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#include <c10/test/util/Macros.h>
#include <c10/util/NetworkFlow.h>
#include <gtest/gtest.h>
#include <cstdlib>
namespace {
template <typename T>
bool vector_contains(const std::vector<T>& vec, const T& element) {
for (const auto& e : vec) {
if (e == element) {
return true;
}
}
return false;
}
template <typename T>
void expect_vector_contains_subset(
const std::vector<T>& vec,
const std::vector<T>& subset) {
for (auto& element : subset) {
if (!vector_contains(vec, element)) {
std::stringstream ss;
ss << "Failed: checking whether {";
for (auto& e : subset) {
ss << e << ", ";
}
ss << "} is a subset of {";
for (auto& e : vec) {
ss << e << ", ";
}
ss << "}, but couldn't find " << element;
FAIL() << ss.str();
}
}
}
namespace test_network_flow {
TEST(NetworkFlowTest, basic) {
/*
* 3 1 2
* -->b-- ->e--
* / 1| \/ \
* / 2 v 2/\ 2 \
* a---->c-/ ->f---->h
* \ 2\/ /
* \3 1/\ 2/
* -->d-- ->g--
*
* Consider these augmenting paths that constitute a blocking flow:
* a -> d -> f -> h (capacity 1), saturates d->f
* a -> c -> g -> h (capacity 2), saturates a->c, c->g, g->h
* a -> b -> c -> e -> h (capacity 1), saturates b->c
* a -> b -> f -> h (capacity 1), saturates b->f, f->h
*/
c10::NetworkFlowGraph g;
g.add_edge("a", "b", 3); // flow: 2
g.add_edge("a", "c", 2); // flow: 2
g.add_edge("a", "d", 3); // flow: 1
g.add_edge("b", "f", 1); // flow: 1
g.add_edge("c", "e", 2); // flow: 1
g.add_edge("c", "g", 2); // flow: 2
g.add_edge("d", "f", 1); // flow: 1
g.add_edge("b", "c", 1); // flow: 1
g.add_edge("e", "h", 2); // flow: 1
g.add_edge("f", "h", 2); // flow: 2
g.add_edge("g", "h", 2); // flow: 2
auto res = g.minimum_cut("a", "h");
EXPECT_EQ(res.status, c10::MinCutStatus::SUCCESS);
EXPECT_EQ(res.max_flow, 5);
// how we "reach" these vertices from "h":
// h -> e: we see the e->h edge has residual capacity
// e -> c: we see the c->e edge has residual capacity
// c -> g: the c->g edge has flow, therefore the g->c edge has residual
// capacity
expect_vector_contains_subset(res.unreachable, {"h", "e", "c", "g"});
expect_vector_contains_subset(res.reachable, {"a", "b", "d", "f"});
}
TEST(NetworkFlowTest, loop) {
/* 1
* -------------------
* / \
* 1 / 1 1 \ 1
* a --------> b --------> c -------> d --------> e
*/
c10::NetworkFlowGraph g;
g.add_edge("a", "b", 1); // flow: 1
g.add_edge("b", "c", 1); // flow: 1
g.add_edge("c", "d", 1); // flow: 1
g.add_edge("d", "e", 1); // flow: 1
g.add_edge("d", "b", 1); // flow: 0
auto res = g.minimum_cut("a", "e");
EXPECT_EQ(res.status, c10::MinCutStatus::SUCCESS);
EXPECT_EQ(res.max_flow, 1);
expect_vector_contains_subset(res.unreachable, {"e"});
expect_vector_contains_subset(res.reachable, {"a", "b", "c", "d"});
}
TEST(NetworkFlowTest, disconnected_vertices) {
/*
* 1
* c --------> d
*
* 1
* a --------> b
*/
c10::NetworkFlowGraph g;
g.add_edge("a", "b", 1); // flow: 1
g.add_edge("c", "d", 1); // flow: 0
auto res = g.minimum_cut("a", "b");
EXPECT_EQ(res.status, c10::MinCutStatus::SUCCESS);
EXPECT_EQ(res.max_flow, 1);
expect_vector_contains_subset(res.unreachable, {"b"});
// unintuitively, "c" and "d" get marked as reachable; this mirrors networkx
// behavior.
expect_vector_contains_subset(res.reachable, {"a", "c", "d"});
}
TEST(NetworkFlowTest, invalid_endpoints) {
c10::NetworkFlowGraph g;
g.add_edge("a", "b", 1);
auto res = g.minimum_cut("a", "c");
EXPECT_EQ(res.status, c10::MinCutStatus::INVALID);
res = g.minimum_cut("c", "b");
EXPECT_EQ(res.status, c10::MinCutStatus::INVALID);
}
TEST(NetworkFlowTest, unbounded) {
c10::NetworkFlowGraph g;
g.add_edge("a", "b", c10::NetworkFlowGraph::INF);
auto res = g.minimum_cut("a", "b");
EXPECT_EQ(res.status, c10::MinCutStatus::UNBOUNDED);
}
TEST(NetworkFlowTest, overflow) {
c10::NetworkFlowGraph g;
auto flow1 = c10::NetworkFlowGraph::INF / 2;
auto flow2 = c10::NetworkFlowGraph::INF - flow1;
g.add_edge("a", "b", flow1);
g.add_edge("a", "b", flow2);
auto res = g.minimum_cut("a", "b");
EXPECT_EQ(res.status, c10::MinCutStatus::OVERFLOW_INF);
}
TEST(NetworkFlowTest, reverse_edge) {
/*
* 100
* --------
* / \
* 1 < 1 \
* a ---------> b ---------> c
*
*/
c10::NetworkFlowGraph g;
g.add_edge("a", "b", 1);
g.add_edge("b", "c", 1);
g.add_edge("c", "a", 100);
auto res = g.minimum_cut("a", "c");
EXPECT_EQ(res.status, c10::MinCutStatus::SUCCESS);
EXPECT_EQ(res.max_flow, 1);
expect_vector_contains_subset(res.unreachable, {"c"});
expect_vector_contains_subset(res.reachable, {"a", "b"});
}
} // namespace test_network_flow
} // namespace
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