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Codeforces Round #381 (Div. 2) D. Alyona and a tree

問題

http://codeforces.com/contest/740/problem/D

ツリーがあり、頂点1が根です。各頂点 u には数字a_uが書き込まれています。各頂点 v について、v の部分木に含まれ、かつ  dist(v, u) \leq a_u を満たす頂点uの数を出力してください。

解法

DFS で辺の重みを BIT に持ちながら潜っていき、各頂点 u についてどのくらい上の頂点まで条件を満たせるか計算します。後はその数を持ちながら登っていき、いもす法の要領で無効になった瞬間に引くようにすれば良いです。

コード

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.*;

/*
                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
            pass System Test!
*/

public class D {
  private static class Task {
    class Edge {
      int to;
      long cost;
      Edge(int to, long cost) {
        this.to = to;
        this.cost = cost;
      }
    }

    ArrayList<Edge>[] graph;
    long[] a;
    FenwickTree bit;
    long[] ans;
    long[] imos;

    int dfs(int v, int d) {
      int x = 0;
      for (Edge edge : graph[v]) {
        int next = d + 1;
        bit.set(d, edge.cost);

        int ok = next;
        int ng = -1;
        while (ok - ng > 1) {
          int m = (ok + ng) / 2;
          long sum = bit.sum(m, next);//[m, next]
          if (sum <= a[edge.to]) {
            ok = m;
          } else {
            ng = m;
          }
        }
        int n = next - ok;
        int target = next - n;
        if (target <= next) imos[target]++;
        int y = dfs(edge.to, next);
        y -= imos[next];
        x += y;
        imos[next] = 0;
      }
      ans[v] = x;
      return x + 1;
    }

    void solve(FastScanner in, PrintWriter out) throws Exception {
      int N = in.nextInt();
      a = new long[N];
      for (int i = 0; i < N; i++) {
        a[i] = in.nextInt();
      }

      graph = new ArrayList[N];
      for (int i = 0; i < N; i++) {
        graph[i] = new ArrayList<>();
      }
      for (int i = 0; i < N - 1; i++) {
        int p = in.nextInt() - 1;
        int to = i + 1;
        long w = in.nextInt();
        graph[p].add(new Edge(to, w));
      }
      bit = new FenwickTree(N + 10);
      ans = new long[N];
      imos = new long[N + 10];
      dfs(0, 0);
      for (long a : ans) out.print(a + " ");
      out.println();
    }

    class FenwickTree {
      int N;
      long[] data;

      FenwickTree(int N) {
        this.N = N + 1;
        data = new long[N + 1];
      }

      void add(int k, long val) {
        for (int x = k; x < N; x |= x + 1) {
          data[x] += val;
        }
      }

      void set(int k, long val) {
        long now = get(k);
        long dv = val - now;
        add(k, dv);
      }

      // [0, k)
      long sum(int k) {
        if (k >= N) k = N - 1;
        long ret = 0;
        for (int x = k - 1; x >= 0; x = (x & (x + 1)) - 1) {
          ret += data[x];
        }
        return ret;
      }

      // [l, r)
      long sum(int l, int r) {
        if (l >= r) return 0;
        return sum(r) - sum(l);
      }

      long get(int k) {
        assert (0 <= k && k < N);
        return sum(k + 1) - sum(k);
      }

      int getAsSetOf(int w) {
        w++;
        if (w <= 0) return -1;
        int x = 0;
        int k = 1;
        while (k * 2 <= N) k *= 2;
        for (; k > 0; k /= 2) {
          if (x + k <= N && data[x + k - 1] < w) {
            w -= data[x + k - 1];
            x += k;
          }
        }
        return x;
      }
    }
  }

  /**
   * ここから下はテンプレートです。
   */
  public static void main(String[] args) throws Exception {
    OutputStream outputStream = System.out;
    FastScanner in = new FastScanner();
    PrintWriter out = new PrintWriter(outputStream);
    Task solver = new Task();
    solver.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;
    }
  }
}