From 12af1ea6143694d8963e463fff463db38ffe013a Mon Sep 17 00:00:00 2001 From: Harui <68176059+Harui-i@users.noreply.github.com> Date: Sun, 10 May 2026 19:53:05 +0900 Subject: [PATCH 1/2] Add general weighted matching (blossom) implementation --- docs/graph/general_weighted_matching.md | 22 ++ graph/general_weighted_matching.hpp | 303 ++++++++++++++++++ .../yosupo-general-weighted-matching.test.cpp | 29 ++ 3 files changed, 354 insertions(+) create mode 100644 docs/graph/general_weighted_matching.md create mode 100644 graph/general_weighted_matching.hpp create mode 100644 test/verify/yosupo-general-weighted-matching.test.cpp diff --git a/docs/graph/general_weighted_matching.md b/docs/graph/general_weighted_matching.md new file mode 100644 index 0000000..97cf8e9 --- /dev/null +++ b/docs/graph/general_weighted_matching.md @@ -0,0 +1,22 @@ +--- +title: General Weighted Matching +documentation_of: //graph/general_weighted_matching.hpp +--- + +一般グラフの最大重みマッチング（Blossom / 花アルゴリズム）を解く。 +重み付き辺を受け取り、重み和が最大となるマッチングを返す。 + +## 使い方 + +```cpp +mylib::GeneralWeightedMatching wm(N); +wm.add_edge(u, v, w); +auto [sum, mate] = wm.solve(); +``` + +- `sum`: 最大重み +- `mate[i]`: 頂点 `i` とマッチした頂点番号（未マッチは `-1`） + +## 計算量 + +- $O(N^3)$ diff --git a/graph/general_weighted_matching.hpp b/graph/general_weighted_matching.hpp new file mode 100644 index 0000000..497df98 --- /dev/null +++ b/graph/general_weighted_matching.hpp @@ -0,0 +1,303 @@ +#ifndef HARUILIB_GRAPH_GENERAL_WEIGHTED_MATCHING_HPP +#define HARUILIB_GRAPH_GENERAL_WEIGHTED_MATCHING_HPP + +#include +#include +#include +#include +#include +#include +#include + +namespace mylib { + +struct GeneralWeightedMatching { + int n; + std::vector> w; + + explicit GeneralWeightedMatching(int n_) : n(n_), w(n_, std::vector(n_, 0)) {} + + void add_edge(int u, int v, long long cost) { + if (u == v) return; + if (w[u][v] < cost) w[u][v] = w[v][u] = cost; + } + + std::pair> solve() const { + if (n == 0) return {0, {}}; + int N = n; + int S = N + 1; + + std::vector> g(N + 1, std::vector(N + 1, 0)); + for (int i = 1; i <= N; i++) { + for (int j = 1; j <= N; j++) { + g[i][j] = w[i - 1][j - 1]; + } + } + + std::vector match(N + 1, 0), slackx(N + 1), prev(N + 1), st(N + 1), pa(N + 1); + std::vector lab(N + 1), slack(N + 1); + std::vector> flower_from(N + 1, std::vector(N + 1, 0)); + std::vector> flower(N + 1); + std::vector> q(2 * N + 5); + std::vector Sstate(N + 1), vis(N + 1); + int qh = 0, qt = 0; + + auto dist = [&](int u, int v) { + return lab[u] + lab[v] - g[u][v] * 2; + }; + + auto update_slack = [&](int u, int x) { + if (!slack[x] || dist(u, x) < dist(slackx[x], x)) { + slack[x] = dist(u, x); + slackx[x] = u; + } + }; + + auto set_slack = [&](int x) { + slack[x] = 0; + for (int u = 1; u <= N; u++) { + if (Sstate[st[u]] == 0 && st[u] != x && g[u][x] > 0) update_slack(u, x); + } + }; + + auto q_push = [&](int x) { + if (x <= N) q[qt++] = {x, 0}; + else for (int v : flower[x]) q[qt++] = {v, x}; + }; + + std::function set_st = [&](int x, int b) { + st[x] = b; + if (x > N) { + for (int v : flower[x]) set_st(v, b); + } + }; + + auto get_pr = [&](int b, int xr) { + int pr = std::find(flower[b].begin(), flower[b].end(), xr) - flower[b].begin(); + if (pr % 2 == 1) { + std::reverse(flower[b].begin() + 1, flower[b].end()); + return (int)flower[b].size() - pr; + } + return pr; + }; + + std::function set_match = [&](int u, int v, int from) { + match[u] = v; + if (u <= N) return; + int xr = flower_from[u][g[st[u]][st[v]] == 0 ? v : from]; + int pr = get_pr(u, xr); + for (int i = 0; i < pr; i++) { + set_match(flower[u][i], flower[u][i ^ 1], from); + } + set_match(xr, v, from); + std::rotate(flower[u].begin(), flower[u].begin() + pr, flower[u].end()); + }; + + std::function augment = [&](int u) { + while (u) { + int v = st[pa[u]]; + int wv = st[match[v]]; + set_match(u, v, 0); + u = wv; + } + }; + + std::function lca = [&](int u, int v) { + std::fill(vis.begin(), vis.end(), 0); + while (u || v) { + if (u) { + if (vis[u] == 1) return u; + vis[u] = 1; + if (match[u]) u = st[pa[match[u]]]; + else u = 0; + } + std::swap(u, v); + } + return 0; + }; + + auto add_blossom = [&](int u, int l, int v) { + int b = N + 1; + while (b <= S && st[b]) b++; + if (b > S) return; + lab[b] = 0; + Sstate[b] = -1; + match[b] = match[l]; + flower[b].clear(); + flower[b].push_back(l); + for (int x = u, y; x != l; x = st[pa[y]]) { + flower[b].push_back(x); + y = st[match[x]]; + flower[b].push_back(y); + q_push(y); + } + std::reverse(flower[b].begin() + 1, flower[b].end()); + for (int x = v, y; x != l; x = st[pa[y]]) { + flower[b].push_back(x); + y = st[match[x]]; + flower[b].push_back(y); + q_push(y); + } + set_st(b, b); + + for (int x = 1; x <= S; x++) { + g[b][x] = g[x][b] = 0; + } + for (int x = 1; x <= N; x++) flower_from[b][x] = 0; + + for (int x : flower[b]) { + for (int y = 1; y <= S; y++) { + if (g[b][y] < g[x][y]) { + g[b][y] = g[x][y]; + g[y][b] = g[y][x]; + } + } + } + + for (int x : flower[b]) { + for (int y = 1; y <= S; y++) { + if (g[x][y] == g[b][y] && flower_from[b][y] == 0) flower_from[b][y] = x; + } + } + + set_slack(b); + }; + + auto expand_blossom = [&](int b) { + for (int x : flower[b]) set_st(x, x); + int xr = flower_from[b][g[b][pa[b]] == 0 ? pa[b] : match[b]]; + int pr = get_pr(b, xr); + for (int i = 0; i < pr; i += 2) { + int xs = flower[b][i], xns = flower[b][i + 1]; + pa[xs] = g[xns][xs] == 0 ? xns : pa[b]; + Sstate[xs] = 1; + Sstate[xns] = 0; + slack[xs] = 0; + set_slack(xns); + q_push(xns); + } + Sstate[xr] = 1; + pa[xr] = pa[b]; + for (int i = pr + 1; i < (int)flower[b].size(); i++) { + int x = flower[b][i]; + Sstate[x] = -1; + set_slack(x); + } + st[b] = 0; + }; + + auto on_found_edge = [&](int u, int v) { + int su = st[u], sv = st[v]; + if (Sstate[sv] == -1) { + pa[sv] = u; + Sstate[sv] = 1; + int nu = st[match[sv]]; + slack[sv] = slack[nu] = 0; + Sstate[nu] = 0; + q_push(nu); + } else if (Sstate[sv] == 0) { + int l = lca(su, sv); + if (l == 0) { + augment(su); + augment(sv); + return true; + } else { + add_blossom(su, l, sv); + } + } + return false; + }; + + auto matching = [&]() { + std::fill(Sstate.begin(), Sstate.end(), -1); + std::fill(slack.begin(), slack.end(), 0); + qh = qt = 0; + + for (int x = 1; x <= S; x++) { + if (st[x] == x && !match[x]) { + pa[x] = 0; + Sstate[x] = 0; + q_push(x); + } + } + if (qt == 0) return false; + + while (true) { + while (qh < qt) { + int u = q[qh++][0]; + if (Sstate[st[u]] == 1) continue; + for (int v = 1; v <= N; v++) { + if (g[u][v] > 0 && st[u] != st[v] && Sstate[st[v]] != 1 && dist(u, v) == 0) { + if (on_found_edge(u, v)) return true; + } + } + } + + long long d = std::numeric_limits::max(); + for (int b = N + 1; b <= S; b++) { + if (st[b] == b && Sstate[st[b]] == 1) d = std::min(d, lab[b] / 2); + } + for (int x = 1; x <= S; x++) { + if (st[x] == x && slack[x] > 0) { + if (Sstate[x] == -1) d = std::min(d, slack[x]); + else if (Sstate[x] == 0) d = std::min(d, slack[x] / 2); + } + } + if (d == std::numeric_limits::max()) return false; + + for (int x = 1; x <= N; x++) { + if (Sstate[st[x]] == 0) { + if (lab[x] <= d) return false; + lab[x] -= d; + } else if (Sstate[st[x]] == 1) { + lab[x] += d; + } + } + for (int b = N + 1; b <= S; b++) { + if (st[b] == b) { + if (Sstate[st[b]] == 0) lab[b] += d * 2; + else if (Sstate[st[b]] == 1) lab[b] -= d * 2; + } + } + + qh = qt = 0; + for (int x = 1; x <= S; x++) { + if (st[x] == x && slack[x] > 0 && st[slackx[x]] != x && dist(slackx[x], x) == 0) { + if (on_found_edge(slackx[x], x)) return true; + } + } + for (int b = N + 1; b <= S; b++) { + if (st[b] == b && Sstate[b] == 1 && lab[b] == 0) expand_blossom(b); + } + } + }; + + for (int i = 1; i <= S; i++) { + st[i] = i; + flower[i].clear(); + } + + long long mx = 0; + for (int i = 1; i <= N; i++) { + for (int j = 1; j <= N; j++) mx = std::max(mx, g[i][j]); + } + for (int i = 1; i <= N; i++) lab[i] = mx; + + int nmatch = 0; + while (matching()) nmatch++; + + std::vector mate(n, -1); + long long total = 0; + for (int i = 1; i <= N; i++) { + if (match[i] && match[i] <= N) { + mate[i - 1] = match[i] - 1; + } + } + for (int i = 0; i < n; i++) if (mate[i] > i) total += w[i][mate[i]]; + return {total, mate}; + } +}; + +} // namespace mylib + +#endif diff --git a/test/verify/yosupo-general-weighted-matching.test.cpp b/test/verify/yosupo-general-weighted-matching.test.cpp new file mode 100644 index 0000000..512d9d3 --- /dev/null +++ b/test/verify/yosupo-general-weighted-matching.test.cpp @@ -0,0 +1,29 @@ +#define PROBLEM "https://judge.yosupo.jp/problem/general_weighted_matching" + +#include "template/template.hpp" +#include "graph/general_weighted_matching.hpp" + +int main() { + ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); + + int N, M; cin >> N >> M; + mylib::GeneralWeightedMatching wm(N); + for (int i = 0; i < M; i++) { + int u, v; + long long w; + cin >> u >> v >> w; + wm.add_edge(u, v, w); + } + + auto ans = wm.solve(); + vector> edges; + for (int i = 0; i < N; i++) { + if (ans.second[i] != -1 && i < ans.second[i]) edges.emplace_back(i, ans.second[i]); + } + + cout << ans.first << " " << edges.size() << "\n"; + for (auto [u, v] : edges) { + cout << u << " " << v << "\n"; + } + return 0; +} From e322315eacb4dcd98d997eae783e1fceffc15580 Mon Sep 17 00:00:00 2001 From: Haruki Oshiro <68176059+Harui-i@users.noreply.github.com> Date: Sun, 10 May 2026 20:38:40 +0900 Subject: [PATCH 2/2] general weighted matching(codex) --- docs/graph/general_weighted_matching.md | 3 + graph/general_weighted_matching.hpp | 313 +++++++++--------- .../yosupo-general-weighted-matching.test.cpp | 2 +- 3 files changed, 169 insertions(+), 149 deletions(-) diff --git a/docs/graph/general_weighted_matching.md b/docs/graph/general_weighted_matching.md index 97cf8e9..a3308b2 100644 --- a/docs/graph/general_weighted_matching.md +++ b/docs/graph/general_weighted_matching.md @@ -5,6 +5,7 @@ documentation_of: //graph/general_weighted_matching.hpp 一般グラフの最大重みマッチング（Blossom / 花アルゴリズム）を解く。 重み付き辺を受け取り、重み和が最大となるマッチングを返す。 +辺重みは非負整数を想定する。 ## 使い方 @@ -17,6 +18,8 @@ auto [sum, mate] = wm.solve(); - `sum`: 最大重み - `mate[i]`: 頂点 `i` とマッチした頂点番号（未マッチは `-1`） +同じ 2 頂点間に複数回 `add_edge` した場合は、最大の重みだけを使う。 + ## 計算量 - $O(N^3)$ diff --git a/graph/general_weighted_matching.hpp b/graph/general_weighted_matching.hpp index 497df98..eee20dd 100644 --- a/graph/general_weighted_matching.hpp +++ b/graph/general_weighted_matching.hpp @@ -2,10 +2,9 @@ #define HARUILIB_GRAPH_GENERAL_WEIGHTED_MATCHING_HPP #include -#include #include #include -#include +#include #include #include @@ -24,276 +23,294 @@ struct GeneralWeightedMatching { std::pair> solve() const { if (n == 0) return {0, {}}; - int N = n; - int S = N + 1; - std::vector> g(N + 1, std::vector(N + 1, 0)); + struct Edge { + int u, v; + long long w; + Edge(int u_ = 0, int v_ = 0, long long w_ = 0) : u(u_), v(v_), w(w_) {} + }; + + const int N = n; + const int max_nodes = 2 * N; + int nodes = N; + + std::vector> g(max_nodes + 1, std::vector(max_nodes + 1)); + for (int i = 1; i <= max_nodes; i++) { + for (int j = 1; j <= max_nodes; j++) { + g[i][j] = Edge(i, j, 0); + } + } for (int i = 1; i <= N; i++) { for (int j = 1; j <= N; j++) { - g[i][j] = w[i - 1][j - 1]; + g[i][j].w = w[i - 1][j - 1]; } } - std::vector match(N + 1, 0), slackx(N + 1), prev(N + 1), st(N + 1), pa(N + 1); - std::vector lab(N + 1), slack(N + 1); - std::vector> flower_from(N + 1, std::vector(N + 1, 0)); - std::vector> flower(N + 1); - std::vector> q(2 * N + 5); - std::vector Sstate(N + 1), vis(N + 1); - int qh = 0, qt = 0; + std::vector match(max_nodes + 1), slack(max_nodes + 1), st(max_nodes + 1), parent(max_nodes + 1); + std::vector state(max_nodes + 1), vis(max_nodes + 1); + std::vector label(max_nodes + 1); + std::vector> blossom_from(max_nodes + 1, std::vector(N + 1)); + std::vector> blossom(max_nodes + 1); + std::queue q; + int vis_timer = 0; - auto dist = [&](int u, int v) { - return lab[u] + lab[v] - g[u][v] * 2; + auto delta = [&](const Edge &e) { + return label[e.u] + label[e.v] - e.w * 2; }; auto update_slack = [&](int u, int x) { - if (!slack[x] || dist(u, x) < dist(slackx[x], x)) { - slack[x] = dist(u, x); - slackx[x] = u; + if (!slack[x] || delta(g[u][x]) < delta(g[slack[x]][x])) { + slack[x] = u; } }; auto set_slack = [&](int x) { slack[x] = 0; for (int u = 1; u <= N; u++) { - if (Sstate[st[u]] == 0 && st[u] != x && g[u][x] > 0) update_slack(u, x); + if (g[u][x].w > 0 && st[u] != x && state[st[u]] == 0) update_slack(u, x); } }; - auto q_push = [&](int x) { - if (x <= N) q[qt++] = {x, 0}; - else for (int v : flower[x]) q[qt++] = {v, x}; + std::function q_push = [&](int x) { + if (x <= N) { + q.push(x); + } else { + for (int v : blossom[x]) q_push(v); + } }; std::function set_st = [&](int x, int b) { st[x] = b; if (x > N) { - for (int v : flower[x]) set_st(v, b); + for (int v : blossom[x]) set_st(v, b); } }; auto get_pr = [&](int b, int xr) { - int pr = std::find(flower[b].begin(), flower[b].end(), xr) - flower[b].begin(); + int pr = std::find(blossom[b].begin(), blossom[b].end(), xr) - blossom[b].begin(); if (pr % 2 == 1) { - std::reverse(flower[b].begin() + 1, flower[b].end()); - return (int)flower[b].size() - pr; + std::reverse(blossom[b].begin() + 1, blossom[b].end()); + return (int)blossom[b].size() - pr; } return pr; }; - std::function set_match = [&](int u, int v, int from) { - match[u] = v; + std::function set_match = [&](int u, int v) { + match[u] = g[u][v].v; if (u <= N) return; - int xr = flower_from[u][g[st[u]][st[v]] == 0 ? v : from]; + int xr = blossom_from[u][g[u][v].u]; int pr = get_pr(u, xr); for (int i = 0; i < pr; i++) { - set_match(flower[u][i], flower[u][i ^ 1], from); + set_match(blossom[u][i], blossom[u][i ^ 1]); } - set_match(xr, v, from); - std::rotate(flower[u].begin(), flower[u].begin() + pr, flower[u].end()); + set_match(xr, v); + std::rotate(blossom[u].begin(), blossom[u].begin() + pr, blossom[u].end()); }; - std::function augment = [&](int u) { - while (u) { - int v = st[pa[u]]; - int wv = st[match[v]]; - set_match(u, v, 0); - u = wv; + auto augment = [&](int u, int v) { + while (true) { + int next = st[match[u]]; + set_match(u, v); + if (!next) return; + set_match(next, st[parent[next]]); + u = st[parent[next]]; + v = next; } }; - std::function lca = [&](int u, int v) { - std::fill(vis.begin(), vis.end(), 0); - while (u || v) { - if (u) { - if (vis[u] == 1) return u; - vis[u] = 1; - if (match[u]) u = st[pa[match[u]]]; - else u = 0; - } - std::swap(u, v); + auto lca = [&](int u, int v) { + ++vis_timer; + for (; u || v; std::swap(u, v)) { + if (!u) continue; + if (vis[u] == vis_timer) return u; + vis[u] = vis_timer; + u = st[match[u]]; + if (u) u = st[parent[u]]; } return 0; }; auto add_blossom = [&](int u, int l, int v) { int b = N + 1; - while (b <= S && st[b]) b++; - if (b > S) return; - lab[b] = 0; - Sstate[b] = -1; + while (b <= nodes && st[b]) b++; + if (b > nodes) nodes++; + + label[b] = 0; + state[b] = 0; match[b] = match[l]; - flower[b].clear(); - flower[b].push_back(l); - for (int x = u, y; x != l; x = st[pa[y]]) { - flower[b].push_back(x); + blossom[b].clear(); + blossom[b].push_back(l); + for (int x = u, y; x != l; x = st[parent[y]]) { + blossom[b].push_back(x); y = st[match[x]]; - flower[b].push_back(y); + blossom[b].push_back(y); q_push(y); } - std::reverse(flower[b].begin() + 1, flower[b].end()); - for (int x = v, y; x != l; x = st[pa[y]]) { - flower[b].push_back(x); + std::reverse(blossom[b].begin() + 1, blossom[b].end()); + for (int x = v, y; x != l; x = st[parent[y]]) { + blossom[b].push_back(x); y = st[match[x]]; - flower[b].push_back(y); + blossom[b].push_back(y); q_push(y); } set_st(b, b); - for (int x = 1; x <= S; x++) { - g[b][x] = g[x][b] = 0; + for (int x = 1; x <= nodes; x++) { + g[b][x] = Edge(b, x, 0); + g[x][b] = Edge(x, b, 0); } - for (int x = 1; x <= N; x++) flower_from[b][x] = 0; + for (int x = 1; x <= N; x++) blossom_from[b][x] = 0; - for (int x : flower[b]) { - for (int y = 1; y <= S; y++) { - if (g[b][y] < g[x][y]) { + for (int x : blossom[b]) { + for (int y = 1; y <= nodes; y++) { + if (g[b][y].w == 0 || delta(g[x][y]) < delta(g[b][y])) { g[b][y] = g[x][y]; g[y][b] = g[y][x]; } } - } - - for (int x : flower[b]) { - for (int y = 1; y <= S; y++) { - if (g[x][y] == g[b][y] && flower_from[b][y] == 0) flower_from[b][y] = x; + for (int y = 1; y <= N; y++) { + if (blossom_from[x][y]) blossom_from[b][y] = x; } } - set_slack(b); }; auto expand_blossom = [&](int b) { - for (int x : flower[b]) set_st(x, x); - int xr = flower_from[b][g[b][pa[b]] == 0 ? pa[b] : match[b]]; + for (int x : blossom[b]) set_st(x, x); + int xr = blossom_from[b][g[b][parent[b]].u]; int pr = get_pr(b, xr); for (int i = 0; i < pr; i += 2) { - int xs = flower[b][i], xns = flower[b][i + 1]; - pa[xs] = g[xns][xs] == 0 ? xns : pa[b]; - Sstate[xs] = 1; - Sstate[xns] = 0; + int xs = blossom[b][i], xns = blossom[b][i + 1]; + parent[xs] = g[xns][xs].u; + state[xs] = 1; + state[xns] = 0; slack[xs] = 0; set_slack(xns); q_push(xns); } - Sstate[xr] = 1; - pa[xr] = pa[b]; - for (int i = pr + 1; i < (int)flower[b].size(); i++) { - int x = flower[b][i]; - Sstate[x] = -1; + state[xr] = 1; + parent[xr] = parent[b]; + for (int i = pr + 1; i < (int)blossom[b].size(); i++) { + int x = blossom[b][i]; + state[x] = -1; set_slack(x); } st[b] = 0; }; - auto on_found_edge = [&](int u, int v) { - int su = st[u], sv = st[v]; - if (Sstate[sv] == -1) { - pa[sv] = u; - Sstate[sv] = 1; - int nu = st[match[sv]]; - slack[sv] = slack[nu] = 0; - Sstate[nu] = 0; - q_push(nu); - } else if (Sstate[sv] == 0) { - int l = lca(su, sv); - if (l == 0) { - augment(su); - augment(sv); + auto on_found_edge = [&](const Edge &e) { + int u = st[e.u], v = st[e.v]; + if (state[v] == -1) { + parent[v] = e.u; + state[v] = 1; + int next = st[match[v]]; + slack[v] = slack[next] = 0; + state[next] = 0; + q_push(next); + } else if (state[v] == 0) { + int l = lca(u, v); + if (!l) { + augment(u, v); + augment(v, u); return true; - } else { - add_blossom(su, l, sv); } + add_blossom(u, l, v); } return false; }; auto matching = [&]() { - std::fill(Sstate.begin(), Sstate.end(), -1); + std::fill(state.begin(), state.end(), -1); std::fill(slack.begin(), slack.end(), 0); - qh = qt = 0; - - for (int x = 1; x <= S; x++) { + q = std::queue(); + for (int x = 1; x <= nodes; x++) { if (st[x] == x && !match[x]) { - pa[x] = 0; - Sstate[x] = 0; + parent[x] = 0; + state[x] = 0; q_push(x); } } - if (qt == 0) return false; + if (q.empty()) return false; while (true) { - while (qh < qt) { - int u = q[qh++][0]; - if (Sstate[st[u]] == 1) continue; + while (!q.empty()) { + int u = q.front(); + q.pop(); + if (state[st[u]] == 1) continue; for (int v = 1; v <= N; v++) { - if (g[u][v] > 0 && st[u] != st[v] && Sstate[st[v]] != 1 && dist(u, v) == 0) { - if (on_found_edge(u, v)) return true; + if (g[u][v].w > 0 && st[u] != st[v]) { + if (delta(g[u][v]) == 0) { + if (on_found_edge(g[u][v])) return true; + } else { + update_slack(u, st[v]); + } } } } long long d = std::numeric_limits::max(); - for (int b = N + 1; b <= S; b++) { - if (st[b] == b && Sstate[st[b]] == 1) d = std::min(d, lab[b] / 2); + for (int u = 1; u <= N; u++) { + if (state[st[u]] == 0) d = std::min(d, label[u]); } - for (int x = 1; x <= S; x++) { - if (st[x] == x && slack[x] > 0) { - if (Sstate[x] == -1) d = std::min(d, slack[x]); - else if (Sstate[x] == 0) d = std::min(d, slack[x] / 2); + for (int b = N + 1; b <= nodes; b++) { + if (st[b] == b && state[b] == 1) d = std::min(d, label[b] / 2); + } + for (int x = 1; x <= nodes; x++) { + if (st[x] == x && slack[x]) { + if (state[x] == -1) d = std::min(d, delta(g[slack[x]][x])); + else if (state[x] == 0) d = std::min(d, delta(g[slack[x]][x]) / 2); } } if (d == std::numeric_limits::max()) return false; - for (int x = 1; x <= N; x++) { - if (Sstate[st[x]] == 0) { - if (lab[x] <= d) return false; - lab[x] -= d; - } else if (Sstate[st[x]] == 1) { - lab[x] += d; + for (int u = 1; u <= N; u++) { + if (state[st[u]] == 0) { + if (label[u] == d) return false; + label[u] -= d; + } else if (state[st[u]] == 1) { + label[u] += d; } } - for (int b = N + 1; b <= S; b++) { + for (int b = N + 1; b <= nodes; b++) { if (st[b] == b) { - if (Sstate[st[b]] == 0) lab[b] += d * 2; - else if (Sstate[st[b]] == 1) lab[b] -= d * 2; + if (state[b] == 0) label[b] += d * 2; + else if (state[b] == 1) label[b] -= d * 2; } } - qh = qt = 0; - for (int x = 1; x <= S; x++) { - if (st[x] == x && slack[x] > 0 && st[slackx[x]] != x && dist(slackx[x], x) == 0) { - if (on_found_edge(slackx[x], x)) return true; + q = std::queue(); + for (int x = 1; x <= nodes; x++) { + if (st[x] == x && slack[x] && st[slack[x]] != x && delta(g[slack[x]][x]) == 0) { + if (on_found_edge(g[slack[x]][x])) return true; } } - for (int b = N + 1; b <= S; b++) { - if (st[b] == b && Sstate[b] == 1 && lab[b] == 0) expand_blossom(b); + for (int b = N + 1; b <= nodes; b++) { + if (st[b] == b && state[b] == 1 && label[b] == 0) expand_blossom(b); } } }; - for (int i = 1; i <= S; i++) { - st[i] = i; - flower[i].clear(); - } - - long long mx = 0; - for (int i = 1; i <= N; i++) { - for (int j = 1; j <= N; j++) mx = std::max(mx, g[i][j]); + long long max_weight = 0; + for (int u = 1; u <= N; u++) { + st[u] = u; + blossom[u].clear(); + for (int v = 1; v <= N; v++) { + blossom_from[u][v] = (u == v ? u : 0); + max_weight = std::max(max_weight, g[u][v].w); + } } - for (int i = 1; i <= N; i++) lab[i] = mx; + for (int u = 1; u <= N; u++) label[u] = max_weight; - int nmatch = 0; - while (matching()) nmatch++; + while (matching()) {} std::vector mate(n, -1); long long total = 0; for (int i = 1; i <= N; i++) { - if (match[i] && match[i] <= N) { - mate[i - 1] = match[i] - 1; - } + if (match[i] && match[i] <= N) mate[i - 1] = match[i] - 1; + } + for (int i = 0; i < n; i++) { + if (mate[i] > i) total += w[i][mate[i]]; } - for (int i = 0; i < n; i++) if (mate[i] > i) total += w[i][mate[i]]; return {total, mate}; } }; diff --git a/test/verify/yosupo-general-weighted-matching.test.cpp b/test/verify/yosupo-general-weighted-matching.test.cpp index 512d9d3..922994e 100644 --- a/test/verify/yosupo-general-weighted-matching.test.cpp +++ b/test/verify/yosupo-general-weighted-matching.test.cpp @@ -21,7 +21,7 @@ int main() { if (ans.second[i] != -1 && i < ans.second[i]) edges.emplace_back(i, ans.second[i]); } - cout << ans.first << " " << edges.size() << "\n"; + cout << edges.size() << " " << ans.first << "\n"; for (auto [u, v] : edges) { cout << u << " " << v << "\n"; }