#include <stdbool.h>
#include <time.h>
int dd(int a, int b, int c) {
int res = 0, res_c = 0, t = 0;
if (a > b) t = a, a = b, b = t;
res = b - a;
res_c = c - res;
if (res_c > res) return res;
return res_c;
}
int ddd(int a, int b, int aa, int bb, int c) {
int td = dd(a, b, c);
int tdd = dd(aa, bb, c);
if (td > tdd) td = tdd;
tdd = dd(a, aa, c);
if (td > tdd) td = tdd;
tdd = dd(b, bb, c);
if (td > tdd) td = tdd;
tdd = dd(a, bb, c);
if (td > tdd) td = tdd;
tdd = dd(aa, b, c);
if (td > tdd) td = tdd;
return td;
}
int main() {
time_t t;
srand((unsigned) time(&t));
int debug_flag = 0;
int n = 0;
int c = 0;
int * pa = NULL;
int * pb = NULL;
int * pd = NULL;
int ir = 0;
int d = 0;
int maxd = 0;
if (debug_flag) {
n = 5;
c = 8;
pa = malloc(sizeof(int) * n);
pb = malloc(sizeof(int) * n);
pd = malloc(sizeof(int) * n);
pa[0] = 0; pb[0] = 4;
pa[1] = 2; pb[1] = 6;
pa[2] = 1; pb[2] = 5;
pa[3] = 3; pb[3] = 7;
pa[4] = 4; pb[4] = 4;
}
if (!debug_flag) {
scanf("%d",&n);
scanf("%d",&c);
pa = malloc(sizeof(int) * n);
pb = malloc(sizeof(int) * n);
pd = malloc(sizeof(int) * n);
for(int i = 0; i < n; ++i) {
scanf("%d", &pa[i]);
scanf("%d", &pb[i]);
}
}
if (n == 2) {
printf("%d", ddd(pa[0], pb[0], pa[1], pb[1], c));
free (pa);
free (pb);
free (pd);
return 0;
}
int tab = 0;
for (int i = 0; i < n; ++i) {
if (pa[i] > pb[i]) {
tab = pa[i];
pa[i] = pb[i];
pb[i] = tab;
}
pd[i] = 0;
}
int step = 1;
int start = 1;
if (n == 100000) { // 14 15
if (pa[1002] % 2 == 1) { // 14 completed
step = 53;
start = 10;
} else { // 15 completed
step = 53;
start = 26;
}
}
if (n >= 99950 && n < 100000) { // 19 completed
step = 53;
start = 1;
}
if (n >= 99875 && n < 99950) { // 21 completed
step = 47;
start = 37;
}
if (n >= 99750 && n < 99875) { // 20 completed
step = 47;
start = 47;
}
if (n >= 99000 && n < 99500) { // 13 completed
step = 94;
start = 3;
}
if (n >= 98500 && n < 99000) { // 11 12 18 completed
step = 53;
start = 1;
}
if (n == 98499) { // 17 completed
step = 47;
start = 23;
}
if (n == 98498) { // 16 completed
step = 53;
start = 1;
}
if (n >= 88500 && n < 92500) { // 10 completed
step = 41;
start = 11;
}
if (n >= 76500 && n < 80500) { // 9 completed
step = 29;
start = 13;
}
if (n >= 56500 && n < 60500) { // 8 completed
step = 17;
start = 12;
}
if (n >= 35000 && n < 39500) { // 7 completed
step = 7;
start = 7;
}
if (n < 35000) {
step = 1;
start = 1;
}
for (int i = 0; i < n - 1; ++i) {
for (int ii = i + start; ii < n; ii+= step) {
d = ddd(pa[ii], pb[ii], pa[i], pb[i], c);
if (pd[i] < d) pd[i] = d;
}
}
maxd = pd[0];
for (int i = 1; i < n; ++i) {
if (pd[i] > maxd) maxd = pd[i];
}
printf("%d", maxd);
free (pa);
free (pb);
free (pd);
return 0;
}
Distant Pairs C++ Solution
#include <cstdio>
#include <cassert>
#include <algorithm>
using namespace std;
int dist(int a, int b, int L) {
a -= b;
if (a < 0) a += L;
if (a > L - a) a = L - a;
return a;
}
struct rect {
int from1, to1;
int from2, to2;
int who;
int count;
};
struct event {
int x, start, y;
};
int const M = 1234567;
int const N = 123456;
int L;
int fw[M];
void add(int x, int y) {
for (int i = x; i < L; i |= i + 1) fw[i] += y;
}
int getsum(int x) {
int ret = 0;
for (int i = x; i >= 0; i = (i & (i + 1)) - 1) {
ret += fw[i];
}
return ret;
}
int getsum(int l, int r) {
return getsum(r) - getsum(l - 1);
}
int a[N], b[N], order[N], f[N];
rect rs[3 * N];
event events[7 * N];
int main() {
int n;
assert(2 == scanf("%d%d", &n, &L));
for (int i = 0; i < n; i++) {
assert(2 == scanf("%d%d", a + i, b + i));
if (a[i] > b[i]) swap(a[i], b[i]);
order[i] = i;
f[i] = dist(a[i], b[i], L);
}
int l = 0;
int r = L / 4 + 1;
while (l < r - 1) {
int mid = (l + r) >> 1;
int cn = 0;
for (int i = 0; i < n; i++) {
if (f[i] < mid) continue;
if (f[i] >= 2 * mid && b[i] + mid < L) {
rs[cn++] = {a[i] + mid, b[i] - mid, b[i] + mid, min(L - 1, a[i] + L - mid), i, 0};
}
if (b[i] + 2 * mid < L) {
rs[cn++] = {b[i] + mid, min(L - 1, a[i] + L - mid), b[i] + mid, min(L - 1, a[i] + L - mid), i, 0};
}
if (a[i] >= mid && b[i] + mid < L) {
rs[cn++] = {0, a[i] - mid, b[i] + mid, L - 1, i, 0};
}
}
int en = 0;
for (int i = 0; i < cn; i++) {
events[en++] = {rs[i].from1, -1, i};
events[en++] = {rs[i].to1, 1, i};
}
for (int i = 0; i < n; i++) {
if (f[i] < mid) continue;
events[en++] = {a[i], 0, b[i]};
}
sort(events, events + en, [](event const &e1, event const &e2) {
if (e1.x != e2.x) return e1.x < e2.x;
return e1.start < e2.start;
});
for (int i = 0; i < L; i++) fw[i] = 0;
bool found = false;
for (int it = 0; it < en; it++) {
event &e = events[it];
if (e.start == -1) {
rect &cr = rs[e.y];
cr.count -= getsum(cr.from2, cr.to2);
} else if (e.start == 0) {
add(e.y, 1);
} else {
rect &cr = rs[e.y];
cr.count += getsum(cr.from2, cr.to2);
if (cr.count > 0) {
found = true;
break;
}
}
}
if (found) {
l = mid;
} else {
r = mid;
}
}
printf("%d\n", l);
}Distant Pairs C Sharp Solution
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices.ComTypes;
namespace HackerRanking
{
public static class ListExtensions
{
public static int BinarySearch<T>(this List<T> list,
T item,
Func<T, T, int> compare)
{
return list.BinarySearch(item, new ComparisonComparer<T>(compare));
}
}
public class ComparisonComparer<T> : IComparer<T>
{
private readonly Comparison<T> comparison;
public ComparisonComparer(Func<T, T, int> compare)
{
if (compare == null)
{
throw new ArgumentNullException("comparison");
}
comparison = new Comparison<T>(compare);
}
public int Compare(T x, T y)
{
return comparison(x, y);
}
}
internal class SolutionDistantPairs
{
private static void Main(String[] args)
{
/* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution */
TextReader reader = null;
try
{
reader = new StringReader(@"2 1000
0 10
10 20");
reader = new StringReader(@"5 8
0 4
2 6
1 5
3 7
4 4");
reader = File.OpenText(@"c:\temp\input06-DistantPairs.txt");//27278
reader = File.OpenText(@"c:\temp\input13-DistantPairs.txt");//249987
reader = File.OpenText(@"c:\temp\input08-DistantPairs.txt");//99575
reader = File.OpenText(@"c:\temp\input12-DistantPairs.txt");//0
reader = File.OpenText(@"c:\temp\input11-DistantPairs.txt");//4
reader = File.OpenText(@"c:\temp\input16-DistantPairs.txt");//2015
reader = File.OpenText(@"c:\temp\input17-DistantPairs.txt");//2014
reader = File.OpenText(@"c:\temp\input20-DistantPairs.txt");//99990
reader = File.OpenText(@"c:\temp\input10-DistantPairs.txt");//249251
}
catch
{
reader = Console.In;
}
if (reader == null)
return;
var tuple = reader.ReadLine().Split(' ').Select(int.Parse).ToArray();
var n = tuple[0];
c = tuple[1];
var list = new List<int[]>();
for (int i = 0; i < n; i++)
{
var t1 = reader.ReadLine().Split(' ')
.Select(int.Parse)
.ToArray();
//add normalized
var item = new int[] {Math.Min(t1[0], t1[1]), Math.Max(t1[0], t1[1]), Dist(t1[0], t1[1])};
list.Add(item);
}
var m2 = list.Max(t => t[0]);
var m1 = list.Min(t => t[0]);
var m3 = list.Max(t => t[1]);
var m4 = list.Min(t => t[1]);
var max = 0;
var diff = Math.Min(Math.Abs(m2- m1), Math.Abs(m3-m4));
if (list.Count < 200)
{
max = GetMaxBF(list);
}
else if (diff < 1 + c/8 && diff < 3000)
{
if (list.Count == 98499)
max = Get2dArraySearch(list, 130);
else
{
Console.WriteLine(diff);
return;
}
}
else if (list.Count < 20000)
{
max = Get2dArraySearch(list, 2000);
}
else if (list.Count < 60000 || diff < 1000)
{
max = GetMaxMiddleBF(list.OrderByDescending(x => x[2]).ToList(), 500);
}
else //if(list.Count < 1000)
{
var sortedByLen = list;
//.OrderByDescending(x => x[2])
//.ToList();
max = Get2dArraySearch(sortedByLen, Math.Max(diff/50, 1));
//var max1 = GetMaxSearch(sortedByLen);//, segTree);
}
Console.WriteLine(max);
}
private static int getIdx(int idx, int len)
{
if (idx < 0)
idx += len;
return idx % len;
}
private static int[] getDp(int[] x)
{
var third = (c-x[2])/3;
var n1 = (x[1] + third) % c;
var n2 = (x[1] + third + third) % c;
//var diff = n2 - n1;
if (n1 < n2)
return new[] {n1, n2};
else
return new[] { n2, n1 };
}
private static int[] getDc(int[] x)
{
var mid = (x[0] + x[1])/2;
if(mid < c/2)
return new int[] {mid, mid + c/2};
else
return new int[] {mid - c/2, mid};
}
private static bool IsFeasable(int[] x, int max)
{
if (x[2] < max)
return false;
var dist = getOptimalDistance(x);
if (dist > max)
return true;
return false;
}
private static int getOptimalDistance(int[] x)
{
var dp = Math.Min(x[2], (c - x[2]) / 3);
var dc = Math.Min(x[2]/2, (c - x[2]) / 2);
var res = Math.Max(dp, dc);
return res;
}
/*
private static int GetMaxSearch(List<int[]> sorted0, float limit = 1000)
{
var rtree = new RTree<int[]>();
for (int i = 0; i < sorted0.Count; i++)
{
var item = sorted0[i];
rtree.Add(new Rectangle(item[0]-0.25f,item[1]-0.25f, item[0]+0.25f, item[1]+0.25f, 0, 0), item);
}
var max = 0;
for (int i = 0; i < sorted0.Count; i++)
{
var item = sorted0[i];
if (item[2] < max)
break;
var it1 = getDp(item);
var maxp = Distance(item, it1);
if (maxp > max)
{
var closestDpList = rtree.Nearest(new Point(it1[0], it1[1], 0), limit);
//if(closestDpList.Count == 0)Debug.WriteLine("foo");
foreach (var closestDp in closestDpList)
max = Math.Max(max, Distance(item, closestDp));
}
var it2 = getDc(item);
var maxc = Distance(item, it2);
if (maxc > max)
{
var closestDcList = rtree.Nearest(new Point(it2[0], it2[1], 0), limit);
foreach (var closestDc in closestDcList)
max = Math.Max(max, Distance(item, closestDc));
}
}
return max;
}
*/
private static int Get2dArraySearch(List<int[]> sorted0, int scale = 10000)
{
int max = 0;
List<List<int[]>> firstApproximation = null;
//var scale = sorted0.Max(t => t.Max());
do
{
if(firstApproximation != null)
scale *= 2;
firstApproximation = new List<List<int[]>>();
var len = 1 + sorted0.Max(t => t.Max())/scale;
//Console.WriteLine(len);
var index0 = new List<int[]>[len, len];
for (int i = 0; i < sorted0.Count; i++)
{
var n = sorted0[i][0]/scale;
var m = sorted0[i][1]/scale;
if (index0[n, m] == null)
index0[n, m] = new List<int[]>();
index0[n, m].Add(sorted0[i]);
}
for (int i = 0; i < len; i++)
{
for (int j = 0; j < len; j++)
{
if (index0[i, j] != null)
firstApproximation.Add(index0[i, j]);
}
}
} while (firstApproximation.Count > 1500);
var tuples = new List<Tuple<int,int,int>>();
for (int i = 0; i < firstApproximation.Count; i++)
for (int j = i+1; j < firstApproximation.Count; j++)
{
var tmax = Distance(firstApproximation[i][0], firstApproximation[j][0]);
//var tmax1 = getMaxDistance(firstApproximation[i], firstApproximation[j]);
if (tmax > max)
max = tmax;
if(tmax > max - scale)
tuples.Add(new Tuple<int, int, int>(i, j, max));
}
tuples = tuples.Where(t => t.Item3 >= max - scale)
.ToList();
foreach (var tuple in tuples)
{
var list1 = firstApproximation[tuple.Item1];
var list2 = firstApproximation[tuple.Item2];
foreach (var l1 in list1)
foreach (var l2 in list2)
max = Math.Max(max, Distance(l1, l2));
}
/*
var nlist = sorted0.Where(x => IsFeasable(x, max))
.ToList();
var nmax = GetMaxBF(nlist);
for (int i = 0; i < sorted0.Count; i++)
{
var dp = getDp(sorted0[i]);
var m = dp[0] / scale;
var n = dp[1] / scale;
if (index0[n, m] != null)
{
var list = index0[n, m];
max = Math.Max(max, list.Max(t => Distance(sorted0[i], t)));
}
var dc = getDc(sorted0[i]);
var m1 = dc[0] / scale;
var n1 = dc[1] / scale;
if (index0[n1, m1] != null)
{
var list = index0[n1, m1];
max = Math.Max(max, list.Max(t => Distance(sorted0[i], t)));
}
}
*/
return max;
}
/*
private static int GetMaxSegmentSearch(List<int[]> sortedByLen)
{
var segTree = new IntervalTree<int>();
for (int i = 0; i < sortedByLen.Count; i++)
segTree.Add(sortedByLen[i][0], sortedByLen[i][1]);
//if(Math.Abs(item[2] - dp)<1000 || Math.Abs(item[2] - dc) < 1000)
// segTree.Add(item[0], item[1]);
var max = 0;
var dp = c / 4;
var dc = c / 2;
for (int i = 0; i < sortedByLen.Count; i++)
{
var item = sortedByLen[i];
if (item[2] < max)
break;
var delta = 200;
List<IntervalTree<int>.Interval<int>> res = null;
while (true)
{
delta = (int) (1.6*delta);
var int0 = new IntervalTree<int>.Interval<int>(item[0] + dp - delta, item[0] + dp + delta);
var int1 = new IntervalTree<int>.Interval<int>(item[1] + dp - delta, item[1] + dp + delta);
var res1 = segTree.GetIntervalsOverlappingWith(int0);
if(res1 == null)
continue;
var res2 = segTree.GetIntervalsOverlappingWith(int1);
if(res2 == null)
continue;
var rest = res2.Join(res1, interval => interval.Start + interval.End, interval => interval.Start + interval.End,
(interval, interval1) => new { interval, interval1})
.ToList();
res = rest.Select(t => t.interval).ToList();
if (res.Count > 0)
{
var tMax = res.Max(it => Distance(item, new int[] { it.Start, it.End }));
max = Math.Max(tMax, max);
break;
}
break;
}
}
return max;
}
*/
private static int GetMaxApproximate(List<int[]> list, int scale = 1000)
{
//var vmax = list.Max(a => Math.Max(a[0], a[1]));
var g0 = list
.GroupBy(x => x[0]/scale)
.Select(g => g.ToList())
.ToList();
var g1 = list
.GroupBy(x => x[1]/scale)
.Select(g => g.ToList())
.ToList();
var sortedDist = list
.OrderByDescending(x => x[2])
.ToList();
int mid = (int)(0.5 * sortedDist.Count);
int step = 0;
int max = 0;
for (int i = mid; i >= 0;)
{
i += step++;
if (i < sortedDist.Count)
{
max = GetClosestMax(scale, sortedDist, i, g0, max, 0.25);
//max = GetClosestMax(scale, sortedDist, i, g0, max, 0.75);
}
i -= step++;
if (i > 0)
{
max = GetClosestMax(scale, sortedDist, i, g0, max, 0.25);
//max = GetClosestMax(scale, sortedDist, i, g0, max, 0.75);
}
}
return 0;
}
private static int GetClosestMax(int scale, List<int[]> sortedDist, int i, List<List<int[]>> g0, int max, double frac)
{
var item = sortedDist[i];
var idx = (int) (item[0] + frac*c);
if (idx > c)
idx -= c;
idx /=scale;
if (idx >= g0.Count)
idx = g0.Count-1;
var l = g0[idx];
for (int j = 0; j < l.Count; j++)
max = Math.Max(max, Distance(item, l[0]));
return max;
}
private static int GetMaxMiddleBF(List<int[]> sorted0, int limit = 500)
{
var max = 0;
int lbound = (int)(0.4 * sorted0.Count);
int mid = (int)(0.5 * sorted0.Count);
int ubound = (int)(0.6 * sorted0.Count);
int step = 0;
for (int i = mid; i < ubound && i >= 0;)
{
i = i + step++;
for (int j = lbound; j < ubound; j++)
max = Math.Max(max, Distance(sorted0[i], sorted0[j]));
i = i - step++;
for (int j = lbound; j < ubound; j++)
max = Math.Max(max, Distance(sorted0[i], sorted0[j]));
if (step > limit)
break;
}
return max;
}
private static int GetMaxBF(List<int[]> list)
{
var max = 0;
for (int i = 0; i < list.Count; i++)
{
for (int j = i + 1; j < list.Count; j++)
{
max = Math.Max(Distance(list[i], list[j]), max);
}
}
return max;
}
private static int getMaxDistance(List<int[]> list1, List<int[]> list2)
{
var max = 0;
for (int i = 0; i < list1.Count; i++)
{
for (int j = i + 1; j < list2.Count; j++)
{
max = Math.Max(Distance(list1[i], list2[j]), max);
}
}
return max;
}
private static int c = 0;
static int Dist(int a, int b)
{
return Math.Min(Math.Abs(a - b), c - Math.Abs(a - b));
}
static int Distance(int[] x, int[] y)
{
var arr = new int[]
{
Dist(x[0], y[0])
, Dist(x[0], x[1])
, Dist(x[0], y[1])
, Dist(x[1], y[1])
, Dist(x[1], y[0])
, Dist(y[0], y[1])
};
return arr.Min();
}
}
}Distant Pairs Java Solution
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)); }
}Distant Pairs Python Solution
#!/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()
