74 lines
1.7 KiB
C++
74 lines
1.7 KiB
C++
// From https://github.com/koosaga/olympiad
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// matching_short.cpp
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const int MAXN = 2020 + 1;
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// 1-based Vertex index
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int vis[MAXN], par[MAXN], orig[MAXN], match[MAXN], aux[MAXN], t, N;
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vector<int> conn[MAXN];
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queue<int> Q;
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void addEdge(int u, int v) { conn[u].push_back(v); conn[v].push_back(u); }
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void init(int n) {
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N = n; t = 0;
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for(int i=0; i<=n; ++i) {
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conn[i].clear();
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match[i] = aux[i] = par[i] = 0;
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}
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}
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void augment(int u, int v) {
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int pv = v, nv;
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do {
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pv = par[v]; nv = match[pv];
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match[v] = pv; match[pv] = v;
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v = nv;
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} while(u != pv);
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}
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int lca(int v, int w) {
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++t;
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while(true) {
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if(v) {
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if(aux[v] == t) return v; aux[v] = t;
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v = orig[par[match[v]]];
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}
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swap(v, w);
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}
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}
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void blossom(int v, int w, int a) {
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while(orig[v] != a) {
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par[v] = w; w = match[v];
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if(vis[w] == 1) Q.push(w), vis[w] = 0;
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orig[v] = orig[w] = a;
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v = par[w];
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}
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}
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bool bfs(int u) {
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fill(vis+1, vis+1+N, -1); iota(orig + 1, orig + N + 1, 1);
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Q = queue<int> (); Q.push(u); vis[u] = 0;
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while(!Q.empty()) {
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int v = Q.front(); Q.pop();
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for(int x: conn[v]) {
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if(vis[x] == -1) {
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par[x] = v; vis[x] = 1;
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if(!match[x]) return augment(u, x), true;
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Q.push(match[x]); vis[match[x]] = 0;
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}
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else if(vis[x] == 0 && orig[v] != orig[x]) {
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int a = lca(orig[v], orig[x]);
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blossom(x, v, a); blossom(v, x, a);
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}
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}
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}
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return false;
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}
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int Match() {
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int ans = 0;
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// find random matching (not necessary, constant improvement)
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vector<int> V(N-1); iota(V.begin(), V.end(), 1);
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shuffle(V.begin(), V.end(), mt19937(0x94949));
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for(auto x: V) if(!match[x]){
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for(auto y: conn[x]) if(!match[y]) {
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match[x] = y, match[y] = x;
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++ans; break;
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}
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}
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for(int i=1; i<=N; ++i) if(!match[i] && bfs(i)) ++ans;
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return ans;
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} |