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bgl-flows.cpp
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bgl-flows.cpp
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#ifdef _MSC_VER
#define _CRT_SECURE_NO_WARNINGS
#endif
// ALGOLAB BGL Tutorial 2
// Flow example demonstrating
// - interior graph properties for flow algorithms
// - custom edge adder
// Compile and run with one of the following:
// g++ -std=c++11 -O2 flows.cpp -o flows ./flows
// g++ -std=c++11 -O2 -I path/to/boost_1_58_0 flows.cpp -o flows; ./flows
// Includes
// ========
// STL includes
#include <iostream>
#include <vector>
#include <queue>
#include <stack>
#include <algorithm>
#include <cstdio>
#include <string>
// BGL includes
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/prim_minimum_spanning_tree.hpp>
#include <boost/graph/kruskal_min_spanning_tree.hpp>
#include <boost/graph/connected_components.hpp>
#include <boost/graph/push_relabel_max_flow.hpp>
#include <boost/graph/edmonds_karp_max_flow.hpp>
#include <boost/graph/cycle_canceling.hpp>
#include <boost/graph/successive_shortest_path_nonnegative_weights.hpp>
#include <boost/graph/find_flow_cost.hpp>
#include <boost/graph/copy.hpp>
// Namespaces
// using namespace std;
using namespace boost;
#define _i std::cin
#define _o std::cout
#define _l std::endl
#define _e std::cerr
void Marathon2();
// Main function to loop over the testcases
int main(int argc, char** argv) {
std::ios_base::sync_with_stdio(false);
if (argc > 1) {
std::string str("C:\\some-path\\");
str += std::string(argv[1]) + ".in";
freopen(str.c_str(), "r", stdin);
}
else freopen("C:\\some-path\\test0.in", "r", stdin);
freopen("C:\\some-path\\out_my.out", "w", stdout);
freopen("C:\\some-path\\err_my.out", "w", stderr);
int T; _i >> T;
for (; T > 0; --T) Marathon2();
return 0;
}
//
// BGL Graph definitions
// =====================
// Graph Type with nested interior edge properties for Flow Algorithms
typedef boost::adjacency_list_traits<boost::vecS, boost::vecS, boost::directedS> Traits;
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS, boost::no_property,
boost::property<boost::edge_capacity_t, long,
boost::property<boost::edge_residual_capacity_t, long,
boost::property<boost::edge_reverse_t, Traits::edge_descriptor,
boost::property<boost::edge_weight_t, long> > > > > Graph; // for MCMF
// Interior Property Maps
typedef boost::property_map<Graph, boost::edge_capacity_t>::type EdgeCapacityMap;
typedef boost::property_map<Graph, boost::edge_weight_t>::type EdgeWeightMap;
typedef boost::property_map<Graph, boost::edge_residual_capacity_t>::type ResidualCapacityMap;
typedef boost::property_map<Graph, boost::edge_reverse_t>::type ReverseEdgeMap;
typedef boost::graph_traits<Graph>::vertex_descriptor Vertex;
typedef boost::graph_traits<Graph>::vertex_iterator VertexIt;
typedef boost::graph_traits<Graph>::edge_descriptor Edge;
typedef boost::graph_traits<Graph>::out_edge_iterator OutEdgeIt;
// Custom Edge Adder Class, that holds the references
// to the graph, capacity map and reverse edge map
// ===================================================
// For ONLY Min-cost Max flow
class EdgeAdderMCMF {
Graph &G;
EdgeCapacityMap &capacitymap;
ReverseEdgeMap &revedgemap;
EdgeWeightMap &weightmap;
public:
// to initialize the Object
EdgeAdderMCMF(Graph & G, EdgeCapacityMap &capacitymap, EdgeWeightMap &weightmap, ReverseEdgeMap &revedgemap) :
G(G), capacitymap(capacitymap), weightmap(weightmap), revedgemap(revedgemap) {}
// to use the Function (add an edge)
void addEdge(int from, int to, long capacity, long weight) {
Edge e, rev_e;
bool success;
boost::tie(e, success) = boost::add_edge(from, to, G);
boost::tie(rev_e, success) = boost::add_edge(to, from, G);
capacitymap[e] = capacity;
weightmap[e] = weight;
capacitymap[rev_e] = 0; // reverse edge has no capacity!
weightmap[rev_e] = -weight;
revedgemap[e] = rev_e;
revedgemap[rev_e] = e;
}
};
// Custom Edge Adder Class, that holds the references
// to the graph, capacity map and reverse edge map
// for ONLY Max flow
// ===================================================
class EdgeAdderMF {
Graph &G;
EdgeCapacityMap &capacitymap;
ReverseEdgeMap &revedgemap;
public:
// to initialize the Object
EdgeAdderMF(Graph & G, EdgeCapacityMap &capacitymap, ReverseEdgeMap &revedgemap) :
G(G), capacitymap(capacitymap), revedgemap(revedgemap) {}
// to use the Function (add an edge)
void addEdge(int from, int to, long capacity) {
Edge e, rev_e;
bool success;
boost::tie(e, success) = boost::add_edge(from, to, G);
boost::tie(rev_e, success) = boost::add_edge(to, from, G);
capacitymap[e] = capacity;
capacitymap[rev_e] = 0; // reverse edge has no capacity!
revedgemap[e] = rev_e;
revedgemap[rev_e] = e;
}
};
bool calcFlowMarathon(Graph &G, Vertex s, Vertex f, long dist, long qflow) {
int n = boost::num_vertices(G) - 2;
Vertex src = n, tgt = n + 1;
EdgeCapacityMap cmap = boost::get(boost::edge_capacity, G);
EdgeWeightMap wmap = boost::get(boost::edge_weight, G);
ResidualCapacityMap rcmap = boost::get(boost::edge_residual_capacity, G);
ReverseEdgeMap remap = boost::get(boost::edge_reverse, G);
EdgeAdderMCMF eaG(G, cmap, wmap, remap);
Edge e; bool suc;
boost::tie(e, suc) = boost::edge(src, s, G);
if (suc) cmap[e] = qflow;
else eaG.addEdge(src, s, qflow, 0);
boost::tie(e, suc) = boost::edge(f, tgt, G);
if (suc) cmap[e] = qflow;
else eaG.addEdge(f, tgt, qflow, 0);
long flow = boost::push_relabel_max_flow(G, src, tgt);
boost::successive_shortest_path_nonnegative_weights(G, src, tgt);
long cost = boost::find_flow_cost(G);
if (cost == dist * qflow) return true;
return false;
}
void Marathon2() {
int n, m, s, f;
_i >> n >> m >> s >> f;
Graph G(n), Gbase(n);
EdgeCapacityMap cmap = boost::get(boost::edge_capacity, G);
EdgeWeightMap wmap = boost::get(boost::edge_weight, G), basewmap = boost::get(boost::edge_weight, Gbase);
ResidualCapacityMap rcmap = boost::get(boost::edge_residual_capacity, G);
ReverseEdgeMap remap = boost::get(boost::edge_reverse, G);
EdgeAdderMCMF eaG(G, cmap, wmap, remap);
for (int j = 0; j < m; j++) {
int a, b, c, d; _i >> a >> b >> c >> d;
if (a == b) continue;
eaG.addEdge(a, b, c, d);
eaG.addEdge(b, a, c, d);
Edge e; bool suc;
boost::tie(e, suc) = boost::add_edge(a, b, Gbase);
basewmap[e] = d;
boost::tie(e, suc) = boost::add_edge(b, a, Gbase);
basewmap[e] = d;
}
std::vector<int> predmap(n);
std::vector<long> distmap(n);
boost::dijkstra_shortest_paths(Gbase, s,
predecessor_map(boost::make_iterator_property_map(predmap.begin(), boost::get(boost::vertex_index, Gbase))).
distance_map(boost::make_iterator_property_map(distmap.begin(), boost::get(boost::vertex_index, Gbase))));
if (predmap[f] == f) {
_o << 0 << _l; return;
}
long d = distmap[f];
_e << "d=" << d << _l;
long maxFlow = boost::push_relabel_max_flow(G, s, f);
_e << "maxFlow=" << maxFlow << _l;
boost::successive_shortest_path_nonnegative_weights(G, s, f);
long maxFlowCost = boost::find_flow_cost(G);
if (maxFlowCost == maxFlow * d) {
_e << "MaxFlow Return!" << _l;
_o << maxFlow << _l; return;
}
Vertex src = boost::add_vertex(G), tgt = boost::add_vertex(G);
int result = 0;
int stflow = 1, endflow = maxFlow;
std::vector<bool> isMinCost(maxFlow + 1);
isMinCost[stflow] = isMinCost[0] = true;
while (true) {
if (endflow - stflow <= 1) {
isMinCost[endflow] = calcFlowMarathon(G, s, f, d, endflow);
if (isMinCost[endflow]) {
result = endflow; break;
}
else {
result = stflow; break;
}
}
int midflow = (stflow + endflow) / 2;
isMinCost[midflow] = calcFlowMarathon(G, s, f, d, midflow);
if (isMinCost[midflow]) {
stflow = midflow;
}
else {
endflow = midflow - 1;
}
}
//for (int flow = 1; flow <= maxFlow; flow++) {
// Edge e; bool success;
// boost::tie(e, success) = edge(src, s, G);
// if (success) {
// cmap[e] = flow;
// }
// else {
// eaG.addEdge(src, s, flow, 0);
// }
// boost::tie(e, success) = edge(f, tgt, G);
// if (success) cmap[e] = flow;
// else eaG.addEdge(f, tgt, flow, 0);
//
// int nowFlow = boost::push_relabel_max_flow(G, src, tgt);
// boost::successive_shortest_path_nonnegative_weights(G, src, tgt);
// int nowCost = boost::find_flow_cost(G);
// if (nowCost > d*flow) break;
// result = flow;
//}
_o << result << _l;
}
// Week 10: avalanche / 100 pts
// 1. calc. distance from a to s
// 2. bipartite graph a->s
// 3. binary search on whether the max matching has a edges
int checkASGraph(int t, std::vector< std::vector<int> > &dist, std::vector<int>& takenout, const std::vector<int>& takenin = std::vector<int>()) {
int a = dist.size();
int s = dist[0].size();
Graph ASGraph(a + s);
EdgeWeightMap aswmap = boost::get(boost::edge_weight, ASGraph);
ReverseEdgeMap asrevmap = boost::get(boost::edge_reverse, ASGraph);
EdgeCapacityMap ascapmap = boost::get(boost::edge_capacity, ASGraph);
ResidualCapacityMap asrescapmap = boost::get(boost::edge_residual_capacity, ASGraph);
EdgeAdderMF eaG(ASGraph, ascapmap, asrevmap);
Vertex src = boost::add_vertex(ASGraph), tgt = boost::add_vertex(ASGraph);
for (int i = 0; i < a; i++) {
if (!takenin.empty() && takenin[i] == 1) continue;
for (int j = 0; j < s; j++) {
if (dist[i][j] == -1) continue;
if (dist[i][j] > t) continue;
eaG.addEdge(i, a + j, 1);
}
eaG.addEdge(src, i, 1);
}
for (int j = 0; j < s; j++) {
eaG.addEdge(a + j, tgt, 1);
}
int flow = boost::push_relabel_max_flow(ASGraph, src, tgt);
if (takenout.empty()) takenout = std::vector<int>(a, 0);
OutEdgeIt ei, eend;
for (boost::tie(ei, eend) = boost::out_edges(src, ASGraph); ei != eend; ++ei) {
Vertex u = boost::target(*ei, ASGraph);
if (asrescapmap[*ei] == 0) {
takenout[u] = 1;
}
}
return flow;
}
void Avalanche() {
int n, m, a, s, c, d;
_i >> n >> m >> a >> s >> c >> d;
_e << "d=" << d << _l;
// run Dijkstra on baseGraph
Graph baseGraph(n);
EdgeWeightMap basewmap = boost::get(boost::edge_weight, baseGraph);
for (int j = 0; j < m; j++) {
char w;
int x, y, z;
_i >> w >> x >> y >> z;
if (w == 'S') {
Edge e; bool su;
boost::tie(e, su) = boost::add_edge(x, y, baseGraph);
basewmap[e] = z;
}
else if (w == 'L') {
Edge e; bool su;
boost::tie(e, su) = boost::add_edge(x, y, baseGraph);
basewmap[e] = z;
boost::tie(e, su) = boost::add_edge(y, x, baseGraph);
basewmap[e] = z;
}
}
std::vector<Vertex> agents(a), shelters(s);
std::map< Vertex, std::vector<int> > distmaps;
for (int i = 0; i < a; i++) _i >> agents[i];
for (int j = 0; j < s; j++) _i >> shelters[j];
const int BIG = 1000000000;
int mindist = BIG, maxdist = 0;
std::vector< std::vector<int> > ASDist(a);
for (int i = 0; i < a; i++) {
ASDist[i] = std::vector<int>(s);
int ca = agents[i];
std::map< Vertex, std::vector<int> >::iterator dmit = distmaps.find(ca);
std::vector<int> distmap;
if (dmit != distmaps.end()) {
distmap = dmit->second;
}
else {
std::vector<int> predmap(n);
distmap = std::vector<int>(n);
boost::dijkstra_shortest_paths(baseGraph, ca,
predecessor_map(boost::make_iterator_property_map(predmap.begin(), boost::get(boost::vertex_index, baseGraph))).
distance_map(boost::make_iterator_property_map(distmap.begin(), boost::get(boost::vertex_index, baseGraph))));
for (int k = 0; k < n; k++) {
if (predmap[k] == k && k != ca)
distmap[k] = -1;
if (k == ca)
distmap[k] = 0;
}
distmaps.insert(std::make_pair(ca, distmap));
}
for (int j = 0; j < s; j++) {
int cs = shelters[j];
if (distmap[cs] == -1) {
ASDist[i][j] = -1;
continue;
}
ASDist[i][j] = distmap[cs];
mindist = std::min(mindist, ASDist[i][j]);
maxdist = std::max(maxdist, ASDist[i][j]);
}
}
std::set<int> possiblet;
std::vector<int> vpt;
for (int i = 0; i < a; i++)
for (int j = 0; j < s; j++)
possiblet.insert(ASDist[i][j]);
std::set<int>::iterator sit = possiblet.begin();
for (; sit != possiblet.end(); sit++) {
vpt.push_back(*sit);
}
std::vector<int>::iterator vit = vpt.begin();
std::vector<int> dummy;
int flow0 = checkASGraph(vpt[0], ASDist, dummy);
if (flow0 == a) {
_o << vpt[0] + d << _l;
return;
}
int st = 0, end = 1;
int npt = vpt.size();
while (true) {
int flowend = checkASGraph(vpt[end], ASDist, dummy);
if (flowend == a) break;
st = end;
end = std::min(end * 2, npt - 1);
}
int mid = (st + end) / 2;
//int st = 0, end = vpt.size() - 1, mid = (st + end) / 2;
int result = 0;
while (true) {
std::vector<int> takenout;
if (end - st <= 1) {
int flowst = checkASGraph(vpt[st], ASDist, takenout);
if (flowst == a) {
result = vpt[st] + d;
break;
}
int flowend = checkASGraph(vpt[end], ASDist, takenout);
if (flowend == a) {
result = vpt[end] + d;
break;
}
}
int t = vpt[mid];
int flow = checkASGraph(t, ASDist, takenout);
if (flow == a) {
end = mid;
mid = (st + end) / 2;
}
else {
st = mid + 1;
mid = (st + end) / 2;
}
}
_o << result << _l;
//for (; vit != vpt.end(); vit++) {
// int t = *vit;
// Graph ASGraph;
// std::vector<int> takenout;
// int flow = checkASGraph(t, ASDist, takenout);
// if (flow == a) {
// _o << t + d << _l;
// return;
// }
// else if (c == 2) {
// std::vector<int> newtakenout;
// int flow2 = checkASGraph(t + d, ASDist, newtakenout, takenout);
// if (flow2 + flow == a) {
// _o << t + d + d << _l;
// return;
// }
// }
//}
return;
}
// Week 14, PotW: Fleetrace
void Fleetrace2() {
typedef boost::adjacency_list_traits<boost::vecS, boost::vecS, boost::directedS> Traits;
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS, boost::no_property,
boost::property<boost::edge_capacity_t, long,
boost::property<boost::edge_residual_capacity_t, long,
boost::property<boost::edge_reverse_t, Traits::edge_descriptor,
boost::property<boost::edge_weight_t, long> > > > > Graph; // for MCMF
// Interior Property Maps
typedef boost::property_map<Graph, boost::edge_capacity_t>::type EdgeCapacityMap;
typedef boost::property_map<Graph, boost::edge_weight_t>::type EdgeWeightMap;
typedef boost::property_map<Graph, boost::edge_residual_capacity_t>::type ResidualCapacityMap;
typedef boost::property_map<Graph, boost::edge_reverse_t>::type ReverseEdgeMap;
typedef boost::graph_traits<Graph>::vertex_descriptor Vertex;
typedef boost::graph_traits<Graph>::vertex_iterator VertexIt;
typedef boost::graph_traits<Graph>::edge_descriptor Edge;
typedef boost::graph_traits<Graph>::out_edge_iterator OutEdgeIt;
int b, s, p; _i >> b >> s >> p;
Graph G(b + s);
EdgeCapacityMap capacitymap = boost::get(boost::edge_capacity, G);
EdgeWeightMap weightmap = boost::get(boost::edge_weight, G);
ReverseEdgeMap revedgemap = boost::get(boost::edge_reverse, G);
ResidualCapacityMap rescapacitymap = boost::get(boost::edge_residual_capacity, G);
EdgeAdderMCMF eaG(G, capacitymap, weightmap, revedgemap);
Vertex src = boost::add_vertex(G), tgt = boost::add_vertex(G);
const int MAXC = 50;
for (int i = 0; i < p; i++) {
int bi, si, ci;
_i >> bi >> si >> ci;
eaG.addEdge(bi, b + si, 1, MAXC - ci);
}
for (int i = 0; i < b; i++) {
eaG.addEdge(src, i, 1, 0);
}
for (int j = 0; j < s; j++) {
eaG.addEdge(src, b + j, 1, MAXC);
eaG.addEdge(b + j, tgt, 1, 0);
}
long flow = boost::push_relabel_max_flow(G, src, tgt);
boost::successive_shortest_path_nonnegative_weights(G, src, tgt);
long cost = boost::find_flow_cost(G);
long result = MAXC * flow - cost;
_o << result << _l;
return;
}
// Week 14: Fleetrace / 60pts
// Max weight bipartite matching -- do we need to implement Hungarian?
// no we don't
// but I can't get 100 pts because of TL.
void copyGraph(Graph & g, Graph & gc) {
EdgeCapacityMap capacitymap = boost::get(boost::edge_capacity, g);
EdgeWeightMap weightmap = boost::get(boost::edge_weight, g);
ReverseEdgeMap revedgemap = boost::get(boost::edge_reverse, g);
ResidualCapacityMap rescapacitymap = boost::get(boost::edge_residual_capacity, g);
EdgeCapacityMap capacitymap1 = boost::get(boost::edge_capacity, gc);
EdgeWeightMap weightmap1 = boost::get(boost::edge_weight, gc);
ReverseEdgeMap revedgemap1 = boost::get(boost::edge_reverse, gc);
ResidualCapacityMap rescapacitymap1 = boost::get(boost::edge_residual_capacity, gc);
EdgeAdderMCMF eaG1(gc, capacitymap1, weightmap1, revedgemap1);
VertexIt vit, vend;
for (boost::tie(vit, vend) = boost::vertices(g); vit != vend; vit++) {
OutEdgeIt oi, oie;
for (boost::tie(oi, oie) = boost::out_edges(*vit, g); oi != oie; oi++) {
eaG1.addEdge(boost::source(*oi, gc), boost::target(*oi, gc), capacitymap[*oi], weightmap[*oi]);
}
}
}
int calcFlowCost(Graph &G, int fl, Vertex src, Vertex tgt, Vertex supersink) {
//Graph G1;
//copyGraph(G, G1);
//EdgeCapacityMap capacitymap1 = boost::get(boost::edge_capacity, G1);
//EdgeWeightMap weightmap1 = boost::get(boost::edge_weight, G1);
//ReverseEdgeMap revedgemap1 = boost::get(boost::edge_reverse, G1);
//ResidualCapacityMap rescapacitymap1 = boost::get(boost::edge_residual_capacity, G1);
//EdgeAdderMCMF eaG1(G1, capacitymap1, weightmap1, revedgemap1);
EdgeCapacityMap capmap = boost::get(boost::edge_capacity, G);
//Vertex supersrc = boost::add_vertex(G1);
//Vertex supersink = boost::add_vertex(G1);
Edge e; bool su;
boost::tie(e, su) = boost::edge(tgt, supersink, G);
capmap[e] = fl;
//eaG1.addEdge(tgt, supersink, fl, 0);
int flow, cost;
flow = boost::push_relabel_max_flow(G, src, supersink);
boost::successive_shortest_path_nonnegative_weights(G, src, supersink);
cost = boost::find_flow_cost(G);
return cost;
}
void Fleetrace() {
typedef boost::adjacency_list_traits<boost::vecS, boost::vecS, boost::directedS> Traits;
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS, boost::no_property,
boost::property<boost::edge_capacity_t, long,
boost::property<boost::edge_residual_capacity_t, long,
boost::property<boost::edge_reverse_t, Traits::edge_descriptor,
boost::property<boost::edge_weight_t, long> > > > > Graph; // for MCMF
// Interior Property Maps
typedef boost::property_map<Graph, boost::edge_capacity_t>::type EdgeCapacityMap;
typedef boost::property_map<Graph, boost::edge_weight_t>::type EdgeWeightMap;
typedef boost::property_map<Graph, boost::edge_residual_capacity_t>::type ResidualCapacityMap;
typedef boost::property_map<Graph, boost::edge_reverse_t>::type ReverseEdgeMap;
typedef boost::graph_traits<Graph>::vertex_descriptor Vertex;
typedef boost::graph_traits<Graph>::vertex_iterator VertexIt;
typedef boost::graph_traits<Graph>::edge_descriptor Edge;
typedef boost::graph_traits<Graph>::out_edge_iterator OutEdgeIt;
int b, s, p; _i >> b >> s >> p;
Graph G(b + s);
EdgeCapacityMap capacitymap = boost::get(boost::edge_capacity, G);
EdgeWeightMap weightmap = boost::get(boost::edge_weight, G);
ReverseEdgeMap revedgemap = boost::get(boost::edge_reverse, G);
ResidualCapacityMap rescapacitymap = boost::get(boost::edge_residual_capacity, G);
EdgeAdderMCMF eaG(G, capacitymap, weightmap, revedgemap);
std::vector<int> coeffs(p), sumcoeffs(p);
// add edges: boat->sailor
const int MAXCOEFF = 50;
for (int i = 0; i < p; i++) {
int boat, sailor, coeff;
_i >> boat >> sailor >> coeff;
coeffs[i] = coeff;
eaG.addEdge(boat, b + sailor, 1, MAXCOEFF - coeff);
}
std::sort(coeffs.begin(), coeffs.end(), [](const int &i1, const int &i2) {return i1 > i2; });
sumcoeffs[0] = coeffs[0];
for (int i = 1; i < p; i++) {
sumcoeffs[i] = sumcoeffs[i - 1] + coeffs[i];
}
// add edges: src->boat, sailor->tgt;
Vertex src = boost::add_vertex(G);
Vertex tgt = boost::add_vertex(G);
Vertex supersink = boost::add_vertex(G);
for (int i = 0; i < b; i++) {
eaG.addEdge(src, i, 1, 0);
}
for (int j = 0; j < s; j++) {
eaG.addEdge(b + j, tgt, 1, 0);
}
eaG.addEdge(tgt, supersink, 0, 0);
Graph G1;
copyGraph(G, G1);
int maxflow = boost::push_relabel_max_flow(G1, (int)src, (int)tgt);
int costMaxFlow = calcFlowCost(G, maxflow, src, tgt, supersink);
int specMaxFlow = maxflow*MAXCOEFF - costMaxFlow;
int costNextFlow = calcFlowCost(G, maxflow - 1, src, tgt, supersink);
int specNextFlow = (maxflow - 1)*MAXCOEFF - costNextFlow;
_e << specMaxFlow << "mn" << specNextFlow << _l;
if (specMaxFlow > specNextFlow) {
_o << specMaxFlow << _l;
return;
}
int maxSpect = specNextFlow, maxSpectFlow = maxflow - 1;
int startFlow = -1, endFlow = -1, midFlow = -1;
int step = 4;
// 1st: linear search for an interval
//for (int r = maxflow; r >= 1; ) {
// int cost = calcFlowCost(G, r, src, tgt);
// int spec = r * MAXCOEFF - cost;
// _e << "flow=" << r << ", spec=" << spec << _l;
// if (maxSpect <= spec) {
// maxSpect = spec;
// maxSpectFlow = r;
// }
// else {
// startFlow = std::min(r + 3 * step / 2, maxflow);
// endFlow = r;
// midFlow = (startFlow + endFlow) / 2;
// _e << "start" << startFlow << " end" << endFlow << _l;
// break;
// }
// step *= 2;
// r -= r > step ? step : 1;
//}
startFlow = maxSpectFlow;
for (endFlow = 0; endFlow < maxflow; endFlow++) {
if (sumcoeffs[endFlow] >= maxSpect) break;
}
endFlow++;
midFlow = (startFlow + endFlow + 1) / 2;
// 2nd: binary search on selected interval
if (startFlow < 0) {
_o << maxSpect << _l;
return;
}
maxSpect = 0;
std::vector<int> specs(startFlow - endFlow + 1);
int base = endFlow;
if (!specs[startFlow - base]) {
//specs[startFlow - base] = startFlow*MAXCOEFF - calcFlowCost(G, startFlow, src, tgt, supersink);
specs[startFlow - base] = maxSpect;
}
if (!specs[endFlow - base]) {
specs[endFlow - base] = endFlow*MAXCOEFF - calcFlowCost(G, endFlow, src, tgt, supersink);
}
while (true) {
if (startFlow - endFlow <= 2) {
if (!specs[startFlow - base])
specs[startFlow - base] = startFlow*MAXCOEFF - calcFlowCost(G, startFlow, src, tgt, supersink);
if (!specs[endFlow - base])
specs[endFlow - base] = endFlow*MAXCOEFF - calcFlowCost(G, endFlow, src, tgt, supersink);
if (!specs[midFlow - base])
specs[midFlow - base] = midFlow*MAXCOEFF - calcFlowCost(G, midFlow, src, tgt, supersink);
maxSpect = std::max(specs[startFlow - base], std::max(specs[endFlow - base], specs[midFlow - base]));
break;
}
if (!specs[midFlow - base]) {
int midCost = calcFlowCost(G, midFlow, src, tgt, supersink);
int midSpec = midFlow * MAXCOEFF - midCost;
specs[midFlow - base] = midSpec;
}
if (specs[midFlow - base] > specs[endFlow - base] && specs[midFlow - base] < specs[startFlow - base]) {
endFlow = midFlow + 1;
midFlow = (startFlow + endFlow) / 2;
continue;
}
else if (specs[midFlow - base] < specs[endFlow - base] && specs[midFlow - base] > specs[startFlow - base]) {
startFlow = midFlow - 1;
midFlow = (startFlow + endFlow) / 2;
continue;
}
bool flag = false;
for (int r = midFlow - 1; r >= endFlow; r--) {
if (!specs[r - base]) {
int cost = calcFlowCost(G, r, src, tgt, supersink);
int spec = r * MAXCOEFF - cost;
specs[r - base] = spec;
}
int spec = specs[r - base];
if (spec < specs[midFlow - base]) {
endFlow = midFlow;
midFlow = (startFlow + endFlow + 1) / 2;
flag = true;
break;
}
else if (spec > specs[midFlow - base]) {
startFlow = r;
midFlow = (startFlow + endFlow + 1) / 2;
flag = true;
break;
}
}
if (!flag) {
endFlow = midFlow;
midFlow = (startFlow + endFlow + 1) / 2;
}
_e << "pos: " << startFlow << " " << midFlow << " " << endFlow << _l;
}
//for (int r = startFlow; r >= endFlow; r--) {
// int cost = calcFlowCost(G, r, src, tgt);
// int spec = r * MAXCOEFF - cost;
// _e << "flow=" << r << ", spec=" << spec << _l;
// if (maxSpect <= spec) {
// maxSpect = spec;
// maxSpectFlow = r;
// }
// else {
// break;
// }
//}
_o << maxSpect << _l;
_e << maxSpectFlow << " " << maxflow << _l << _l;
return;
}
// Week 12: Casino Royale
// MCMF?
// Damn it I thought too much about DP.
// Easy version of Car Sharing
void CasinoRoyale() {
int n, m, l; _i >> n >> m >> l;
Graph G(n);
EdgeWeightMap wmap = boost::get(boost::edge_weight, G);
ReverseEdgeMap revmap = boost::get(boost::edge_reverse, G);
ResidualCapacityMap rescmap = boost::get(boost::edge_residual_capacity, G);
EdgeCapacityMap cmap = boost::get(boost::edge_capacity, G);
EdgeAdderMCMF eaG(G, cmap, wmap, revmap);
Vertex src = boost::add_vertex(G);
const int MAXQ = 128;
eaG.addEdge(src, 0, l, 0);
for (int i = 0; i < n - 1; i++) {
eaG.addEdge(i, i + 1, l, MAXQ);
}
for (int j = 0; j < m; j++) {
int x, y, q;
_i >> x >> y >> q;
eaG.addEdge(x, y, 1, (y - x)*MAXQ - q);
}
long flow = boost::push_relabel_max_flow(G, src, n - 1);
boost::successive_shortest_path_nonnegative_weights(G, src, n - 1);
long cost = boost::find_flow_cost(G);
long sumq = flow * MAXQ * (n - 1) - cost;
_o << sumq << _l;
return;
}
// Week 13: Bob's Burden
// Split vertices and 3 Dijkstras
inline Vertex getVertex(int i, int j, int k) {
return (Vertex)(i*(i + 1) / 2 + j);
}
inline bool inRange(int i, int j, int k) {
return(i >= 0 && i < k && j >= 0 && j < k && i >= j);
}
void BobsBurden() {
int k; _i >> k;
std::vector< std::vector<int> > val(k);
for (int i = 0; i < k; i++) val[i] = std::vector<int>(k);
// k*(k+1)/2 balls
int n = k*(k + 1) / 2;
Graph G(n * 2); // split nodes: other_out -> v_in -> v_out -> other_in
int nv = boost::num_vertices(G);
EdgeWeightMap wmap = boost::get(boost::edge_weight, G);
for (int i = 0; i < k; i++) {
for (int j = 0; j <= i; j++) {
int vv; _i >> vv;
val[i][j] = vv;
Vertex node = getVertex(i, j, k);
Edge e; bool suc;
boost::tie(e, suc) = boost::add_edge(node, n + node, G);
wmap[e] = val[i][j];
}
}
for (int i = 0; i < k; i++) {
for (int j = 0; j <= i; j++) {
Vertex v = getVertex(i, j, k);
if (inRange(i - 1, j - 1, k)) {
Vertex u = getVertex(i - 1, j - 1, k);
Edge e; bool suc;
boost::tie(e, suc) = boost::add_edge(n + v, u, G);
wmap[e] = 0;
}
if (inRange(i, j - 1, k)) {
Vertex u = getVertex(i, j - 1, k);
Edge e; bool suc;
boost::tie(e, suc) = boost::add_edge(n + v, u, G);
wmap[e] = 0;
}
if (inRange(i - 1, j, k)) {
Vertex u = getVertex(i - 1, j, k);
Edge e; bool suc;
boost::tie(e, suc) = boost::add_edge(n + v, u, G);
wmap[e] = 0;
}
if (inRange(i, j + 1, k)) {
Vertex u = getVertex(i, j + 1, k);
Edge e; bool suc;
boost::tie(e, suc) = boost::add_edge(n + v, u, G);
wmap[e] = 0;
}
if (inRange(i + 1, j + 1, k)) {
Vertex u = getVertex(i + 1, j + 1, k);
Edge e; bool suc;
boost::tie(e, suc) = boost::add_edge(n + v, u, G);
wmap[e] = 0;
}
if (inRange(i + 1, j, k)) {
Vertex u = getVertex(i + 1, j, k);
Edge e; bool suc;
boost::tie(e, suc) = boost::add_edge(n + v, u, G);
wmap[e] = 0;
}
}
}
std::vector<Vertex> p11(nv), pk1(nv), pkk(nv);
std::vector<long> d11(nv), dk1(nv), dkk(nv);
//boost::connected_components(G, &d11[0]);
//for (int r = 0; r < nv; r++) {
// _e << d11[r] << " ";
//}_e << _l;
boost::dijkstra_shortest_paths(G, getVertex(0, 0, k),
predecessor_map(boost::make_iterator_property_map(p11.begin(), boost::get(boost::vertex_index, G))).
distance_map(boost::make_iterator_property_map(d11.begin(), boost::get(boost::vertex_index, G))));
boost::dijkstra_shortest_paths(G, getVertex(k - 1, 0, k),
predecessor_map(boost::make_iterator_property_map(pk1.begin(), boost::get(boost::vertex_index, G))).
distance_map(boost::make_iterator_property_map(dk1.begin(), boost::get(boost::vertex_index, G))));
boost::dijkstra_shortest_paths(G, getVertex(k - 1, k - 1, k),
predecessor_map(boost::make_iterator_property_map(pkk.begin(), boost::get(boost::vertex_index, G))).
distance_map(boost::make_iterator_property_map(dkk.begin(), boost::get(boost::vertex_index, G))));
long minw = 1000000000;
for (int i = 0; i < k; i++) {
for (int j = 0; j <= i; j++) {
Vertex v = getVertex(i, j, k);
long dist11 = d11[v + n], distk1 = dk1[v], distkk = dkk[v];
//_e << i << "," << j <<": "<< dist11 << " " << distk1 << " " << distkk << _l;
long sumw = dist11 + distk1 + distkk;
if (minw > sumw) {
minw = sumw;
}
}
}
_o << minw << _l;
return;
}
// Week 4: Ant Challenge
// Multiple MST + Dijkstra
void AntChallenge() {
typedef boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS,
boost::no_property, boost::property < boost::edge_weight_t, long > > UGraph;
typedef boost::property_map < UGraph, boost::edge_weight_t >::type UWeightMap;
typedef boost::graph_traits < UGraph >::edge_descriptor UEdge;
typedef boost::graph_traits < UGraph >::edge_iterator UEdgeIt;
typedef boost::graph_traits < UGraph >::out_edge_iterator UOutEdgeIt;
typedef boost::graph_traits < UGraph >::vertex_descriptor UVertex;
int n, e, s, a, b;
_i >> n >> e >> s >> a >> b;
// Construct the mst for each species
std::vector<UGraph> graphs(s), msts(s);
std::vector<UWeightMap> wmaps(s);
std::vector<UVertex> hives(s);
for (int k = 0; k < s; k++) {
graphs[k] = UGraph(n);
msts[k] = UGraph(n);
wmaps[k] = boost::get(boost::edge_weight, graphs[k]);
}
for (int j = 0; j < e; j++) {
int t1, t2; _i >> t1 >> t2;
for (int k = 0; k < s; k++) {
int w; _i >> w;
UEdge e; bool suc;
boost::tie(e, suc) = boost::add_edge(t1, t2, graphs[k]);
wmaps[k][e] = w;
}
}
UGraph finalGraph(n);
UWeightMap finalWmap = boost::get(boost::edge_weight, finalGraph);
for (int k = 0; k < s; k++) {
// find MST
_i >> hives[k];
std::vector<UVertex> p(n);
boost::prim_minimum_spanning_tree(graphs[k], &p[0]);
// construct finalGraph = minimum of each MST
for (int i = 0; i < n; i++) {
if (p[i] == i)continue;
UEdge e, efin; bool suc, sfin;
boost::tie(e, suc) = boost::edge(p[i], i, graphs[k]);
boost::tie(efin, sfin) = boost::edge(p[i], i, finalGraph);
if (sfin) {
if (finalWmap[efin] > wmaps[k][e]) {
finalWmap[efin] = wmaps[k][e];
}
}
else {
boost::tie(efin, sfin) = boost::add_edge(p[i], i, finalGraph);
finalWmap[efin] = wmaps[k][e];
}
}
}
std::vector<UVertex> p(n);
std::vector<long> d(n);
boost::dijkstra_shortest_paths(finalGraph, a,
predecessor_map(boost::make_iterator_property_map(p.begin(), boost::get(boost::vertex_index, finalGraph))).
distance_map(boost::make_iterator_property_map(d.begin(), boost::get(boost::vertex_index, finalGraph))));
_o << d[b] << _l;
return;
}
// Week 5: Tracking / 100 pts
// Force Dijkstra to pass k times on certain edges
// Beware of the direction of edges!
void Tracking() {
typedef boost::adjacency_list < boost::vecS, boost::vecS, boost::undirectedS,
boost::no_property, boost::property < boost::edge_weight_t, long > > UGraph;
typedef boost::property_map < UGraph, boost::edge_weight_t >::type UWeightMap;
typedef boost::graph_traits < UGraph >::edge_descriptor UEdge;
typedef boost::graph_traits < UGraph >::edge_iterator UEdgeIt;
typedef boost::graph_traits < UGraph >::out_edge_iterator UOutEdgeIt;
typedef boost::graph_traits < UGraph >::vertex_descriptor UVertex;
struct MyEdge {
int a; int b; int c;
MyEdge(int a = 0, int b = 0, int c = 0) : a(a), b(b), c(c) {}
};
int n, m, k, x, y;
_i >> n >> m >> k >> x >> y;
UGraph G(n*(k + 1));
int nv = boost::num_vertices(G);
y += n*k;
UWeightMap wmap = boost::get(boost::edge_weight, G);
std::vector<MyEdge> riveredges;
for (int i = 0; i < m; i++) {
int a, b, c, d;
_i >> a >> b >> c >> d;
if (d == 1) {
riveredges.push_back(MyEdge(a, b, c));
}
for (int l = 0; l <= k; l++) {
Vertex va = l*n + a;
Vertex vb = l*n + b;
UEdge e; bool success;
boost::tie(e, success) = boost::add_edge(va, vb, G);
wmap[e] = c;
}
}
int mr = riveredges.size();
for (int i = 0; i < mr; i++) {
MyEdge me = riveredges[i];
for (int l = 0; l < k; l++) {
Vertex va = l*n + me.a;
Vertex vb = (l + 1)*n + me.b;
UEdge e; bool success;
boost::tie(e, success) = boost::add_edge(va, vb, G);
wmap[e] = me.c;
Vertex var = va + n;
Vertex vbr = vb - n;
boost::tie(e, success) = boost::add_edge(var, vbr, G);
wmap[e] = me.c;
}
}