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Codeforces Round #397 E. Tree Folding

問題

Problem - E - Codeforces

ツリーがあって、ある頂点から同じ長さの枝が2本出ている時、そのうち1本を取り除くことが出来ます。この操作を繰り返してツリーを直線に出来る場合、その最小の長さを出力してください。

解法

葉から登っていき、自分より下方向にある枝の種類を保存しながら登っていく。自分より下の枝が3種類以上ある場合は即アウト。

コード

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.NoSuchElementException;
import java.util.TreeSet;

public class E2 {

  private ArrayList<Integer>[] tree;

  //branches[i] := iにぶら下がっている枝の数
  private TreeSet<Integer>[] branches;

  private int[] reached;
  private boolean[] used;

  private int solve() {
    int N = tree.length;
    ArrayDeque<Integer> deque = new ArrayDeque<>();

    //葉をキューに詰める
    for (int i = 0; i < N; i++) {
      if (tree[i].size() == 1) {
        deque.add(i);
      }
    }

    while (!deque.isEmpty()) {
      int v = deque.poll();
      used[v] = true;

      //vに3種類以上の長さの枝がぶら下がっている場合どうやっても不可能なので終了する
      if (branches[v].size() >= 3) {
        return -1;
      }

      //v以外の枝のマージが全て終わったとき、ツリーは直線になっているはずである
      if (reached[v] == tree[v].size()) {
        int ans = 0;
        for (int branch : branches[v]) {
          ans += branch;
        }

        //半分に折れる限り折る
        while (ans % 2 == 0) {
          ans /= 2;
        }
        return ans;
      }

      if (branches[v].size() == 2) {
        return -1;
      }

      int length = branches[v].isEmpty() ? 1 : branches[v].first() + 1;
      for (int parent : tree[v]) {
        if (used[parent]) {
          continue;
        }

        reached[parent]++;
        branches[parent].add(length);

        //parentより下の枝のマージが終わったらキューに詰める
        if (reached[parent] + 1 == tree[parent].size()) {
          deque.add(parent);
        }
      }
    }
    throw new IllegalStateException();
  }

  private void solve(FastScanner in, PrintWriter out) {
    int N = in.nextInt();
    tree = new ArrayList[N];
    branches = new TreeSet[N];
    reached = new int[N];
    used = new boolean[N];
    for (int i = 0; i < N; i++) {
      tree[i] = new ArrayList<>();
      branches[i] = new TreeSet<>();
    }

    for (int i = 0; i < N - 1; i++) {
      int u = in.nextInt() - 1;
      int v = in.nextInt() - 1;
      tree[v].add(u);
      tree[u].add(v);
    }

    out.println(solve());
  }


  public static void main(String[] args) {
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(System.out);
    new E2().solve(in, out);
    out.close();
  }

  private static class FastScanner {

    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int bufferLength = 0;

    private boolean hasNextByte() {
      if (ptr < bufferLength) {
        return true;
      } else {
        ptr = 0;
        try {
          bufferLength = in.read(buffer);
        } catch (IOException e) {
          e.printStackTrace();
        }
        if (bufferLength <= 0) {
          return false;
        }
      }
      return true;
    }

    private int readByte() {
      if (hasNextByte()) {
        return buffer[ptr++];
      } else {
        return -1;
      }
    }

    private static boolean isPrintableChar(int c) {
      return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
      while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
        ptr++;
      }
    }

    boolean hasNext() {
      skipUnprintable();
      return hasNextByte();
    }

    public String next() {
      if (!hasNext()) {
        throw new NoSuchElementException();
      }
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while (isPrintableChar(b)) {
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb.toString();
    }

    long nextLong() {
      if (!hasNext()) {
        throw new NoSuchElementException();
      }
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
        minus = true;
        b = readByte();
      }
      if (b < '0' || '9' < b) {
        throw new NumberFormatException();
      }
      while (true) {
        if ('0' <= b && b <= '9') {
          n *= 10;
          n += b - '0';
        } else if (b == -1 || !isPrintableChar(b)) {
          return minus ? -n : n;
        } else {
          throw new NumberFormatException();
        }
        b = readByte();
      }
    }

    double nextDouble() {
      return Double.parseDouble(next());
    }

    double[] nextDoubleArray(int n) {
      double[] array = new double[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextDouble();
      }
      return array;
    }

    double[][] nextDoubleMap(int n, int m) {
      double[][] map = new double[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextDoubleArray(m);
      }
      return map;
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public int[] nextIntArray(int n) {
      int[] array = new int[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextInt();
      }
      return array;
    }

    public long[] nextLongArray(int n) {
      long[] array = new long[n];
      for (int i = 0; i < n; i++) {
        array[i] = nextLong();
      }
      return array;
    }

    public String[] nextStringArray(int n) {
      String[] array = new String[n];
      for (int i = 0; i < n; i++) {
        array[i] = next();
      }
      return array;
    }

    public char[][] nextCharMap(int n) {
      char[][] array = new char[n][];
      for (int i = 0; i < n; i++) {
        array[i] = next().toCharArray();
      }
      return array;
    }

    public int[][] nextIntMap(int n, int m) {
      int[][] map = new int[n][];
      for (int i = 0; i < n; i++) {
        map[i] = nextIntArray(m);
      }
      return map;
    }
  }
}