/*
Firstly bi-colored all nodes using a simple dfs. After that all red nodes is on left side
and all black nodes on the right side. Now made connection between nodes according to given edge.
Result is: N - bpm.
Why it works?
-------------
We need to find maximum set which are not connected at all.
As we calculated bpm, it's maximum flow that can run through this network.
Now, we know max-flow = min-cut.
Here in bipartite graph, min-cut will be applied only on the edges like source->node or node->sink (can be proven
by greedy choice).
Thus, min-cut means: minimum number of node to be deleted to make this graph disconnected, i.e, no flow will
pass through this network after removing those node.
so, (N - bpm) is maximum set size which are not connected by any edge. That's the answer.
*/
/***********Template Starts Here***********/
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <deque>
#include <functional>
#include <string>
#include <iostream>
#include <cctype>
#include <set>
#include <climits>
#include <iomanip>
#include <cassert>
//#include <unordered_map>
#define pb push_back
#define nl puts ("")
#define sp printf ( " " )
#define phl printf ( "hello\n" )
#define ff first
#define ss second
#define POPCOUNT __builtin_popcountll
#define RIGHTMOST __builtin_ctzll
#define LEFTMOST(x) (63-__builtin_clzll((x)))
#define MP make_pair
#define FOR(i,x,y) for(int i = (x) ; i <= (y) ; ++i)
#define ROF(i,x,y) for(int i = (y) ; i >= (x) ; --i)
#define CLR(x,y) memset(x,y,sizeof(x))
#define UNIQUE(V) (V).erase(unique((V).begin(),(V).end()),(V).end())
#define MIN(a,b) ((a)<(b)?(a):(b))
#define MAX(a,b) ((a)>(b)?(a):(b))
#define NUMDIGIT(x,y) (((int)(log10((x))/log10((y))))+1)
#define SQ(x) ((x)*(x))
#define ABS(x) ((x)<0?-(x):(x))
#define FABS(x) ((x)+eps<0?-(x):(x))
#define ALL(x) (x).begin(),(x).end()
#define LCM(x,y) (((x)/gcd((x),(y)))*(y))
#define SZ(x) ((int)(x).size())
#define NORM(x) if(x>=mod)x-=mod;
using namespace std;
typedef long long vlong;
typedef unsigned long long uvlong;
typedef pair < int, int > pii;
typedef pair < vlong, vlong > pll;
typedef vector<pii> vii;
typedef vector<int> vi;
const vlong inf = 2147383647;
const double pi = 2 * acos ( 0.0 );
const double eps = 1e-9;
#ifdef forthright48
#include <ctime>
clock_t tStart = clock();
#define debug(args...) {dbg,args; cerr<<endl;}
#define timeStamp printf("Execution Time: %.2fs\n", (double)(clock() - tStart)/CLOCKS_PER_SEC)
#else
#define debug(args...) // Just strip off all debug tokens
#define timeStamp
#endif
struct debugger{
template<typename T> debugger& operator , (const T& v){
cerr<<v<<" ";
return *this;
}
}dbg;
//int knightDir[8][2] = { {-2,1},{-1,2},{1,2},{2,1},{2,-1},{-1,-2},{1,-2},{-2,-1} };
//int dir4[4][2] = {{-1,0},{0,1},{1,0},{0,-1}};
inline vlong gcd ( vlong a, vlong b ) {
a = ABS ( a ); b = ABS ( b );
while ( b ) { a = a % b; swap ( a, b ); } return a;
}
vlong ext_gcd ( vlong A, vlong B, vlong *X, vlong *Y ){
vlong x2, y2, x1, y1, x, y, r2, r1, q, r;
x2 = 1; y2 = 0;
x1 = 0; y1 = 1;
for (r2 = A, r1 = B; r1 != 0; r2 = r1, r1 = r, x2 = x1, y2 = y1, x1 = x, y1 = y ) {
q = r2 / r1;
r = r2 % r1;
x = x2 - (q * x1);
y = y2 - (q * y1);
}
*X = x2; *Y = y2;
return r2;
}
inline vlong modInv ( vlong a, vlong m ) {
vlong x, y;
ext_gcd( a, m, &x, &y );
if ( x < 0 ) x += m; //modInv is never negative
return x;
}
inline vlong power ( vlong a, vlong p ) {
vlong res = 1, x = a;
while ( p ) {
if ( p & 1 ) res = ( res * x );
x = ( x * x ); p >>= 1;
}
return res;
}
inline vlong bigmod ( vlong a, vlong p, vlong m ) {
vlong res = 1 % m, x = a % m;
while ( p ) {
if ( p & 1 ) res = ( res * x ) % m;
x = ( x * x ) % m; p >>= 1;
}
return res;
}
/***********Template Ends Here***********/
/*********** Hasib Templates Starts Here**********/
#include<bits/stdc++.h>
using namespace std;
#define loop(i, n) for(int i=0; i<(n); i++)
#define sf scanf
#define pf printf
#define fr first
#define sc second
#define ll long long
#define dd double
#define all(v) (v).begin(), (v).end()
#define PI acos(-1.0)
#define mem(ara, val) memset(ara, val, sizeof(ara))
#define paii pair<int, int>
#define pall pair<ll, ll>
#define read(nm) freopen(nm, "r", stdin)
#define write(nm) freopen(nm, "w", stdout)
#define vdump(x) cerr<<#x<<" = "<<x<<endl;
#define dump(args...) cerr,args; cerr<<endl
template<typename T>
ostream& operator<<(ostream& out, vector<T> v)
{
out<<"[ ";
loop(i, SZ(v))
{
if(i) out<<", ";
out<<v[i];
}
out<<" ]";
return out;
}
template<typename T1, typename T2>
ostream& operator<<(ostream &out, pair<T1, T2> p)
{
out<<"( "<<p.fr<<", "<<p.sc<<")";
return out;
}
template<typename T>
ostream& operator,(ostream &out, T x)
{
out<<x<<" ";
return out;
}
/**********Hasib Templates Ends Here**************/
/**
* WARTNING for me:
* Never use FOR
* Never use pii, pll, vi, vi
* Never use ff, ss, phl, sp, nl
*/
#define NODE 1007
#define MAXX NODE
struct KUHN{
int left[NODE], right[NODE], vis[NODE], cc;
vector<int> adj[NODE];
KUHN() : cc(1) {}
void clear( int n ) {
FOR(i,0,n) adj[i].clear();
}
bool tryK ( int v ) {
if ( vis[v] == cc ) return false;
vis[v] = cc;
for ( int i = 0; i < SZ(adj[v]); i++ ) {
int t = adj[v][i];
if ( right[t] == -1 ) {
right[t] = v; left[v] = t;
return true;
}
}
for ( int i = 0; i < SZ(adj[v]); i++ ) {
int t = adj[v][i];
if ( tryK ( right[t] ) ) {
right[t] = v; left[v] = t;
return true;
}
}
return false;
}
int match(int n) {
int res = 0;
bool done;
CLR(left,-1); CLR(right,-1);
do {
done = true; cc++;
FOR(i,0,n) {
if(left[i]==-1 && tryK(i)) {
done = false;
}
}
} while(!done);
FOR(i,0,n) res += (left[i]!=-1);
return res;
}
}kuhn;
vector<int>graph[MAXX];
int N, M;
int color[MAXX];
void init()
{
for(int i=1; i<=N; i++)
{
graph[i].clear();
kuhn.adj[i].clear();
color[i] = -1;
}
}
void dfs(int u, int c)
{
color[u] = c;
int v;
loop(i, SZ(graph[u]))
{
v = graph[u][i];
if(color[v] == -1)
{
dfs(v, c ^ 1);
}
}
return;
}
int solve()
{
for(int i=1; i<=N; i++)
{
if(color[i] == -1)
{
dfs(i, 0);
}
}
for(int i=1; i<=N; i++)
{
if(color[i] == 0)
{
loop(j, SZ(graph[i]))
{
kuhn.adj[i].pb(graph[i][j]);
}
}
}
return N - kuhn.match(N);
}
int main ()
{
#ifdef hasibpc
//read("input.txt");
//write("output.txt");
#endif // hasibpc
int kases, kaseno = 0;
int a, b;
sf("%d", &kases);
while(kases--)
{
sf("%d %d", &N, &M);
init();
while(M--)
{
sf("%d %d", &a, &b);
graph[a].pb(b);
graph[b].pb(a);
}
pf("Case %d: %d\n", ++kaseno, solve());
}
return 0;
}
Category Archives: Flow
(LightOj) 1154 – Penguins
0
/****************************************************************
▄█ █▄ ▄████████ ▄████████ ▄█ ▀█████████▄
███ ███ ███ ███ ███ ███ ███ ███ ███
███ ███ ███ ███ ███ █▀ ███ ███ ███
▄███▄▄▄▄███▄▄ ███ ███ ███ ███ ▄███▄▄▄██▀
▀▀███▀▀▀▀███▀ ▀███████████ ▀███████████ ███ ▀▀███▀▀▀██▄
███ ███ ███ ███ ███ ███ ███ ██▄
███ ███ ███ ███ ▄█ ███ ███ ███ ███
███ █▀ ███ █▀ ▄████████▀ █▀ ▄█████████▀
****************************************************************/
#include<bits/stdc++.h>
#define FOR(i, s, e) for(int i=s; i<e; i++)
#define loop(i, n) FOR(i, 0, n)
#define sf scanf
#define pf printf
#define pb push_back
#define MP make_pair
#define fr first
#define sc second
#define ll long long
#define dd double
#define all(v) v.begin(), v.end()
#define PI acos(-1.0)
#define mem(ara, value) memset(ara, value, sizeof(ara))
#define paii pair<int, int>
#define pall pair<ll, ll>
#define SZ(a) int(a.size())
#define read(nm) freopen(nm, "r", stdin)
#define write(nm) freopen(nm, "w", stdout)
#define take(args...) asdf,args
#define dump(x) cerr<<#x<<" = "<<x<<endl
#define debug(args...) cerr,args; cerr<<endl;
using namespace std;
template<typename T>
ostream& operator<<(ostream& output, vector<T>&v)
{
output<<"[ ";
if(SZ(v))
{
output<<v[0];
}
FOR(i, 1, SZ(v))
{
output<<", "<<v[i];
}
output<<" ]";
return output;
}
template<typename T1, typename T2>
ostream& operator<<(ostream& output, pair<T1, T2>&p)
{
output<<"( "<<p.fr<<", "<<p.sc<<" )";
return output;
}
template<typename T>
ostream& operator,(ostream& output, T x)
{
output<<x<<" ";
return output;
}
struct ASDF{
ASDF& operator,(int &a) {
sf("%d", &a);
return *this;
}
ASDF& operator,(long int &a){
sf("%ld", &a);
return *this;
}
ASDF& operator,(long long int &a){
sf("%lld", &a);
return *this;
}
ASDF& operator,(char &c){
sf("%c", &c);
return *this;
}
ASDF& operator,(double &d){
sf("%lf", &d);
return *this;
}
template<typename T>
ASDF& operator,(T &a){
cin>>a;
return *this;
}
}asdf;
//Header ends here
#define MAXX 208
#define INF (1<<29)
int capacity[MAXX][MAXX], tmpCapacity[MAXX][MAXX];
int N;
double D;
pair<double, double>points[MAXX/2];
vector<int>graph[MAXX];
int source, sink;
int total;
double sq(double x)
{
return x*x;
}
double dist(pair<double, double>A, pair<double, double>B)
{
return sqrt( sq(A.fr - B.fr) + sq(A.sc - B.sc) );
}
int findPath()
{
bool visited[MAXX];
bool found = false;
int parent[MAXX];
mem(parent, -1);
mem(visited, 0);
queue<int>Q;
Q.push(source);
visited = true;
while(!Q.empty())
{
int u = Q.front(); Q.pop();
loop(i, SZ(graph[u]))
{
int v = graph[u][i];
if(!visited[v] && tmpCapacity[u][v] > 0)
{
visited[v] = true;
parent[v] = u;
Q.push(v);
if(v == sink)
{
found = true;
break;
}
}
}
if(found)
{
break;
}
}
int pathCapacity = INF;
int u, v = sink;
while(parent[v] != -1)
{
u = parent[v];
pathCapacity = min(pathCapacity, tmpCapacity[u][v]);
v = u;
}
v = sink;
while(parent[v] != -1)
{
u = parent[v];
tmpCapacity[u][v] -= pathCapacity;
tmpCapacity[v][u] += pathCapacity;
v = u;
}
return found?pathCapacity:0;
}
int FLOW()
{
loop(i, MAXX)
{
loop(j, MAXX)
{
tmpCapacity[i][j] = capacity[i][j];
}
}
int ret = 0;
int pathCapacity;
while(pathCapacity = findPath())
{
ret += pathCapacity;
}
return ret;
}
void init()
{
}
int main()
{
init();
int kases, kaseno = 0;
int n, c;
int u, v;
sf("%d", &kases);
while(kases--)
{
mem(capacity, 0);
loop(i, MAXX) graph[i].clear();
total = 0;
sf("%d %lf", &N, &D);
source = 0;
for(int i=1; i<=N; i++)
{
sf("%lf %lf %d %d", &points[i].fr, &points[i].sc, &n, &c);
total += n;
v = 2*i;
u = v - 1;
graph[u].pb(v);
graph[v].pb(u);
capacity[u][v] = c;
graph.pb(u);
graph[u].pb(source);
capacity[u] = n;
}
for(int i=1; i<=N; i++)
{
for(int j=1; j<=N; j++)
{
if(i == j) continue;
if(dist(points[i], points[j]) <= D)
{
u = 2*i;
v = 2*j - 1;
capacity[u][v] = INF;
graph[u].pb(v);
graph[v].pb(u);
}
}
}
vector<int>vv;
for(int i=1; i<=N; i++)
{
sink = 2*i - 1;
if(FLOW() == total)
{
vv.pb(i);
}
}
printf("Case %d:", ++kaseno);
if(SZ(vv) == 0)
{
printf(" -1");
}
else
{
loop(i, SZ(vv))
{
printf(" %d", vv[i] - 1);
}
}
pf("\n");
}
return 0;
}
(LightOj) 1155 – Power Transmission
0
/****************************************************************
▄█ █▄ ▄████████ ▄████████ ▄█ ▀█████████▄
███ ███ ███ ███ ███ ███ ███ ███ ███
███ ███ ███ ███ ███ █▀ ███ ███ ███
▄███▄▄▄▄███▄▄ ███ ███ ███ ███ ▄███▄▄▄██▀
▀▀███▀▀▀▀███▀ ▀███████████ ▀███████████ ███ ▀▀███▀▀▀██▄
███ ███ ███ ███ ███ ███ ███ ██▄
███ ███ ███ ███ ▄█ ███ ███ ███ ███
███ █▀ ███ █▀ ▄████████▀ █▀ ▄█████████▀
****************************************************************/
#include<bits/stdc++.h>
#define FOR(i, s, e) for(int i=s; i<e; i++)
#define loop(i, n) FOR(i, 0, n)
#define sf scanf
#define pf printf
#define pb push_back
#define MP make_pair
#define fr first
#define sc second
#define ll long long
#define dd double
#define all(v) v.begin(), v.end()
#define PI acos(-1.0)
#define mem(ara, value) memset(ara, value, sizeof(ara))
#define paii pair<int, int>
#define pall pair<ll, ll>
#define SZ(a) int(a.size())
#define read(nm) freopen(nm, "r", stdin)
#define write(nm) freopen(nm, "w", stdout)
#define take(args...) asdf,args
#define dump(x) cerr<<#x<<" = "<<x<<endl
#define debug(args...) cerr,args; cerr<<endl;
using namespace std;
template<typename T>
ostream& operator<<(ostream& output, vector<T>&v)
{
output<<"[ ";
if(SZ(v))
{
output<<v[0];
}
FOR(i, 1, SZ(v))
{
output<<", "<<v[i];
}
output<<" ]";
return output;
}
template<typename T1, typename T2>
ostream& operator<<(ostream& output, pair<T1, T2>&p)
{
output<<"( "<<p.fr<<", "<<p.sc<<" )";
return output;
}
template<typename T>
ostream& operator,(ostream& output, T x)
{
output<<x<<" ";
return output;
}
struct ASDF{
ASDF& operator,(int &a) {
sf("%d", &a);
return *this;
}
ASDF& operator,(long int &a){
sf("%ld", &a);
return *this;
}
ASDF& operator,(long long int &a){
sf("%lld", &a);
return *this;
}
ASDF& operator,(char &c){
sf("%c", &c);
return *this;
}
ASDF& operator,(double &d){
sf("%lf", &d);
return *this;
}
template<typename T>
ASDF& operator,(T &a){
cin>>a;
return *this;
}
}asdf;
//Header ends here
#define MAXX 207
#define INF (1<<29)
int source, sink;
int N;
int M;
int capacity[MAXX][MAXX];
vector<int>graph[MAXX];
int findPath()
{
bool visited[MAXX];
int parent[MAXX];
mem(parent, -1);
mem(visited, 0);
queue<int>Q;
Q.push(source);
visited = true;
bool found = false;
while(!Q.empty())
{
int u = Q.front(); Q.pop();
loop(i, SZ(graph[u]))
{
int v = graph[u][i];
if(!visited[v] && capacity[u][v] > 0)
{
visited[v] = true;
Q.push(v);
parent[v] = u;
if(v == sink)
{
found = true;
break;
}
}
}
if(found)
{
break;
}
}
int v = sink;
int pathCapacity = INF;
while(parent[v] != -1)
{
int u = parent[v];
pathCapacity = min(pathCapacity, capacity[u][v] );
v = u;
}
v = sink;
while(parent[v] != -1)
{
int u = parent[v];
capacity[u][v] -= pathCapacity;
capacity[v][u] += pathCapacity;
v = u;
}
if(found)
{
return pathCapacity;
}
else
{
return 0;
}
}
int FLOW()
{
int result = 0;
int pathCapacity;
while(true)
{
pathCapacity = findPath();
if(pathCapacity == 0)
{
break;
}
else
{
result += pathCapacity;
}
}
return result;
}
int solve()
{
return FLOW();
}
void init()
{
}
int main()
{
init();
int kases, kaseno = 0;
int B, D;
int u, v, c;
sf("%d", &kases);
while(kases--)
{
mem(capacity, 0);
sf("%d", &N);
source = 0;
sink = 2*(N + 1); // A number out of the range of node id.
for(int i=0; i<=sink; i++)
{
graph[i].clear();
}
for(int i=1; i<=N; i++)
{
u = 2*i - 1;
v = u + 1;
graph[u].pb(v);
graph[v].pb(u);
sf("%d", &capacity[u][v]);
}
sf("%d", &M);
loop(i, M)
{
sf("%d %d %d", &u, &v, &c);
u = 2*u;
v = 2*v - 1;
graph[u].pb(v);
graph[v].pb(u);
capacity[u][v] = c;
}
sf("%d %d", &B, &D);
loop(i, B)
{
sf("%d", &u);
u = 2*u - 1;
graph.pb(u);
graph[u].pb(source);
capacity[ source ][u] = INF;
}
loop(i, D)
{
sf("%d", &v);
{
v = 2*v;
graph[v].pb(sink);
graph[sink].pb(v);
capacity[v][sink] = INF;
}
}
pf("Case %d: %d\n", ++kaseno, solve());
}
return 0;
}
(LightOj) 1153 – Internet Bandwidth
0
/****************************************************************
▄█ █▄ ▄████████ ▄████████ ▄█ ▀█████████▄
███ ███ ███ ███ ███ ███ ███ ███ ███
███ ███ ███ ███ ███ █▀ ███ ███ ███
▄███▄▄▄▄███▄▄ ███ ███ ███ ███ ▄███▄▄▄██▀
▀▀███▀▀▀▀███▀ ▀███████████ ▀███████████ ███ ▀▀███▀▀▀██▄
███ ███ ███ ███ ███ ███ ███ ██▄
███ ███ ███ ███ ▄█ ███ ███ ███ ███
███ █▀ ███ █▀ ▄████████▀ █▀ ▄█████████▀
****************************************************************/
#include<bits/stdc++.h>
#define FOR(i, s, e) for(int i=s; i<e; i++)
#define loop(i, n) FOR(i, 0, n)
#define sf scanf
#define pf printf
#define pb push_back
#define MP make_pair
#define fr first
#define sc second
#define ll long long
#define dd double
#define all(v) v.begin(), v.end()
#define PI acos(-1.0)
#define mem(ara, value) memset(ara, value, sizeof(ara))
#define paii pair<int, int>
#define pall pair<ll, ll>
#define SZ(a) int(a.size())
#define read(nm) freopen(nm, "r", stdin)
#define write(nm) freopen(nm, "w", stdout)
#define take(args...) asdf,args
#define dump(x) cerr<<#x<<" = "<<x<<endl
#define debug(args...) cerr,args; cerr<<endl;
using namespace std;
template<typename T>
ostream& operator<<(ostream& output, vector<T>&v)
{
output<<"[ ";
if(SZ(v))
{
output<<v[0];
}
FOR(i, 1, SZ(v))
{
output<<", "<<v[i];
}
output<<" ]";
return output;
}
template<typename T1, typename T2>
ostream& operator<<(ostream& output, pair<T1, T2>&p)
{
output<<"( "<<p.fr<<", "<<p.sc<<" )";
return output;
}
template<typename T>
ostream& operator,(ostream& output, T x)
{
output<<x<<" ";
return output;
}
struct ASDF{
ASDF& operator,(int &a) {
sf("%d", &a);
return *this;
}
ASDF& operator,(long int &a){
sf("%ld", &a);
return *this;
}
ASDF& operator,(long long int &a){
sf("%lld", &a);
return *this;
}
ASDF& operator,(char &c){
sf("%c", &c);
return *this;
}
ASDF& operator,(double &d){
sf("%lf", &d);
return *this;
}
template<typename T>
ASDF& operator,(T &a){
cin>>a;
return *this;
}
}asdf;
//Header ends here
#define MAXX 107
#define INF (1<<29)
int capacity[MAXX][MAXX];
int parent[MAXX];
vector<int>graph[MAXX];
int source, sink, N, m;
int findPath() // BFS
{
bool visited[MAXX];
mem(visited, 0);
queue<int>Q;
Q.push(source);
visited = true;
mem(parent, -1);
while(!Q.empty())
{
int u = Q.front(); Q.pop();
loop(i, SZ(graph[u]))
{
int v = graph[u][i];
if(!visited[v] && capacity[u][v] > 0)
{
Q.push(v);
visited[v] = true;
parent[v] = u;
if(v == sink)
{
break;
}
}
}
}
int v = sink, path_capacity = INF;
while(parent[v] != -1)
{
int u = parent[v];
path_capacity = min(path_capacity, capacity[u][v] );
v = u;
}
v = sink;
while(parent[v] != -1)
{
int u = parent[v];
capacity[u][v] -= path_capacity;
capacity[v][u] += path_capacity;
v = u;
}
if(path_capacity == INF)
return 0;
else
return path_capacity;
}
int FLOW()
{
int result = 0;
while(true)
{
int pathCapacity = findPath();
if(pathCapacity == 0)
{
break;
}
else
{
result += pathCapacity;
}
}
return result;
}
int solve()
{
return FLOW();
}
void init()
{
}
int main()
{
init();
int kases, kaseno = 0;
int u, v, c;
sf("%d", &kases);
while(kases--)
{
sf("%d", &N);
sf("%d %d %d", &source, &sink, &m);
for(int i=0; i<=N; i++)
{
graph[i].clear();
}
mem(capacity, 0);
loop(i, m)
{
sf("%d %d %d", &u, &v, &c);
graph[u].pb(v);
graph[v].pb(u);
capacity[u][v] = capacity[v][u] = capacity[u][v] + c;
}
pf("Case %d: %d\n", ++kaseno, solve());
}
return 0;
}
UnLucky Codes 