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Codeforces Round #378 (Div. 2) E. Sleep in Class

問題

http://codeforces.com/contest/733/problem/E

N 階建ての建物の中にいます。各階には 'U' または 'D' の文字が書かれています。 i 階にいて U と書かれているときは i+1 階へ、D と書かれているときは i-1 階へ移動します。移動すると、直前にいた階の文字は切り替わります。i 回にいるとき、何回移動すると N+1 階もしくは 0 階へ移動できるか出力してください。

解法

実は、状況は問題文ほどややこしくありません。右側の一番近くのDで跳ね返り、左側の一番近くのUで跳ね返り、右側の二番目に近いDで跳ね返り…を外に出るまで繰り返します。累積和を上手に使うと O(N) で N 個分を一気に求めることができます。

コード

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

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

public class Main {
  private static class Task {

    void solve(FastScanner in, PrintWriter out) throws Exception {
      int N = in.nextInt();
      char[] S = in.next().toCharArray();
      int[] leftUp = new int[N];
      for (int i = 1; i < N; i++) {
        leftUp[i] = leftUp[i - 1];
        if (S[i - 1] == 'U') leftUp[i]++;
      }

      int[] rightDown = new int[N];
      for (int i = N - 2; i >= 0; i--) {
        rightDown[i] = rightDown[i + 1];
        if (S[i + 1] == 'D') rightDown[i]++;
      }
      long[] leftWing = new long[N];
      long[] rightWing = new long[N];
      {
        long rightSum = 0;
        int cur = 0;
        int right = 0;
        for (int i = 0; i < N; i++) {
          rightSum -= right * 2;
          if (S[i] == 'D' && right > 0) right--;
          int left = leftUp[i];
          if (S[i] == 'U') left++;
          if (cur <= i) cur = i + 1;
          while (cur < N && right < left) {
            if (S[cur] == 'D') {
              right++;
              rightSum += (cur - i) * 2;
            }
            cur++;
          }
          rightWing[i] = rightSum;
        }
      }
      {
        long leftSum = 0;
        int cur = N - 1;
        int left = 0;
        for (int i = N - 1; i >= 0; i--) {
          leftSum -= left * 2;
          if (S[i] == 'U' && left > 0) left--;
          int right = rightDown[i];
          if (S[i] == 'D') right++;
          if (i <= cur) cur = i - 1;
          while (cur >= 0 && left < right) {
            if (S[cur] == 'U') {
              left++;
              leftSum += (i - cur) * 2;
            }
            cur--;
          }
          leftWing[i] = leftSum;
        }
      }
      for (int i = 0; i < N; i++) {
        long ans = leftWing[i] + rightWing[i];
        if (S[i] == 'U') leftUp[i]++;
        else rightDown[i]++;
        if (leftUp[i] < rightDown[i] || (leftUp[i] == rightDown[i] && S[i] == 'U')) ans += (i + 1);
        if (leftUp[i] > rightDown[i] || (leftUp[i] == rightDown[i] && S[i] == 'D')) ans += (N - i);

        out.print(ans + " ");
      }
      out.println();

    }
  }

  /**
   * 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;
    }
  }
}