In this HackerRank Computer Game problem solution, Sophia is playing a game on the computer. There are two random arrays A & B, each having the same number of elements. The game begins with Sophia removing a pair (Ai, Bj) from the array if they are not co-prime. She keeps a count on the number of times this operation is done.
Sophia wants to find out the maximum number of times(S) she can do this on the arrays. Could you help Sophia find the value?
Problem solution in Java.
import java.io.*;
import java.util.*;
public class Solution {
private static BufferedReader in;
private static Integer n, pi, vn, source, dest, result;
private static Map<Integer, Integer> primeNodes;
private static Integer[] primeSieve;
private static List<Edge>[] graph;
public static void main(String args[]) throws IOException {
String[] s;
int[] n1, n2;
in = new BufferedReader(new InputStreamReader(System.in));
n = Integer.parseInt(in.readLine());
n1 = new int[n];
s = in.readLine().split("\\s");
for (int i = 0; i < n; i++)
n1[i] = Integer.parseInt(s[i]);
n2 = new int[n];
s = in.readLine().split("\\s");
for (int i = 0; i < n; i++)
n2[i] = Integer.parseInt(s[i]);
source = 0;
dest = 1;
graph = createGraph(300000);
primeNodes = new HashMap<>();
primeSieve = primeSieve(1000000000);
for (int i = 0; i < n; i++) {
vn = i + 2;
addEdge(graph, source, vn, 1);
for (Integer p : primeFactors(n1[i], primeSieve)) {
pi = primeNodes.get(p);
if (pi == null) {
pi = n * 2 + primeNodes.size() + 1;
primeNodes.put(p, pi);
}
addEdge(graph, vn, pi, 1);
}
}
for (int i = 0; i < n; i++) {
vn = n + i + 2;
addEdge(graph, vn, dest, 1);
for (Integer p : primeFactors(n2[i], primeSieve)) {
pi = primeNodes.get(p);
if (pi != null)
addEdge(graph, pi, vn, 1);
}
}
result = maxFlow(graph, source, dest);
System.out.println(result);
}
private static Integer[] primeSieve(int max) {
List<Integer> sieve = new ArrayList<>();
int[] divisor = new int[(int) Math.sqrt(max) - 2];
boolean[] prime = new boolean[(int) Math.sqrt(max) + 3];
Arrays.fill(prime, true);
for (int i = 2; i < prime.length; i++) {
if (!prime[i])
continue;
divisor[i] = i;
int j = i * i;
while (j < prime.length) {
prime[j] = false;
if (j < divisor.length)
divisor[j] = i;
j += i;
}
sieve.add(i);
}
return sieve.toArray(new Integer[0]);
}
private static Set<Integer> primeFactors(int n, Integer[] primeSieve) {
final Set<Integer> primes = new HashSet<>();
for (Integer p : primeSieve) {
if(p > Math.sqrt(n) + 1) break;
while (n % p == 0) {
primes.add(p);
n /= p;
}
}
if (n > 2)
primes.add(n);
return primes;
}
private static List<Edge>[] createGraph(int nodes) {
List<Edge>[] graph = new List[nodes];
for (int i = 0; i < nodes; i++)
graph[i] = new ArrayList<>();
return graph;
}
private static void addEdge(List<Edge>[] graph, int s, int t, int cap) {
graph[s].add(new Edge(t, graph[t].size(), cap));
graph[t].add(new Edge(s, graph[s].size() - 1, 0));
}
private static boolean BFS(List<Edge>[] graph, int src, int dest, int[] dist) {
Arrays.fill(dist, -1);
dist[src] = 0;
int[] Q = new int[graph.length];
int sizeQ = 0;
Q[sizeQ++] = src;
for (int i = 0; i < sizeQ; i++) {
int u = Q[i];
for (Edge e : graph[u])
if (dist[e.t] < 0 && e.f < e.cap) {
dist[e.t] = dist[u] + 1;
Q[sizeQ++] = e.t;
}
}
return dist[dest] >= 0;
}
private static int DFS(List<Edge>[] graph, int[] ptr, int[] dist, int dest, int u, int f) {
if (u == dest)
return f;
for (; ptr[u] < graph[u].size(); ++ptr[u]) {
Edge e = graph[u].get(ptr[u]);
if (dist[e.t] == dist[u] + 1 && e.f < e.cap) {
int df = DFS(graph, ptr, dist, dest, e.t, Math.min(f, e.cap - e.f));
if (df > 0) {
e.f += df;
graph[e.t].get(e.rev).f -= df;
return df;
}
}
}
return 0;
}
private static int maxFlow(List<Edge>[] graph, int src, int dest) {
int flow = 0;
int[] dist = new int[graph.length];
while (BFS(graph, src, dest, dist)) {
int[] ptr = new int[graph.length];
while (true) {
int df = DFS(graph, ptr, dist, dest, src, Integer.MAX_VALUE);
if (df == 0)
break;
flow += df;
}
}
return flow;
}
private static class Edge {
int t, rev, cap, f;
public Edge(int t, int rev, int cap) {
this.t = t;
this.rev = rev;
this.cap = cap;
}
}
}
Problem solution in C++.
#include <iostream>
#include <cstring>
#include <cmath>
#include <map>
#include <set>
#include <vector>
using namespace std;
vector<bool> calcSieve(int maxValue) {
vector<bool> isPrime = vector<bool>(maxValue, true);
isPrime[0] = isPrime[1] = false;
int L = sqrt(maxValue);
for (int i = 2; i <= L; i++) {
if (isPrime[i]) {
for (int j = i * i; j < maxValue; j += i) {
isPrime[j] = false;
}
}
}
return isPrime;
}
vector<int> compressSieve(vector<bool> isPrime) {
vector<int> primes;
int maxValue = isPrime.size();
for (int i = 2; i < maxValue; i++) {
if (isPrime[i])
primes.push_back(i);
}
return primes;
}
bool match(int u,
int ** primeIdsA,
int * primeIdsLength,
int ** bMatchArr,
int * bMatchLength,
int * visitedL,
int * visitedR,
int * matchL,
int * matchR,
int visitedI) {
if (visitedL[u] == visitedI)
return false;
visitedL[u] = visitedI;
int * factors = primeIdsA[u];
for (int i = 0; i < primeIdsLength[u]; i++) {
if (visitedR[factors[i]] == visitedI)
continue;
for (int j = 0; j < bMatchLength[factors[i]]; j++) {
int v = bMatchArr[factors[i]][j];
if (matchR[v] < 0) {
matchL[u] = v;
matchR[v] = u;
return true;
}
}
}
for (int i = 0; i < primeIdsLength[u]; i++) {
if (visitedR[factors[i]] == visitedI)
continue;
visitedR[factors[i]] = visitedI;
for (int j = 0; j < bMatchLength[factors[i]]; j++) {
int v = bMatchArr[factors[i]][j];
if (matchL[u] != v &&
match(matchR[v],
primeIdsA,
primeIdsLength,
bMatchArr,
bMatchLength,
visitedL,
visitedR,
matchL,
matchR,
visitedI)) {
matchL[u] = v;
matchR[v] = u;
return true;
}
}
}
return false;
}
int getPrimeId(int prime, map<int, int> & primeIds) {
if (primeIds.find(prime) == primeIds.end())
primeIds[prime] = primeIds.size();
return primeIds[prime];
}
int getMaximumRemovals(vector<int> a, vector<int> b) {
static int MAX = 1000000000;
vector<bool> isPrime = calcSieve(sqrt(MAX));
vector<int> primes = compressSieve(isPrime);
map<int, int> primeIds;
int * primeFactors = new int[primes.size()];
int ** primeIdsA = new int*[a.size()];
int * primeIdsALength = new int[a.size()];
for (unsigned int i = 0; i < a.size(); i++) {
int x = a[i];
int p = 0;
for (unsigned int j = 0; j < primes.size() && primes[j] * primes[j] <= x; j++) {
if (x % primes[j] == 0)
primeFactors[p++] = primes[j];
while (x % primes[j] == 0)
x /= primes[j];
}
if (x > 1)
primeFactors[p++] = x;
primeIdsA[i] = new int[p];
primeIdsALength[i] = p;
for (int j = 0; j < p; j++) {
primeIdsA[i][p - j - 1] =
getPrimeId(primeFactors[j], primeIds);
}
}
vector<vector<int> > bMatchList = vector<vector<int> >(primeIds.size() + 1, vector<int>());
for (unsigned int i = 0; i < b.size(); i++) {
int x = b[i];
for (unsigned int j = 0; j < primes.size() && primes[j] * primes[j] <= x; j++) {
if (x % primes[j] == 0 && primeIds.find(primes[j]) != primeIds.end())
bMatchList[primeIds[primes[j]]].push_back(i);
while (x % primes[j] == 0)
x /= primes[j];
}
if (x > 1 && primeIds.find(x) != primeIds.end())
bMatchList[primeIds[x]].push_back(i);
}
int * matchL = new int[a.size()];
int * matchR = new int[b.size()];
int * visitedL = new int[a.size()];
int * visitedR = new int[primeIds.size()];
memset(matchL, -1, a.size() * sizeof(int));
memset(matchR, -1, b.size() * sizeof(int));
memset(visitedL, -1, a.size() * sizeof(int));
memset(visitedR, -1, primeIds.size() * sizeof(int));
int ** bMatchArr = new int*[bMatchList.size()];
int * bMatchLength = new int[bMatchList.size()];
for (unsigned int i = 0; i < bMatchList.size(); i++) {
bMatchArr[i] = new int[bMatchList[i].size()];
bMatchLength[i] = bMatchList[i].size();
for (unsigned int j = 0; j < bMatchList[i].size(); j++)
bMatchArr[i][j] = bMatchList[i][j];
}
int t = 0;
for (unsigned int i = 0; i < a.size(); i++) {
if (match(i,
primeIdsA,
primeIdsALength,
bMatchArr,
bMatchLength,
visitedL,
visitedR,
matchL,
matchR,
i))
t++;
}
return t;
}
int main() {
int N, temp;
vector<int> a, b;
cin >> N;
for (int i = 0; i < N; i++) {
cin >> temp;
a.push_back(temp);
}
for (int i = 0; i < N; i++) {
cin >> temp;
b.push_back(temp);
}
cout << getMaximumRemovals(a, b) << endl;
return 0;
}
Problem solution in C.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#define LIM 32100
#define NUM 123456
typedef struct _node{
int x;
int id;
struct _node *next;
} node;
typedef struct _list_node{
int x;
struct _list_node *next;
} list_node;
typedef struct _list{
int size;
list_node *head;
} list;
node **hash;
int *p,hash_size=0,*A,*B,*ALength,**AD,*BLength,**BD,*MA,*MB,*VA,*VB;
int match(int u,int vi);
void getp(long long N,int *prim);
int findid(int x,int iflag);
void freehash();
void insert(list *l,int x);
void freelist(list *l);
int main(){
p=(int*)malloc(LIM*sizeof(int));
hash=(node**)malloc(NUM*sizeof(node*));
memset(hash,0,NUM*sizeof(node*));
getp(LIM,p);
int i,j,ans=0,n,t;
scanf("%d",&n);
A=(int*)malloc(n*sizeof(int));
B=(int*)malloc(n*sizeof(int));
int *Alist=(int*)malloc(13*sizeof(int));
ALength=(int*)malloc(n*sizeof(int));
AD=(int**)malloc(n*sizeof(int*));
list_node *temp;
for(i=0;i<n;i++)
scanf("%d",A+i);
for(i=0;i<n;i++)
scanf("%d",B+i);
for(i=0;i<n;i++){
Alist[0]=0;
for(j=0;p[j]*p[j]<=A[i];j++)
if(A[i]%p[j]==0){
Alist[++Alist[0]]=findid(p[j],1);
while(A[i]%p[j]==0)
A[i]/=p[j];
}
if(A[i]!=1)
Alist[++Alist[0]]=findid(A[i],1);
ALength[i]=Alist[0];
AD[i]=(int*)malloc(Alist[0]*sizeof(int));
for(j=0;j<Alist[0];j++)
AD[i][j]=Alist[Alist[0]-j];
}
free(A);
free(Alist);
list *Blist=(list*)malloc(hash_size*sizeof(list));
BLength=(int*)malloc(hash_size*sizeof(int));
BD=(int**)malloc(hash_size*sizeof(int*));
memset(Blist,0,hash_size*sizeof(list));
for(i=0;i<n;i++){
for(j=0;p[j]*p[j]<=B[i];j++)
if(B[i]%p[j]==0){
t=findid(p[j],0);
if(t!=-1)
insert(Blist+t,i);
while(B[i]%p[j]==0)
B[i]/=p[j];
}
if(B[i]!=1){
t=findid(B[i],0);
if(t!=-1)
insert(Blist+t,i);
}
}
for(i=0;i<hash_size;i++){
BD[i]=(int*)malloc(Blist[i].size*sizeof(int));
BLength[i]=Blist[i].size;
j=Blist[i].size-1;
temp=Blist[i].head;
while(temp){
BD[i][j]=temp->x;
temp=temp->next;
j--;
}
freelist(Blist+i);
}
free(B);
free(Blist);
free(p);
freehash();
MA=(int*)malloc(n*sizeof(int));
MB=(int*)malloc(n*sizeof(int));
VA=(int*)malloc(n*sizeof(int));
VB=(int*)malloc(hash_size*sizeof(int));
memset(MA,-1,n*sizeof(int));
memset(MB,-1,n*sizeof(int));
memset(VA,-1,n*sizeof(int));
memset(VB,-1,hash_size*sizeof(int));
for(i=0;i<n;i++)
if(match(i,i))
ans++;
printf("%d",ans);
return 0;
}
int match(int u,int vi){
int i,j,v;
if(VA[u]==vi)
return 0;
VA[u]=vi;
int *FA=AD[u];
for(i=0;i<ALength[u];i++){
if(VB[FA[i]]==vi)
continue;
for(j=0;j<BLength[FA[i]];j++){
v=BD[FA[i]][j];
if(MB[v]==-1){
MA[u]=v;
MB[v]=u;
return 1;
}
}
}
for(i=0;i<ALength[u];i++){
if(VB[FA[i]]==vi)
continue;
VB[FA[i]]=vi;
for(j=0;j<BLength[FA[i]];j++){
v=BD[FA[i]][j];
if(MA[u]!=v && match(MB[v],vi)){
MA[u]=v;
MB[v]=u;
return 1;
}
}
}
return 0;
}
void getp(long long N,int *prim){
long long i,j,index=2,flag;
prim[0]=2;
prim[1]=3;
for(i=5;i<=N;i=i+2)
{
for(j=1,flag=1;prim[j]<=sqrt(i);j++)
{
if(i%prim[j]==0){
flag=0;
break;}
}
if(flag==1)
{prim[index]=i;
index++;}
}
prim[index]=0;
return;
}
int findid(int x,int iflag){
int b=x%NUM;
node *t=hash[b];
while(t){
if(t->x==x)
return t->id;
t=t->next;
}
if(iflag){
t=(node*)malloc(sizeof(node));
t->x=x;
t->id=hash_size++;
t->next=hash[b];
hash[b]=t;
return t->id;
}
return -1;
}
void freehash(){
int i;
node *t,*p;
for(i=0;i<NUM;i++){
t=hash[i];
while(t){
p=t->next;
free(t);
t=p;
}
}
free(hash);
return;
}
void insert(list *l,int x){
list_node *t=(list_node*)malloc(sizeof(list_node));
t->x=x;
t->next=l->head;
l->head=t;
l->size++;
return;
}
void freelist(list *l){
list_node *t,*p;
t=l->head;
while(t){
p=t->next;
free(t);
t=p;}return;}
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