Note Book: [UVa Live] Rahyab

Author            : Dipu Kumar Mohanto 
                    CSE, Batch - 6
                    BRUR.
Problem Statement : Rahyab
Source            : UVA Live Archive
Category          : Graph Theory, Maximum Flow
Algorithm         : Dinic Algorithm
Verdict           : Accepted

Dinic Algorithm for maximum flow (directed graph).
Use undirected edge instead of directed.
Optimize in dfs.

#include "bits/stdc++.h"
using namespace std;
#define FI freopen("in.txt", "r", stdin)
#define FO freopen("out.txt", "w", stdout)
#define FAST ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL)
#define FOR(i, n) for (int i = 1; i <= n; i++)
#define For(i, n) for (int i = 0; i < n; i++)
#define ROF(i, n) for (int i = n; i >= 1; i--)
#define Rof(i, n) for (int i = n-1; i >= 0; i--)
#define FORI(i, n) for (auto i : n)
#define REP(i, a, b) for (int i = a; i <= b; i++)
#define ll long long
#define ull unsigned long long
#define vi vector <int>
#define vl vector <ll>
#define pii pair <int, int>
#define pll pair <ll, ll>
#define mk make_pair
#define ff first
#define ss second
#define eb emplace_back
#define em emplace
#define pb push_back
#define ppb pop_back
#define All(a) a.begin(), a.end()
#define memo(a, b) memset(a, b, sizeof a)
#define Sort(a) sort(All(a))
#define ED(a) Sort(a), a.erase(unique(All(a)), a.end())
#define rev(a) reverse(All(a))
#define sz(a) (int)a.size()
#define max3(a, b, c) max(a, max(b, c))
#define min3(a, b, c) min(a, min(b, c))
#define maxAll(a) *max_element(All(a))
#define minAll(a) *min_element(All(a))
#define allUpper(a) transform(All(a), a.begin(), :: toupper)
#define allLower(a) transform(All(a), a.begin(), :: tolower)
#define endl '\n'
#define nl puts("")
#define ub upper_bound
#define lb lower_bound
#define Exp exp(1.0)
#define PIE 2*acos(0.0)
#define Sin(a) sin(((a)*PIE)/180.0)
#define EPS 1e-9
#include "ext/pb_ds/assoc_container.hpp"
#include "ext/pb_ds/tree_policy.hpp"
using namespace __gnu_pbds;
template <typename T> using orderset = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>;
#include "ext/rope"
using namespace __gnu_cxx;
// rope <int> Rope;
// int dr[] = {1, -1, 0, 0}; // 4 Direction
// int dc[] = {0, 0, 1, -1};
// int dr[] = {0, 0, 1, -1, 1, 1, -1, -1}; // 8 Direction
// int dc[] = {1, -1, 0, 0, 1, -1, 1, -1};
// int dr[] = {-1, 1, -2, -2, -1, 1, 2, 2}; // knight Moves
// int dc[] = {-2, -2, -1, 1, 2, 2, 1, -1};
#define here cerr << "Here" << endl;
#define trace1(x) cerr << #x << ": " << x << endl;
#define trace2(x, y) cerr << #x << ": " << x << " | " << #y << ": " << y << endl;
#define trace3(x, y, z) cerr << #x << ": " << x << " | " << #y << ": " << y << " | " << #z << ": " << z << endl;
#define trace4(a, b, c, d) cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << endl;
#define trace5(a, b, c, d, e) cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << " | " << #e << ": " << e << endl;
#define trace6(a, b, c, d, e, f) cerr << #a << ": " << a << " | " << #b << ": " << b << " | " << #c << ": " << c << " | " << #d << ": " << d << " | " << #e << ": " << e << " | " << #f << ": " << f << endl;
inline int setbit(int mask, int pos) { return mask |= (1 << pos); }
inline int resetbit(int mask, int pos) { return mask &= ~(1 << pos); }
inline int togglebit(int mask, int pos) { return mask ^= (1 << pos); }
inline bool checkbit(int mask, int pos) { return (bool)(mask & (1 << pos)); }
#define popcount(mask) __builtin_popcount(mask) // count set bit
#define popcountLL(mask) __builtin_popcountll(mask) // for long long
inline int read() { int a; scanf("%d", &a); return a; }
inline ll readLL() { ll a; scanf("%lld", &a); return a; }
inline double readDD() { double a; scanf("%lf", &a); return a; }
template <typename T> string toString(T num) { stringstream ss; ss << num; return ss.str(); }
int toInt(string s) { int num; istringstream iss(s); iss >> num; return num; }
ll toLLong(string s) { ll num; istringstream iss(s); iss >> num; return num; }
#define inf 1234567
#define mod 1000000007
static const int maxn = 500 + 5;
static const int logn = 18;
int tnode, tedge;
vi graph[maxn];
int cap[maxn][maxn];
int flow[maxn][maxn];
int level[maxn];
int ptr[maxn];
inline bool bfs(int src, int des)
{
memo(level, -1);
queue <int> PQ;
PQ.emplace(src);
level[src] = 0;
while (!PQ.empty())
{
int u = PQ.front(); PQ.pop();
for (int v : graph[u])
{
if (level[v] != -1 || flow[u][v] >= cap[u][v]) continue;
level[v] = level[u] + 1;
PQ.emplace(v);
}
}
return level[des] != -1;
}
inline int dfs(int u, int minCap, int sink)
{
if (u == sink) return minCap;
for (int &i = ptr[u]; i < sz(graph[u]); i++)
{
int v = graph[u][i];
if (level[v] == level[u] + 1 && flow[u][v] < cap[u][v])
{
int minFlow = dfs(v, min(minCap, cap[u][v] - flow[u][v]), sink);
if (minFlow > 0)
{
flow[u][v] += minFlow;
flow[v][u] -= minFlow;
return minFlow;
}
}
}
return 0;
}
inline int dinic(int src, int sink)
{
int maxFlow = 0;
while (bfs(src, sink))
{
memo(ptr, 0);
while (int bottleneck = dfs(src, inf, sink))
{
maxFlow += bottleneck;
}
}
return maxFlow;
}
int main()
{
FI;
int tnode, tedge, src, sink;
ll c;
while (scanf("%d %d %d %d %lld", &tnode, &tedge, &src, &sink, &c) == 5)
{
if (tnode == 0 && tedge == 0 && src == 0 && sink == 0 && c == 0) break;
for (int e = 1; e <= tedge; e++)
{
int u, v;
scanf("%d %d", &u, &v);
cap[u][v] += 1;
if (cap[u][v] == 1)
{
graph[u].eb(v);
graph[v].eb(u);
}
}
ll f = dinic(src, sink);
ll d = c / f;
ll r = c % f;
ll ans = r * (d + 1) * (d + 1) * (d + 1) + (c - r * (d + 1)) * (d * d);
printf("%lld\n", ans);
for (int i = 1; i <= tnode; i++)
{
graph[i].clear();
for (int j = 1; j <= tnode; j++)
{
cap[i][j] = 0;
flow[i][j] = 0;
}
}
}
}

Note Book

Saturday, February 2, 2019

[UVa Live] Rahyab

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