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Luogu P4412. [SHOI2004]最小生成树

 1 year ago
source link: https://www.shuizilong.com/house/archives/luogu-p4412-shoi2004%e6%9c%80%e5%b0%8f%e7%94%9f%e6%88%90%e6%a0%91/
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July 5, 2022

这个题主要麻烦的点还是找环。。。

const int N = 50 + 9, M = int(1.5e3) + 9;
struct Graph {
int id[N][N];
struct edge {
int x, y, w;
void in() {
RD(x, y, w);
}
} E[M];
int n, m;
void in() {
RD(n, m); REP_1(i, m) {
E[i].in();
id[E[i].x][E[i].y] = id[E[i].y][E[i].x] = i;
}
}
} G;
struct Tree {
VI adj[N]; int fa[N], dep[N];
void dfs(int u = 1, int p = -1) {
for (auto v: adj[u]) if (v != p) {
fa[v] = u; dep[v] = dep[u] + 1;
dfs(v, u);
}
}
void in() {
DO(G.n-1) {
int x, y; RD(x, y);
adj[x].PB(y);
adj[y].PB(x);
}
dfs();
}
} T;
struct Simplex {
const static int N = ::M, M = int(1e3) + 9;
DB a[N+1][M+1];
int n, m;
void pivot(int in, int out) {
REP(i, m+1) if(i!=in) a[out][i] /= -a[out][in]; //重置out约束
a[out][in] = 1/a[out][in];
REP(i, n+1) if (i!=out && sgn(a[i][in])) { //重新计算其他约束
DB t = a[i][in]; a[i][in] = 0;
REP(j, m+1) a[i][j] += t*a[out][j];
}
}
DB run() {
while (true) {
int in=0, out=0; DB Min=OO;
REP_1(i, m) if(sgn(a[0][i])>0) {
in=i;
break;
}
if(!in)return a[0][0];
REP_1(i, n) if(sgn(a[i][in])<0&&a[i][0]/-a[i][in]<Min) {
Min=a[i][0]/-a[i][in];
out=i;
}
if(!out)throw; //unbounded
pivot(in, out);
}
}
int gao() {
// z b
// c A
G.in(); T.in();
n = G.m; m = 0; REP_1(i, n) {
a[i][0] = 1;
int u = G.E[i].x, v = G.E[i].y;
if (T.dep[u] < T.dep[v]) swap(u, v);
if (T.fa[u] != v) { // E[i] is not a tree edge
while (u != v) {
int p = T.fa[u];
int j = G.id[p][u]; // E[j] is a tree edge
if (G.E[i].w < G.E[j].w) {
++m; a[i][m] = a[j][m] = -1;
a[0][m] = G.E[j].w - G.E[i].w;
}
u = p; if (T.dep[u] < T.dep[v]) swap(u, v);
}
}
}
return run();
}
} fst;
int main() {
#ifndef ONLINE_JUDGE
freopen("in.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
#endif
OT(fst.gao());
}

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Category: 日常


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