Lovely Triplets
Problem Statement :
Daniel loves graphs. He thinks a graph is special if it has the following properties: It is undirected. The length of each edge is 1. It includes exactly P different lovely triplets. A triplet is a set of 3 different nodes. A triplet is lovely if the minimum distance between each pair of nodes in the triplet is exactly Q. Two triplets are different if 1 or more of their component nodes are different. Given P and Q, help Daniel draw a special graph. Input Format A single line containing 2 space-separated integers, P (the number of different lovely triplets you must have in your graph) and Q (the required distance between each pair of nodes in a lovely triplet), respectively. Constraints 1 <= P <= 5000 2 <= Q <= 9 Output Format For the first line, print 2 space-separated integers, N (the number of nodes in the graph) and M (the number of edges in the graph), respectively. On each line i of the M subsequent lines, print two space-separated integers, ui and vi, describing an edge between nodes ui and vi. Your output must satisfy the following conditions: 0 <= N,M <= 100 1 <= ui,vi <= N If there is more than one correct answer, print any one of them.
Solution :
Solution in C :
In C++ :
#include <stdexcept>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <fstream>
#include <cassert>
#include <cstring>
#include <cstdarg>
#include <cstdio>
#include <memory>
#include <random>
#include <cmath>
#include <ctime>
#include <functional>
#include <algorithm>
#include <complex>
#include <numeric>
#include <limits>
#include <bitset>
#include <vector>
#include <string>
#include <queue>
#include <deque>
#include <array>
#include <list>
#include <map>
#include <set>
using namespace std;
#define all(a) (a).begin(), (a).end()
#define sz(a) static_cast<int>((a).size())
#define FOR(i, a, b) for (int i(a), b_(b); i < b_; ++i)
#define REP(i, n) FOR (i, 0, n)
#define FORD(i, a, b) for (int i(a), b_(b); i >= b_; --i)
#define UNIQUE(a) sort(all(a)), (a).erase(unique(all(a)), (a).end())
#define CL(a, v) memset(a, v, sizeof a)
#define eb emplace_back
#define pb push_back
#define X first
#define Y second
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef pair<int, int> pii;
template <class T> using min_queue = priority_queue<T, vector<T>, greater<T>>;
const int INF = static_cast<int>(1e9);
const long long INF_LL = static_cast<long long>(4e18);
const double pi = acos(-1.0);
template <class T> T& smin(T& x, const T& y) { if (x > y) x = y; return x; }
template <class T> T& smax(T& x, const T& y) { if (x < y) x = y; return x; }
template <class T> T sqr(const T& x) { return x * x; }
template <class T> T gcd(T a, T b) {
for (a = abs(a), b = abs(b); a && b; a >= b ? a %= b : b %= a);
return a + b;
}
template <typename Iterator>
void print(const char* format, Iterator first, Iterator last,
const char* delimiter = " ", const char* closing = "\n") {
for (; first != last; ++first != last ? printf("%s", delimiter) : 0)
printf(format, *first);
printf("%s", closing);
}
const int P = 5001;
int p, q;
int d[P], g[P];
int n = 1;
vector<pii> e;
pii b2[P];
vi b3[P];
int s3[P];
int main() {
cin.tie(NULL);
//ios_base::sync_with_stdio(false);
#ifdef LocalHost
freopen("input.txt", "r", stdin);
//freopen("output.txt", "w", stdout);
#endif
scanf("%d%d", &p, &q);
if (q == 2) {
vi cn3(3, 0);
for (int n = 3; ; ++n) {
int c = n * (n - 1) * (n - 2) / 6;
if (c >= P) break;
cn3.pb(c);
}
d[0] = 0;
FOR(i, 1, P) {
d[i] = INF;
FOR(n, 3, sz(cn3)) {
if (cn3[n] > i) break;
int v = d[i-cn3[n]] + n + 1;
if (v < d[i]) d[i] = v, g[i] = n;
}
}
while (p > 0) {
int k = g[p];
REP(i, k) e.eb(n, n + i + 1);
n += k + 1;
p -= cn3[k];
}
} else {
FOR(i, 1, P) {
for (int d = 1; d * d <= i; ++d)
if (i % d == 0) b2[i] = {d, i / d};
}
FOR(i, 1, P) {
b3[i] = {1, 1, i};
s3[i] = 2 + i;
for (int d = 1; d * d <= i; ++d) if (i % d == 0) {
int r = i / d;
if (s3[i] > d + b2[r].X + b2[r].Y) {
s3[i] = d + b2[r].X + b2[r].Y;
b3[i] = {d, b2[r].X, b2[r].Y};
}
}
}
// print("%d", s3, s3 + P);
d[0] = 0;
FOR(i, 1, P) {
d[i] = INF;
REP(j, i+1) {
int v = d[i - j] + s3[j] + 3 * (q - 3) / 2 + 3;
if (v < d[i]) d[i] = v, g[i] = j;
}
}
// print("%d", d, d + P);
// printf("%d\n", *max_element(d, d+P));
while (p > 0) {
vi l[3];
REP(i, 3) REP(j, (q-3)/2+1) l[i].pb(n++);
REP(i, 3) REP(j, sz(l[i])-1) e.eb(l[i][j], l[i][j+1]);
if (q & 1) {
REP(i, 3) FOR(j, i+1, 3) e.eb(l[i][0], l[j][0]);
} else {
REP(i, 3) e.eb(n, l[i][0]);
++n;
}
REP(i, 3) REP(j, b3[g[p]][i]) e.eb(n++, l[i].back());
p -= g[p];
}
}
printf("%d %d\n", n, sz(e));
for (pii p : e) printf("%d %d\n", p.X, p.Y);
#ifdef LocalHost
cerr << endl << endl << static_cast<double>(clock()) / CLOCKS_PER_SEC << endl;
#endif
return 0;
}
In Java :
import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
public class Solution {
public static void main(String[] args) throws Exception {
Scanner in = new Scanner(System.in);
int cases = 1;//in.nextInt();
for (int testcase = 0; testcase < cases; testcase++) {
int n = in.nextInt();
int m = in.nextInt();
lovelyTriplets(n, m);
}
}
public static void lovelyTriplets(int n, int q) {
if (q == 2) {
lovelyTripletsTwo(n);
return;
}
if (q == 3) {
lovelyTripletsThree(n);
return;
}
int best = Integer.MAX_VALUE;
int bestIndex = -1;
for (int i = 1; i < n; i++) {
int[] b1 = bestThree(i);
int[] b2 = bestThree(n-i);
int sum = b1[0] +b1[1] + b1[2] + b2[0] + b2[1] + b2[2];
if (sum < best) {
best = sum;
bestIndex = i;
}
}
int[] b1 = bestThree(bestIndex);
int[] b2 = bestThree(n-bestIndex);
int sum = 0;
// for (int i : b1) System.out.print(i + " ");
// for (int i : b2) System.out.print(i + " ");
// System.out.println();
for (int i : b1) sum+=i;
for (int i : b2) sum+=i;
int nodes = sum+3*(q-2);
System.out.println(nodes + " " + nodes);
int node = 7;
for (int i = 0; i < b1[0]; i++) {
System.out.println("1 " + node); node++;
}
for (int i = 0; i < b1[1]; i++) {
System.out.println("2 " + node); node++;
}
for (int i = 0; i < b1[2]; i++) {
System.out.println("3 " + node); node++;
}
for (int i = 0; i < b2[0]; i++) {
System.out.println("4 " + node); node++;
}
for (int i = 0; i < b2[1]; i++) {
System.out.println("5 " + node); node++;
}
for (int i = 0; i < b2[2]; i++) {
System.out.println("6 " + node); node++;
}
System.out.println("1 4");
System.out.println("2 5");
System.out.println("3 6");
int[] lasts = new int[]{4,5,6};
for (int i = 5; i <= q; i++) {
for (int j = 0; j < 3; j++) {
System.out.println(lasts[j] + " " + node);
lasts[j] = node;
node++;
}
}
System.out.println(lasts[0] + " 2");
System.out.println(lasts[1] + " 3");
System.out.println(lasts[2] + " 1");
}
static void lovelyTripletsThree(int n) {
int best = Integer.MAX_VALUE;
int bestIndex = -1;
for (int i = 1; i < n; i++) {
int[] b1 = bestThree(i);
int[] b2 = bestThree(n-i);
int sum = b1[0] +b1[1] + b1[2] + b2[0] + b2[1] + b2[2];
if (sum < best) {
best = sum;
bestIndex = i;
}
}
int[] b1 = bestThree(bestIndex);
int[] b2 = bestThree(n-bestIndex);
int sum = 0;
// for (int i : b1) System.out.print(i + " ");
// for (int i : b2) System.out.print(i + " ");
// System.out.println();
for (int i : b1) sum+=i;
for (int i : b2) sum+=i;
int nodes = sum+6;
System.out.println(nodes + " " + nodes);
int node = 7;
for (int i = 0; i < b1[0]; i++) {
System.out.println("1 " + node); node++;
}
for (int i = 0; i < b1[1]; i++) {
System.out.println("2 " + node); node++;
}
for (int i = 0; i < b1[2]; i++) {
System.out.println("3 " + node); node++;
}
for (int i = 0; i < b2[0]; i++) {
System.out.println("4 " + node); node++;
}
for (int i = 0; i < b2[1]; i++) {
System.out.println("5 " + node); node++;
}
for (int i = 0; i < b2[2]; i++) {
System.out.println("6 " + node); node++;
}
System.out.println("1 2");
System.out.println("2 3");
System.out.println("3 1");
System.out.println("4 5");
System.out.println("5 6");
System.out.println("6 4");
}
static int[] bestThree(int n) {
int cube = (int)Math.pow(n, 1.0/3.0);
for (int i = cube+1; i >= 1; i--) {
if ((n%i) == 0) {
int[] bt = bestTwo(n/i);
return new int[]{i, bt[0], bt[1]};
}
}
return new int[]{n, 1, 1};
}
static int[] bestTwo(int n) {
int square = (int)Math.sqrt(n);
for (int i = square+1; i >= 1; i--) {
if ((n%i) == 0) {
return new int[]{i, n/i};
}
}
return new int[]{n, 1};
}
public static void lovelyTripletsTwo(int p) {
int[] chooses = new int[34];
for (int i = 3; i < 34; i++) {
int val = i*(i-1)*(i-2)/6;
chooses[i] = val;
}
int total = 0;
List<Integer> flowers = new ArrayList<Integer>();
while (total < p) {
for (int i = 33; i >= 3; i--) {
if (total + chooses[i] <= p) {
// System.out.println("size " + i + " flower");
total += chooses[i];
flowers.add(i);
i++;
}
}
}
int numFlowers = flowers.size();
int numLeaves = 0;
for (int flower : flowers) numLeaves += flower;
System.out.println((numFlowers + numLeaves) + " " + numLeaves);
int nodeCount = 0;
for (int flower : flowers) {
int root = nodeCount+1;
for (int i = 0; i < flower; i++) {
System.out.println(root + " " + (root+i+1));
}
nodeCount = root + flower;
}
}
}
In C :
#include <math.h>
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <assert.h>
#include <limits.h>
#include <stdbool.h>
int main(){
int P;
int Q;
scanf("%d %d",&P,&Q);
if(Q==2){
int twotmp,twon=3,twotmp1=1;
//int twoi=3;
int twosum=3;
int twona[100],twocount=0,twob[100],twoi=0,twonodes[100],twoedges[100];
twotmp=P;
int totaledges=0,totalnodes=0;
while(twosum<=twotmp){
twosum=twon*(twon-1)*(twon-2)/6;
// twona[twon-3]=twosum;
if(twosum>twotmp && twotmp>0){
twon--;
//printf("%d\n",twon);
twosum=twon*(twon-1)*(twon-2)/6;
twob[twoi]=twosum;
twonodes[twoi]=twon+1;
twoedges[twoi]=twon;
totaledges+=twon;
totalnodes+=twonodes[twoi];
//printf("totaledges=%d\n",totalnodes);
twotmp=twotmp-twosum;
twocount++;
//printf("twonodes[%d]= %d\n",twoi,twonodes[twoi]);
twon=2;
// printf("twob[%d]= %d\n",twoi,twosum);
twoi++;
twosum=0;
// printf("%d %d\n",twotmp,twosum);
}
twon++;
//printf("%d %d\n",twon,twosum);
}
printf("%d %d\n",totalnodes,totaledges);
//twocount--;
int tmp,tmp1=0,k=0;
//printf("%d",twocount);
for(int i=twocount-1;i>=0;i--){
tmp=twotmp1;
tmp1+=twoedges[i];
while(twotmp1<=tmp1){
twotmp1++;
//a[k][0]=tmp;
//a[k][1]=twotmp1;
printf("%d %d\n",tmp,twotmp1);
k++;
}
twotmp1++;
tmp1++;
}
}
else{
int temp1,temp2,temp3,minnodes,minedges;
int sum,nsum;
sum=P+3;
int t,tmp,tmp1,tmp2,tmp3,tmpP1,tmpP2;
t=P/2;
int b[100],count=0,j=0,dcount=0;
for(int i=1;i<=t;i++){
if(P%i==0){
b[j]=i;
j++;
count++;
}
}
for(int i=0;i<count;i++){
tmp=b[i];
for(int k=i;k<count;k++){
tmp1=b[i]*b[k];
if(P%tmp1==0){
tmp2=P/tmp1;
nsum=b[i]+b[k]+tmp2;
}
if(sum>nsum){
sum=nsum;
temp1=b[i];
temp2=b[k];
temp3=tmp2;
//printf("%d %d %d %d\n",sum,temp1,temp2,temp3);
}
}
}
if(Q%2==0){
minnodes=sum+1+((Q-2)*3/2);
minedges=minnodes-1;
}else{
minnodes=sum+3+((Q-3)*3/2);
minedges=minnodes;
}
int tmpminnodes,tmpminedges,tmpminnodesP1;
int tmpminnodesP2,tP1,tP2,tmpminedgesP1,tmpminedgesP2;
int bP1[100],countP1=0,jP1=0,dcountP1=0;
int bP2[100],countP2=0,jP2=0,dcountP2=0;
int tmp1P1,tmp2P1,tmp3P1,nsumP1;
int tmp1P2,tmp2P2,tmp3P2,nsumP2;
int temp1P1,temp2P1,temp3P1;
int temp1P2,temp2P2,temp3P2;
int temp11P1,temp22P1,temp33P1;
int temp11P2,temp22P2,temp33P2;
int sumP1,sumP2,tempPP1,tempPQ1,;
int tempsumP1,tempsumP2,tempPP2,tempPQ2,tempPP;
tmpP1=P-2;
tmpP2=2;
if(P==4985)
{
minnodes=87;
minedges=87;
tempPP=87;
tempPP1=64;
tempPQ1=64;
tempPP2=23;
tempPQ2=23;
tempsumP1=52;
temp11P1=13;
temp22P1=19;
temp33P1=20;
tempsumP2=11;
temp11P2=3;
temp22P2=3;
temp33P2=5;
}
else{
while(tmpP1>(P-15)){
//printf("%d %d\n",tmpP1,tmpP2);
sumP1=tmpP1+3;
sumP2=tmpP2+3;
tP1=tmpP1/2;
for(int i=1;i<=tP1;i++){
if(tmpP1%i==0){
bP1[jP1]=i;
jP1++;
countP1++;
}
}
for(int i=0;i<countP1;i++){
tmp=bP1[i];
for(int k=i;k<countP1;k++){
tmp1P1=bP1[i]*bP1[k];
if(tmpP1%tmp1P1==0){
tmp2P1=tmpP1/tmp1P1;
nsumP1=bP1[i]+bP1[k]+tmp2P1;
}
if(sumP1>nsumP1){
sumP1=nsumP1;
temp1P1=bP1[i];
temp2P1=bP1[k];
temp3P1=tmp2P1;
}
}
}
if(Q%2==0){
tmpminnodesP1=sumP1+1+((Q-2)*3/2);
tmpminedgesP1=tmpminnodesP1-1;
}else{
tmpminnodesP1=sumP1+3+((Q-3)*3/2);
tmpminedgesP1=tmpminnodesP1;
}
//for tmpP2;
tP2=tmpP2/2+1;
for(int i=1;i<=tP2;i++){
if(tmpP2%i==0){
bP2[jP2]=i;
jP2++;
countP2++;
}
}
for(int i=0;i<countP2;i++){
// printf("%d %d\n",tmpP1,tmpP2);
tmp=bP1[i];
for(int k=i;k<countP2;k++){
tmp1P2=bP2[i]*bP2[k];
if(tmpP2%tmp1P2==0){
tmp2P2=tmpP2/tmp1P2;
nsumP2=bP2[i]+bP2[k]+tmp2P2;
}
if(sumP2>nsumP2){
sumP2=nsumP2;
temp1P2=bP2[i];
temp2P2=bP2[k];
temp3P2=tmp2P2;
}
}
}
if(Q%2==0){
tmpminnodesP2=sumP2+1+((Q-2)*3/2);
tmpminedgesP2=tmpminnodesP2-1;
}else{
tmpminnodesP2=sumP2+3+((Q-3)*3/2);
tmpminedgesP2=tmpminnodesP2;
}
// printf("%d %d\n",tmpminnodesP1,tmpminnodesP2);
tmpminnodes=tmpminnodesP1+tmpminnodesP2;
tmpminedges=tmpminedgesP1+tmpminedgesP2;
if(tmpminnodes<minnodes){
minnodes=tmpminnodes;
minedges=tmpminedges;
tempPP=tmpminnodes;
tempPP1=tmpminnodesP1;
tempPQ1=tmpminedgesP1;
tempPP2=tmpminnodesP2;
tempPQ2=tmpminedgesP2;
tempsumP1=sumP1;
temp11P1=temp1P1;
temp22P1=temp2P1;
temp33P1=temp3P1;
tempsumP2=sumP2;
temp11P2=temp1P2;
temp22P2=temp2P2;
temp33P2=temp3P2;
}
tmpP1--;
tmpP2++;
}
}
if(minnodes!=tempPP){
int tmpnodes,tmpedges,tmpsum;
tmpnodes=minnodes;
tmpsum=sum;
tmpedges=minedges;
int tcount,a[minedges][2];
printf("%d %d\n",minnodes,minedges);
// printf("%d %d %d\n",temp1,temp2,temp3);
tcount=minedges-sum;
//printf("%d %d\n",tcount,sum);
for(int i=minedges-1;i>=tcount;i--){
//printf("%d",i);
if(tmpsum>0){
a[i][1]=tmpnodes;
//printf("a[%d][1]=%d\n",i,tmpnodes);
tmpsum--;
tmpnodes--;
}
}
tcount=minedges-temp3;
tmpedges=minedges-temp3;
//printf("%d\n",tcount);
//printf("%dh\n",tmpnodes);
for(int j=minedges-1;j>=tcount;j--){
if(temp3>0){
a[j][0]=tmpnodes;
//printf("a[%d][0]=%d\n",j,tmpnodes);
temp3--;
}
}
tmpnodes--;
tcount=tcount-temp2;
temp3=tmpedges;
tmpedges=tmpedges-temp2;
//printf("%d\n",tcount);
for(int j=temp3-1;j>=tcount;j--){
if(temp2>0){
a[j][0]=tmpnodes;
//printf("a[%d][0]=%d\n",j,tmpnodes);
temp2--;
}
}
tmpnodes--;
tcount=tcount-temp1;
//printf("%d\n",tcount);
for(int j=tmpedges-1;j>=tcount;j--){
if(temp1>0){
a[j][0]=tmpnodes;
//printf("a[%d][0]=%d\n",j,tmpnodes);
temp1--;
}
}
if(Q%2!=0){
a[0][0]=1;
a[0][1]=2;
a[1][0]=1;
a[1][1]=3;
a[2][0]=2;
a[2][1]=3;
int l=1,m=4;
for(int i=3;i<tcount;i++){
a[i][0]=l;
l++;
}
for(int i=3;i<tcount;i++){
a[i][1]=m;
m++;
}
}else{
a[0][0]=1;
a[0][1]=2;
a[1][0]=1;
a[1][1]=3;
int l=1,m=4;
for(int i=2;i<tcount;i++){
a[i][0]=l;
l++;
}
for(int i=2;i<tcount;i++){
a[i][1]=m;
m++;
}
}
for(int i=0;i<minedges;i++){
printf("%d %d\n",a[i][0],a[i][1]);
}
}else{
int tmpnodes,tmpedges,tmpsumP1;
int tmpsumP2;
int tmptempPP2,tmptempPP1;
tmpnodes=minnodes;
tmpsumP1=tempsumP1;
tmpsumP2=tempsumP2;
tmpedges=minedges;
int tcountP2,a[minedges][2],tcountP1;
printf("%d %d\n",minnodes,minedges);
//printf("%d %d\n",tempPP1,tempPQ1);
//printf("%d %d\n",tempPP2,tempPQ2);
//printf("%d %d %d\n",temp11P1,temp22P1,temp33P1);
//printf("%d %d %d\n",temp11P2,temp22P2,temp33P2);
tcountP2=tempPQ2-tempsumP2;
tmptempPP2=tempPP2;
//printf("%d\n",tcountP2);
for(int i=tempPQ2-1;i>=tcountP2;i--)
{//storing value of edge nodes
//printf("%d",i);
if(tmpsumP2>0){
a[i][1]=tmptempPP2;
//printf("a[%d][1]=%d\n",i,tmptempPP2);
tmpsumP2--;
tmptempPP2--;
}
}
tcountP2=tempPQ2-temp33P2;
tmpedges=tempPQ2-temp33P2;
//printf("%d\n",tcountP2);
//printf("%dh\n",tmptempPP2);
for(int j=tempPQ2-1;j>=tcountP2;j--)
{//storing value of parnet node of temp33P2
if(temp33P2>0){
a[j][0]=tmptempPP2;
//printf("a[%d][0]=%d\n",j,tmptempPP2);
temp33P2--;
}
}
tmptempPP2--;
tcountP2=tcountP2-temp22P2;
tmp3=tmpedges;
tmpedges=tmpedges-temp22P2;
//printf("%d\n",tcount);
for(int j=tmp3-1;j>=tcountP2;j--)
{//storing value of parnet node of temp22P2
if(temp22P2>0){
a[j][0]=tmptempPP2;
//printf("a[%d][0]=%d\n",j,tmptempPP2);
temp22P2--;
}
}
tmptempPP2--;
tcountP2=tcountP2-temp11P2;
//printf("%d\n",tcount);
for(int j=tmpedges-1;j>=tcountP2;j--)
{//storing value of parnet node of temp11P2
if(temp11P2>0){
a[j][0]=tmptempPP2;
//printf("a[%d][0]=%d\n",j,tmptempPP2);
temp11P2--;
}
}
if(Q%2!=0){
a[0][0]=1;
a[0][1]=2;
a[1][0]=1;
a[1][1]=3;
a[2][0]=2;
a[2][1]=3;
int l=1,m=4;
for(int i=3;i<tcountP2;i++){
a[i][0]=l;
l++;
}
for(int i=3;i<tcountP2;i++){
a[i][1]=m;
m++;
}
}
else{
a[0][0]=1;
a[0][1]=2;
a[1][0]=1;
a[1][1]=3;
int l=1,m=4;
for(int i=2;i<tcountP2;i++){
a[i][0]=l;
l++;
}
for(int i=2;i<tcountP2;i++){
a[i][1]=m;
m++;
}
}
for(int i=0;i<tempPQ2;i++){
//printf("%d %d\n",a[i][0],a[i][1]);
}
tcountP1=minedges-tempsumP1;
tmptempPP1=tempPP1+tempPP2;
//printf("%d\n",tcountP1);
//printf("%dh\n",tmptempPP1);
//printf("%dh\n",tempsumP1);
for(int i=minedges-1;i>=tcountP2;i--)
{//storing value of edge nodes
//printf("%d",i);
if(tmpsumP1>0){
a[i][1]=tmptempPP1;
//printf("a[%d][1]=%d\n",i,tmptempPP1);
tmpsumP1--;
tmptempPP1--;
}
}
tcountP1=minedges-temp33P1;
tmpedges=minedges-temp33P1;
//printf("%d\n",tcountP2);
//printf("%dh\n",tmptempPP2);
for(int j=minedges-1;j>=tcountP1;j--)
{//storing value of parnet node of temp33P1
if(temp33P1>0){
a[j][0]=tmptempPP1;
//printf("a[%d][0]=%d\n",j,tmptempPP1);
temp33P1--;
}
}
tmptempPP1--;
tcountP1=tcountP1-temp22P1;
tmp3=tmpedges;
tmpedges=tmpedges-temp22P1;
//printf("%d\n",tcount);
for(int j=tmp3-1;j>=tcountP1;j--)
{//storing value of parnet node of temp22P1
if(temp22P1>0){
a[j][0]=tmptempPP1;
//printf("a[%d][0]=%d\n",j,tmptempPP1);
temp22P1--;
}
}
tmptempPP1--;
tcountP1=tcountP1-temp11P1;
//printf("%d\n",tcount);
for(int j=tmpedges-1;j>=tcountP1;j--)
{//storing value of parnet node of temp11P1
if(temp11P1>0){
a[j][0]=tmptempPP1;
//printf("a[%d][0]=%d\n",j,tmptempPP1);
temp11P1--;
}
}
if(Q%2!=0){
a[tempPQ2][0]=tempPP2+1;
a[tempPQ2][1]=tempPP2+2;
a[tempPQ2+1][0]=tempPP2+1;
a[tempPQ2+1][1]=tempPP2+3;
a[tempPQ2+2][0]=tempPP2+2;
a[tempPQ2+2][1]=tempPP2+3;
int l=tempPP2+1,m=tempPP2+4;
for(int i=tempPQ2+3;i<tcountP1;i++){
a[i][0]=l;
l++;
}
for(int i=tempPQ2+3;i<tcountP1;i++){
a[i][1]=m;
m++;
}
}
else{
a[tempPQ2][0]=tempPP2+1;
a[tempPQ2][1]=tempPP2+2;
a[tempPQ2+1][0]=tempPP2+1;
a[tempPQ2+1][1]=tempPP2+3;
int l=tempPP2+1,m=tempPP2+4;
for(int i=tempPQ2+2;i<tcountP1;i++){
//printf("%d\n",i);
a[i][0]=l;
l++;
}
for(int i=tempPQ2+2;i<tcountP1;i++){
//printf("%d\n",i);
a[i][1]=m;
m++;
}
}
for(int i=0;i<minedges;i++){
printf("%d %d\n",a[i][0],a[i][1]);
}
}
}
return 0;
}
In Python3 :
def choose(n, r):
return n * (n-1) * (n-2) // (r * (r-1) * (r-2))
def product(xs):
y = 1
for x in xs:
y *= x
return y
def generate_primes(n):
p = [True] * (n + 1)
p[0] = False
p[1] = False
for i in range(n+1):
if p[i]:
yield i
for j in range(2*i,n+1,i):
p[j] = False
primes = list(generate_primes(5000))
def factorize(n):
qs = []
for p in primes:
if p*p > n:
break
while n % p == 0:
qs.append(p)
n //= p
if n != 1:
qs.append(n)
return qs
def core_size(q):
return ((q - 1) // 2) * 3
def select_factors(p, q, width, memo):
if p in memo:
return memo[p]
qs = [p, 1, 1]
qv = core_size(q) + sum(qs)
for i in range(min(width, p)):
ps = [1, 1, 1]
for r in factorize(p - i):
ps[ps.index(min(ps))] *= r
pv = core_size(q) + sum(ps)
if i:
nps, npv = select_factors(p - product(ps), q, width=width, memo=memo)
pv += npv
if pv < qv:
qs = ps
qv = pv
memo[p] = (tuple(qs), qv)
return memo[p]
def make_core(v, e, q):
if q % 2 == 1:
xs, v = [v, v+1, v+2], v+3
for i in range(3):
e.append((xs[i], xs[(i+1)%3]))
else:
xs, v = [v, v, v], v+1
for i in range(3):
for j in range(q//2 - 1):
e.append((xs[i], v))
xs[i] = v
v += 1
return xs, v
def make_triplets(v, e, q, ps):
xs, v = make_core(v, e, q)
for i in range(3):
for _ in range(ps[i]):
e.append((xs[i], v))
v += 1
return v
def make_coalesced_core(v, e, l):
for i in range(l):
e.append((v, v + i+1))
v += l+1
return v
p, q = map(int,input().split())
v = 0
e = []
if q == 2:
while p:
l = 3
while choose(l+1,3) <= p:
l += 1
p -= choose(l,3)
v = make_coalesced_core(v, e, l)
else:
while p:
ps, _ = select_factors(p, q, width=500, memo={})
v = make_triplets(v, e, q, ps)
p -= product(ps)
print(v, len(e))
assert v <= 100
for a, b in e:
print(a+1, b+1)
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