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ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#917167 | #602. 最小费用最大流(随机数据) | definieren# | 100 ✓ | 467ms | 4716kb | C++20 | 3.4kb | 2025-02-27 09:15:39 | 2025-02-27 09:15:39 |
Judging History
answer
#include <bits/stdc++.h>
template<class Cap, class Cost>
struct Flow {
struct Edge {
int from, to;
Cap cap, flow;
Cost cost;
};
struct _Edge {
int to, rev;
Cap cap;
Cost cost;
};
struct Graph {
std::vector<int> head;
std::vector<_Edge> elist;
explicit Graph(int n,
const std::vector<std::pair<int, _Edge>>& edges) {
head.assign(n + 1, 0), elist.resize(edges.size());
for (auto e : edges) ++ head[e.first + 1];
for (int i = 0; i < n; i ++) head[i + 1] += head[i];
auto cnt = head;
for (auto e : edges) {
elist[cnt[e.first] ++] = e.second;
}
}
};
int n;
std::vector<Edge> edge;
Flow(int _n): n(_n), edge{} {}
void Add_Edge(int u, int v, Cap cap, Cost cost) {
assert(0 <= u && u < n);
assert(0 <= v && v < n);
assert(cap >= 0), assert(0 <= cost);
edge.emplace_back(u, v, cap, 0, cost);
return;
}
std::pair<Cap, Cost> MCMF(int S, int T) {
assert(0 <= S && S < n);
assert(0 <= T && T < n);
const int m = static_cast<int>(edge.size());
std::vector<int> idx(m), rev(m), deg(n);
std::vector<std::pair<int, _Edge>> elist(2 * m);
for (int i = 0; i < m; i ++) {
auto e = edge[i];
idx[i] = deg[e.from] ++;
rev[i] = deg[e.to] ++;
elist[2 * i] = {e.from, {e.to, -1, e.cap - e.flow, e.cost}};
elist[2 * i + 1] = {e.to, {e.from, -1, e.flow, - e.cost}};
}
auto G = Graph(n, elist);
for (int i = 0; i < m; i ++) {
auto e = edge[i];
idx[i] += G.head[e.from];
rev[i] += G.head[e.to];
G.elist[idx[i]].rev = rev[i];
G.elist[rev[i]].rev = idx[i];
}
auto ans = Slope(G, S, T).back();
for (int i = 0; i < m; i ++) {
auto e = G.elist[idx[i]];
edge[i].flow = edge[i].cap - e.cap;
}
return ans;
}
std::vector<std::pair<Cap, Cost>> Slope(Graph G, int S, int T) {
const Cap inf = std::numeric_limits<Cap>::max();
const Cost INF = std::numeric_limits<Cost>::max();
std::vector<int> pre(n);
std::vector<Cost> dist(n);
std::vector<bool> vis(n);
auto SPFA = [&]() {
std::queue<int> Q;
fill(dist.begin(), dist.end(), INF);
fill(vis.begin(), vis.end(), false);
Q.emplace(S), dist[S] = 0, vis[S] = true;
while (Q.size()) {
int u = Q.front();
vis[u] = false, Q.pop();
for (int i = G.head[u]; i < G.head[u + 1]; i ++) {
auto e = G.elist[i];
if (e.cap && dist[u] + e.cost < dist[e.to]) {
dist[e.to] = dist[u] + e.cost, pre[e.to] = e.rev;
if (!vis[e.to]) Q.emplace(e.to), vis[e.to] = true;
}
}
}
return dist[T] != INF;
};
Cap flow = 0; Cost cost = 0, pre_slope = -1;
std::vector<std::pair<Cap, Cost>> slope{{Cap(0), Cost(0)}};
while (SPFA()) {
Cap c = inf, d = dist[T];
for (int u = T; u != S; u = G.elist[pre[u]].to)
c = std::min(c, G.elist[G.elist[pre[u]].rev].cap);
for (int u = T; u != S; u = G.elist[pre[u]].to) {
auto &e = G.elist[pre[u]];
e.cap += c, G.elist[e.rev].cap -= c;
}
flow += c, cost += c * d;
if (pre_slope == d) slope.back() = {flow, cost};
else slope.emplace_back(flow, cost);
pre_slope = d;
}
return slope;
}
};
int main() {
int n, m;
std::cin >> n >> m;
int S = 0, T = n - 1;
Flow<int, int> G(n);
for (int i = 0; i < m; i ++) {
int u, v, c, w;
std::cin >> u >> v >> c >> w;
G.Add_Edge(-- u, -- v, c, w);
}
auto [mxf, mnc] = G.MCMF(S, T);
std::cout << mxf << ' ' << mnc << '\n';
return 0;
}
详细
Pretests
Final Tests
Test #1:
score: 10
Accepted
time: 0ms
memory: 3584kb
input:
8 27 2 3 2147483647 100 1 3 1 100 2 4 2147483647 10 1 4 1 10 2 4 2147483647 10 1 4 1 10 2 8 3 0 3 5 2147483647 100 1 5 1 100 3 8 1 0 3 2 2147483647 0 4 5 2147483647 10 1 5 1 10 4 8 1 0 4 2 2147483647 0 5 6 2147483647 1 1 6 1 1 5 6 2147483647 1 1 6 1 1 5 7 2147483647 1 1 7 1 1 5 8 3 0 5 2 2147483647 ...
output:
8 243
result:
ok 2 number(s): "8 243"
Test #2:
score: 10
Accepted
time: 1ms
memory: 3584kb
input:
12 49 2 10 2147483647 5 1 10 1 5 2 5 2147483647 50 1 5 1 50 2 9 2147483647 8 1 9 1 8 2 8 2147483647 47 1 8 1 47 2 11 2147483647 17 1 11 1 17 2 12 5 0 3 12 0 0 3 2 2147483647 0 4 6 2147483647 18 1 6 1 18 4 11 2147483647 12 1 11 1 12 4 9 2147483647 14 1 9 1 14 4 12 3 0 4 2 2147483647 0 5 11 2147483647...
output:
15 436
result:
ok 2 number(s): "15 436"
Test #3:
score: 10
Accepted
time: 0ms
memory: 3584kb
input:
27 169 2 15 2147483647 24 1 15 1 24 2 19 2147483647 96 1 19 1 96 2 12 2147483647 49 1 12 1 49 2 13 2147483647 75 1 13 1 75 2 24 2147483647 2 1 24 1 2 2 27 5 0 3 27 0 0 3 2 2147483647 0 4 11 2147483647 99 1 11 1 99 4 3 2147483647 85 1 3 1 85 4 27 2 0 4 2 2147483647 0 5 27 0 0 5 2 2147483647 0 6 9 214...
output:
60 4338
result:
ok 2 number(s): "60 4338"
Test #4:
score: 10
Accepted
time: 12ms
memory: 3776kb
input:
77 2149 2 42 2147483647 33 1 42 1 33 2 68 2147483647 30 1 68 1 30 2 76 2147483647 13 1 76 1 13 2 51 2147483647 93 1 51 1 93 2 12 2147483647 39 1 12 1 39 2 57 2147483647 74 1 57 1 74 2 70 2147483647 21 1 70 1 21 2 73 2147483647 24 1 73 1 24 2 52 2147483647 54 1 52 1 54 2 15 2147483647 99 1 15 1 99 2 ...
output:
1000 74606
result:
ok 2 number(s): "1000 74606"
Test #5:
score: 10
Accepted
time: 49ms
memory: 3840kb
input:
102 4199 2 48 2147483647 42 1 48 1 42 2 85 2147483647 50 1 85 1 50 2 22 2147483647 83 1 22 1 83 2 95 2147483647 97 1 95 1 97 2 82 2147483647 34 1 82 1 34 2 25 2147483647 72 1 25 1 72 2 4 2147483647 17 1 4 1 17 2 47 2147483647 10 1 47 1 10 2 71 2147483647 12 1 71 1 12 2 68 2147483647 39 1 68 1 39 2 2...
output:
2000 161420
result:
ok 2 number(s): "2000 161420"
Test #6:
score: 10
Accepted
time: 51ms
memory: 3968kb
input:
102 4199 2 79 2147483647 13 1 79 1 13 2 83 2147483647 73 1 83 1 73 2 75 2147483647 90 1 75 1 90 2 30 2147483647 92 1 30 1 92 2 54 2147483647 25 1 54 1 25 2 66 2147483647 53 1 66 1 53 2 52 2147483647 37 1 52 1 37 2 63 2147483647 46 1 63 1 46 2 11 2147483647 20 1 11 1 20 2 55 2147483647 53 1 55 1 53 2...
output:
2000 143072
result:
ok 2 number(s): "2000 143072"
Test #7:
score: 10
Accepted
time: 49ms
memory: 3840kb
input:
102 4199 2 39 2147483647 45 1 39 1 45 2 51 2147483647 11 1 51 1 11 2 86 2147483647 63 1 86 1 63 2 23 2147483647 46 1 23 1 46 2 48 2147483647 63 1 48 1 63 2 87 2147483647 8 1 87 1 8 2 73 2147483647 63 1 73 1 63 2 5 2147483647 52 1 5 1 52 2 80 2147483647 21 1 80 1 21 2 31 2147483647 44 1 31 1 44 2 101...
output:
2000 146132
result:
ok 2 number(s): "2000 146132"
Test #8:
score: 10
Accepted
time: 413ms
memory: 4716kb
input:
302 10599 2 72 2147483647 169 1 72 1 169 2 260 2147483647 165 1 260 1 165 2 12 2147483647 108 1 12 1 108 2 16 2147483647 26 1 16 1 26 2 28 2147483647 148 1 28 1 148 2 7 2147483647 74 1 7 1 74 2 139 2147483647 199 1 139 1 199 2 231 2147483647 9 1 231 1 9 2 287 2147483647 123 1 287 1 123 2 135 2147483...
output:
5000 1106316
result:
ok 2 number(s): "5000 1106316"
Test #9:
score: 10
Accepted
time: 467ms
memory: 4588kb
input:
302 10599 2 222 2147483647 132 1 222 1 132 2 17 2147483647 7 1 17 1 7 2 177 2147483647 253 1 177 1 253 2 90 2147483647 195 1 90 1 195 2 128 2147483647 289 1 128 1 289 2 42 2147483647 193 1 42 1 193 2 213 2147483647 133 1 213 1 133 2 263 2147483647 293 1 263 1 293 2 50 2147483647 155 1 50 1 155 2 228...
output:
5000 1290871
result:
ok 2 number(s): "5000 1290871"
Test #10:
score: 10
Accepted
time: 430ms
memory: 4592kb
input:
302 10599 2 176 2147483647 289 1 176 1 289 2 190 2147483647 99 1 190 1 99 2 10 2147483647 96 1 10 1 96 2 240 2147483647 165 1 240 1 165 2 273 2147483647 205 1 273 1 205 2 248 2147483647 194 1 248 1 194 2 220 2147483647 122 1 220 1 122 2 194 2147483647 167 1 194 1 167 2 8 2147483647 67 1 8 1 67 2 227...
output:
5000 1395897
result:
ok 2 number(s): "5000 1395897"