結果

問題 No.1316 Maximum Minimum Spanning Tree
コンテスト
ユーザー hos.lyric
提出日時 2020-12-25 05:11:50
言語 D
(dmd 2.109.1)
結果
TLE  
実行時間 -
コード長 5,177 bytes
コンパイル時間 1,051 ms
コンパイル使用メモリ 133,300 KB
実行使用メモリ 13,756 KB
最終ジャッジ日時 2024-06-22 10:31:44
合計ジャッジ時間 4,943 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 3 TLE * 1 -- * 74
権限があれば一括ダウンロードができます

ソースコード

diff # 

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;
import core.bitop;

class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }

bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }

int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }


class MaxFlow(Capa, Capa wEPS = 0, Capa wINF = 10^^9) {
  int n, m;
  int[][] g;
  int[] zu;
  Capa[] capa;
  Capa tof;
  int[] lev, see, que;
  this(int n) {
    this.n = n; m = 0; g = new int[][n]; zu = []; capa = [];
    lev = new int[n]; see = new int[n]; que = new int[n];
  }
  void addEdge(int u, int v, Capa w0, Capa w1 = 0) {
    g[u] ~= m; zu ~= v; capa ~= w0; ++m;
    g[v] ~= m; zu ~= u; capa ~= w1; ++m;
  }
  Capa augment(int src, int ink, Capa flo) {
    if (src == ink) return flo;
    foreach (i; g[src][see[src] .. $]) {
      if (capa[i] > wEPS && lev[src] < lev[zu[i]]) {
        Capa f = augment(zu[i], ink, min(flo, capa[i]));
        if (f > wEPS) { capa[i] -= f; capa[i ^ 1] += f; return f; }
      }
      ++see[src];
    }
    return 0;
  }
  bool dinic(int src, int ink, Capa flo = wINF) {
    for (tof = 0; tof + wEPS < flo; ) {
      int qb, qe;
      lev[] = -1;
     dinicBFS:
      for (lev[src] = 0, que[qe++] = src; qb != qe; ) {
        const u = que[qb++];
        foreach (i; g[u]) {
          const v = zu[i];
          if (capa[i] > wEPS && lev[v] == -1) {
            lev[v] = lev[u] + 1; que[qe++] = v;
            if (v == ink) break dinicBFS;
          }
        }
      }
      if (lev[ink] == -1) return false;
      see[] = 0;
      for (; ; ) {
        Capa f = augment(src, ink, flo - tof);
        if (f <= wEPS) break;
        tof += f;
      }
    }
    return true;
  }
}


/*
  http://www.columbia.edu/~cs2035/courses/ieor6614.S16/mst-lp.pdf
  max_x { K min_y { \sum_i (c_i + x_i) y_i | MST-LP } - \sum_i d_i x_i | x_i >= 0 }
  
  https://www.jstage.jst.go.jp/article/kodaimath1978/11/1/11_1_5/_pdf
  min_y { max_x { \sum_i K (c_i + x_i) y_i - \sum_i d_i x_i | x_i >= 0 } | MST-LP }
  = min_y { max_x { \sum_i (K c_i y_i + (K y_i - d_i) x_i) | x_i >= 0 } | MST-LP }
  = min_y { \sum_i K c_i y_i + \sum_i INF [K y_i - d_i > 0] | MST-LP }
  = min_y { \sum_i K c_i y_i | MST-LP, K y_i <= d_i }
  
  MST-LP
    y_i >= 0
    \sum_i y_i = N - 1
    \sum_{i=uv, u,v\in S} y_i <= |S| - 1
  
  ("cut >= 1" instead: not nec integer!)
  
  min_S { |S| - \sum_{i=uv, u,v\in S} y_i } >= 1
  take i ==> take u and take v
  take i: cost -y_i
  take u: cost 1
  need to take some u
*/

enum INF = 10L^^18;

void main() {
  try {
    for (; ; ) {
      const N = readInt();
      const M = readInt();
      const K = readLong();
      auto A = new int[M];
      auto B = new int[M];
      auto C = new long[M];
      auto D = new long[M];
      foreach (i; 0 .. M) {
        A[i] = readInt() - 1;
        B[i] = readInt() - 1;
        C[i] = readLong();
        D[i] = readLong();
      }
      
      alias Edge = Tuple!(long, "c", int, "i");
      auto edges = new Edge[M];
      foreach (i; 0 .. M) {
        edges[i] = Edge(C[i], i);
      }
      edges.sort;
      
      auto ys = new long[M];
      bool check() {
        foreach (u0; 0 .. N) {
          auto mf = new MaxFlow!(long, 0, INF)(2 + M + N);
          long cost;
          foreach (i; 0 .. M) {
            cost -= ys[i];
            mf.addEdge(0, 2 + i, ys[i]);
            mf.addEdge(2 + i, 2 + M + A[i], INF);
            mf.addEdge(2 + i, 2 + M + B[i], INF);
          }
          foreach (u; 0 .. N) {
            mf.addEdge(2 + M + u, 1, K);
          }
          mf.addEdge(0, 2 + M + u0, INF);
          mf.dinic(0, 1);
          if (cost + mf.tof < K) {
            return false;
          }
        }
        return true;
      }
      
      foreach (ref edge; edges) {
        const i = edge.i;
        long lo = -1, hi = D[i] + 1;
        for (; lo + 1 < hi; ) {
          const mid = (lo + hi) / 2;
          ys[i] = mid;
          (check() ? lo : hi) = mid;
        }
        ys[i] = lo;
      }
      debug {
        writeln("ys = ", ys);
      }
      
      if (ys.sum < K * (N - 1)) {
        writeln(-1);
      } else {
        long ans;
        foreach (i; 0 .. M) {
          ans += C[i] * ys[i];
        }
        writeln(ans);
      }
    }
  } catch (EOFException e) {
  }
}
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