結果
| 問題 |
No.119 旅行のツアーの問題
|
| コンテスト | |
| ユーザー |
 schwarzahl
|
| 提出日時 | 2017-12-23 15:00:45 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 220 ms / 5,000 ms |
| コード長 | 6,486 bytes |
| コンパイル時間 | 2,715 ms |
| コンパイル使用メモリ | 80,516 KB |
| 実行使用メモリ | 56,900 KB |
| 最終ジャッジ日時 | 2024-12-21 11:04:32 |
| 合計ジャッジ時間 | 6,871 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 19 |
ソースコード
package practice;
import java.util.Optional;
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Main main = new Main();
main.solveB();
}
private void solveB() {
Scanner sc = new Scanner(System.in);
int N = sc.nextInt();
int[] B = new int[N];
int[] C = new int[N];
for (int i = 0; i < N; i++) {
B[i] = sc.nextInt();
C[i] = sc.nextInt();
}
int M = sc.nextInt();
int[] D = new int[M];
int[] E = new int[M];
for (int i = 0; i < M; i++) {
D[i] = sc.nextInt();
E[i] = sc.nextInt();
}
final int VERTEX_NUM = 2 * N + 2;
final int SOURCE = 0;
final int TARGET = VERTEX_NUM - 1;
int sum = 0;
Graph graph = new ArrayGraph(VERTEX_NUM);
for (int i = 0; i < N; i++) {
graph.link(SOURCE, i+1, B[i]);
graph.link(i+1, N+i+1, B[i] + C[i]);
graph.link(N+i+1, TARGET, C[i]);
sum += B[i] + C[i];
}
for (int i = 0; i < M; i++) {
graph.link(N+1+D[i], 1+E[i], Integer.MAX_VALUE / 3);
}
FlowResolver fr = new BfsFlowResolver(graph);
System.out.println(sum - fr.maxFlow(SOURCE, TARGET));
}
interface Graph {
void link(int from, int to, int cost);
Optional<Integer> getCost(int from, int to);
int getVertexNum();
}
interface FlowResolver {
int maxFlow(int from, int to);
}
/**
* グラフの行列による実装
* 接点数の大きいグラフで使うとMLEで死にそう
*/
class ArrayGraph implements Graph {
private Integer[][] costArray;
private int vertexNum;
public ArrayGraph(int n) {
costArray = new Integer[n][];
for (int i = 0; i < n; i++) {
costArray[i] = new Integer[n];
}
vertexNum = n;
}
@Override
public void link(int from, int to, int cost) {
costArray[from][to] = new Integer(cost);
}
@Override
public Optional<Integer> getCost(int from, int to) {
return Optional.ofNullable(costArray[from][to]);
}
@Override
public int getVertexNum() {
return vertexNum;
}
}
class BfsFlowResolver implements FlowResolver {
private Graph graph;
public BfsFlowResolver(Graph graph) {
this.graph = graph;
}
public int maxFlow(int from, int to) {
boolean finish = false;
while (!finish) {
Integer[] flows = new Integer[graph.getVertexNum()];
flows[from] = Integer.MAX_VALUE / 3;
Integer[] froms = new Integer[graph.getVertexNum()];
boolean[] isPassed = new boolean[graph.getVertexNum()];
finish = false;
while (!finish) {
finish = true;
for (int id = 0; id < graph.getVertexNum(); id++) {
if (flows[id] != null) {
if (flow(id, flows, froms)) {
finish = false;
}
}
}
if (flows[to] != null) {
int to_i = to;
while (froms[to_i] != null) {
graph.link(froms[to_i], to_i, graph.getCost(froms[to_i], to_i).get() - flows[to]);
graph.link(to_i, froms[to_i], graph.getCost(to_i, froms[to_i]).orElse(0) + flows[to]);
to_i = froms[to_i];
}
finish = false;
break;
}
}
}
int sum = 0;
for (int id = 0; id < graph.getVertexNum(); id++) {
sum += graph.getCost(to, id).orElse(0);
}
return sum;
}
public boolean flow(int from, Integer[] flows, Integer[] froms) {
boolean change = false;
for (int next = 0; next < graph.getVertexNum(); next++) {
Optional<Integer> cost = graph.getCost(from, next);
if (cost.orElse(0) > 0 && flows[next] == null) {
int nextFlow = flows[from] < cost.get() ? flows[from] : cost.get();
flows[next] = nextFlow;
froms[next] = from;
change = true;
}
}
return change;
}
}
/**
* IDDFS(反復深化深さ優先探索)による実装
* 終了条件は同じ節点を2度通らないDFS(深さ優先探索)で0が返ってきたとき
* ほぼDinic法なので計算量はO(E*V*V)のはず (E:辺の数, V:節点の数)
*/
class IddfsFlowResolver implements FlowResolver {
private Graph graph;
public IddfsFlowResolver(Graph graph) {
this.graph = graph;
}
/**
* 最大フロー(最小カット)を求める
* @param from 始点(source)のID
* @param to 終点(target)のID
* @return 最大フロー(最小カット)
*/
public int maxFlow(int from, int to) {
int sum = 0;
int limitDepth = 0;
while (isExistFlow(from, to)) {
int currentFlow = flow(from, to,Integer.MAX_VALUE / 3, 0, limitDepth);
sum += currentFlow;
if (currentFlow == 0) {
limitDepth++;
}
}
return sum;
}
/**
* フローの実行 グラフの更新も行う
* @param from 現在いる節点のID
* @param to 終点(target)のID
* @param current_flow ここまでの流量
* @param depth 探索(ネスト)の深さ
* @param limitDepth 深さ制限
* @return 終点(target)に流した流量/戻りのグラフの流量
*/
private int flow(int from, int to, int current_flow, int depth, int limitDepth) {
if (from == to) {
return current_flow;
}
if (depth >= limitDepth) {
return 0;
}
for (int id = 0; id < graph.getVertexNum(); id++) {
Optional<Integer> cost = graph.getCost(from, id);
if (cost.orElse(0) > 0) {
int nextFlow = current_flow < cost.get() ? current_flow : cost.get();
int returnFlow = flow(id, to, nextFlow, depth+1, limitDepth);
if (returnFlow > 0) {
graph.link(from, id, cost.get() - returnFlow);
graph.link(id, from, graph.getCost(id, from).orElse(0) + returnFlow);
return returnFlow;
}
}
}
return 0;
}
/**
* fromからtoに0以上の流量を流せるか調べる
* @param from 始点(source)のID
* @param to 終点(target)のID
* @return 0以上流せればtrue
*/
private boolean isExistFlow(int from, int to) {
boolean[] passed = new boolean[graph.getVertexNum()];
return search(from, to, passed);
}
/**
* 今までに通ったことのない節点だけを調べるDFS(深さ優先探索)
* 計算量は高々O(V)のはず (V:節点の数)
* @param from 現在いる節点のID
* @param to 終点(target)のID
* @param passed 通過済みの節点IDにtrueが格納されている配列
* @return toに0以上流せればtrue
*/
private boolean search(int from, int to, boolean[] passed) {
if (from == to) {
return true;
}
passed[from] = true;
for (int id = 0; id < graph.getVertexNum(); id++) {
if (!passed[id] && graph.getCost(from, id).orElse(0) > 0 && search(id, to, passed)) {
return true;
}
}
return false;
}
}
}