結果
| 問題 | No.1316 Maximum Minimum Spanning Tree |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2020-12-25 05:11:50 |
| 言語 | D (dmd 2.106.1) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 5,177 bytes |
| コンパイル時間 | 1,033 ms |
| コンパイル使用メモリ | 118,524 KB |
| 実行使用メモリ | 11,484 KB |
| 最終ジャッジ日時 | 2023-09-04 11:45:08 |
| 合計ジャッジ時間 | 5,585 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge14 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
11,484 KB |
| testcase_01 | AC | 1 ms
4,380 KB |
| testcase_02 | AC | 3 ms
4,384 KB |
| testcase_03 | AC | 340 ms
4,380 KB |
| testcase_04 | AC | 1 ms
4,384 KB |
| testcase_05 | AC | 1 ms
4,384 KB |
| testcase_06 | AC | 8 ms
4,384 KB |
| testcase_07 | TLE | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
| testcase_40 | -- | - |
| testcase_41 | -- | - |
| testcase_42 | -- | - |
| testcase_43 | -- | - |
| testcase_44 | -- | - |
| testcase_45 | -- | - |
| testcase_46 | -- | - |
| testcase_47 | -- | - |
| testcase_48 | -- | - |
| testcase_49 | -- | - |
| testcase_50 | -- | - |
| testcase_51 | -- | - |
| testcase_52 | -- | - |
| testcase_53 | -- | - |
| testcase_54 | -- | - |
| testcase_55 | -- | - |
| testcase_56 | -- | - |
| testcase_57 | -- | - |
| testcase_58 | -- | - |
| testcase_59 | -- | - |
| testcase_60 | -- | - |
| testcase_61 | -- | - |
| testcase_62 | -- | - |
| testcase_63 | -- | - |
| testcase_64 | -- | - |
| testcase_65 | -- | - |
| testcase_66 | -- | - |
| testcase_67 | -- | - |
| testcase_68 | -- | - |
| testcase_69 | -- | - |
| testcase_70 | -- | - |
| testcase_71 | -- | - |
| testcase_72 | -- | - |
| testcase_73 | -- | - |
| testcase_74 | -- | - |
| testcase_75 | -- | - |
| testcase_76 | -- | - |
| testcase_77 | -- | - |
| testcase_78 | -- | - |
| testcase_79 | -- | - |
| testcase_80 | -- | - |
| testcase_81 | -- | - |
ソースコード
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) {
}
}