#809870 (D) No.2107 Entangled LIS

提出ソース

結果

問題	No.2107 Entangled LIS
ユーザー	👑 hos.lyric
提出日時	2022-10-22 01:25:35
言語	D (dmd 2.106.1)
結果	AC
実行時間	201 ms / 2,000 ms
コード長	7,746 bytes
コンパイル時間	4,486 ms
コンパイル使用メモリ	164,168 KB
実行使用メモリ	9,712 KB
最終ジャッジ日時	2023-09-04 18:37:10
合計ジャッジ時間	4,539 ms
ジャッジサーバーID （参考情報）	judge14 / judge12

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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 4,380 KB
testcase_01	AC	165 ms 4,380 KB
testcase_02	AC	172 ms 4,380 KB
testcase_03	AC	101 ms 4,380 KB
testcase_04	AC	127 ms 4,380 KB
testcase_05	AC	180 ms 6,356 KB
testcase_06	AC	180 ms 6,592 KB
testcase_07	AC	183 ms 8,908 KB
testcase_08	AC	201 ms 9,712 KB
testcase_09	AC	189 ms 9,668 KB
testcase_10	AC	102 ms 6,336 KB

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ソースコード

raw source code

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)); }


int lis(const(int[]) as) {
  int[] seq;
  foreach (a; as) {
    const pos = seq.lowerBound(a);
    if (pos == seq.length) {
      seq ~= a;
    } else {
      seq[pos] = a;
    }
  }
  return cast(int)(seq.length);
}

void judge(const(int) N, const(int) A, const(int) B, const(string) S, const(int[]) xs, const(int[]) ys) {
  const msg = format("FAIL %s %s %s %s: %s %s", N, A, B, S, xs, ys);
  assert(xs.length == N, msg);
  assert(ys.length == N, msg);
  auto freq = new int[2 * N];
  foreach (i; 0 .. N) {
    assert(0 <= xs[i], msg); assert(xs[i] < 2 * N, msg);
    assert(0 <= ys[i], msg); assert(ys[i] < 2 * N, msg);
    ++freq[xs[i]];
    ++freq[ys[i]];
  }
  assert(freq.all!"a == 1");
  foreach (i; 0 .. N) {
    final switch (S[i]) {
      case 'a': assert(xs[i] > ys[i], msg); break;
      case 'b': assert(xs[i] < ys[i], msg); break;
    }
  }
  assert(lis(xs) == A, msg);
  assert(lis(ys) == B, msg);
}


// (left non-C) < (right C)
int[] sub(const(int) N, const(int) A, const(string) S, const(char) C) {
  assert(2 <= A); assert(A <= N);
  auto tail = new bool[N + 1];
  {
    bool hasC;
    foreach_reverse (i; 0 .. N) {
      tail[i] = tail[i + 1];
      if (S[i] == C) {
        hasC = true;
      } else {
        if (hasC) {
          tail[i] = true;
        }
      }
    }
  }
  foreach (k; 0 .. N) {
    if (k + (tail[k] ? 2 : 1) == A) {
      auto ps = new int[N];
      ps[] = -1;
      int val = 0;
      foreach (i; 0 .. k) {
        ps[i] = val++;
      }
      foreach_reverse (i; k .. N) if (S[i] != C) {
        ps[i] = val++;
      }
      foreach_reverse (i; k .. N) if (S[i] == C) {
        ps[i] = val++;
      }
      return ps;
    }
  }
  assert(false);
}

alias Result = Tuple!(int[], "xs", int[], "ys");

Result entangle(const(int) N, const(string) S, const(int[]) ps, const(int[]) qs) {
  debug {
    // writeln("[entangle] ", N, " ", S, " ", ps, " ", qs);
  }
  auto posP = new int[N];
  auto posQ = new int[N];
  posP[] = -1;
  posQ[] = -1;
  foreach (i; 0 .. N) {
    posP[ps[i]] = i;
    posQ[qs[i]] = i;
  }
  auto xs = new int[N];
  auto ys = new int[N];
  xs[] = -1;
  ys[] = -1;
  int val;
  for (int j, k; ; ++j) {
    for (; k < N; ++k) {
      const i = posQ[k];
      if (~xs[i]) {
        if (S[i] == 'a') {
          assert(false);
        } else {
          ys[i] = val++;
        }
      } else {
        if (S[i] == 'a') {
          ys[i] = val++;
        } else {
          break;
        }
      }
    }
    if (j == N) break;
    xs[posP[j]] = val++;
  }
  return Result(xs, ys);
}

Result solve(const(int) N, const(int) A, const(int) B, const(string) S) {
  debug {
    writeln("[solve] ", N, " ", A, " ", B, " ", S);
  }
  int[] xs, ys;
  if (A == 1) {
    if (B == 1) {
      auto ps = iota(N).array;
      ps.reverse;
      auto res = entangle(N, S, ps, ps);
      xs = res.xs;
      ys = res.ys;
    } else {
      // (left b) > (right a)  ==>  IS: a...ab...b
      auto sumA = new int[N + 1];
      foreach (i; 0 .. N) {
        sumA[i + 1] = sumA[i] + ((S[i] == 'a') ? 1 : 0);
      }
      
      // discard [0, pre)
      bool check(int pre) {
        foreach (k; pre .. N + 1) {
          const l = sumA[k] - sumA[pre];
          const r = (N - k) - (sumA[N] - sumA[k]);
          if (B <= l + r) {
            return true;
          }
        }
        return false;
      }
      if (check(0)) {
        int lo = 0, hi = N + 1;
        for (; lo + 1 < hi; ) {
          const mid = (lo + hi) / 2;
          (check(mid) ? lo : hi) = mid;
        }
        const pre = lo;
        foreach (k; pre .. N + 1) {
          const l = sumA[k] - sumA[pre];
          const r = (N - k) - (sumA[N] - sumA[k]);
          if (B == l + r) {
            auto ps = iota(N).array;
            ps.reverse;
            auto qs = new int[N];
            qs[] = -1;
            int val;
            foreach_reverse (i; k .. N) if (S[i] == 'a') qs[i] = val++;
            foreach (i; pre .. N) if ((i < k) == (S[i] == 'a')) qs[i] = val++;
            foreach_reverse (i; pre .. k) if (S[i] == 'b') qs[i] = val++;
            foreach_reverse (i; 0 .. pre) qs[i] = val++;
            auto res = entangle(N, S, ps, qs);
            xs = res.xs;
            ys = res.ys;
            break;
          }
        }
      }
    }
  } else if (B == 1) {
    auto res = solve(N, B, A, S.map!(c => cast(char)('a' ^ 'b' ^ c)).array);
    xs = res.ys;
    ys = res.xs;
  } else {
    const ps = sub(N, A, S, 'a');
    const qs = sub(N, B, S, 'b');
    auto res = entangle(N, S, ps, qs);
    xs = res.xs;
    ys = res.ys;
  }
  return Result(xs, ys);
}

void main() {
  /*
  debug {
    foreach (n; 1 .. 5 + 1) {
      auto can = new char[][][](1 << n, n + 1, n + 1);
      foreach (h; 0 .. 1 << n) foreach (a; 0 .. n + 1) {
        can[h][a][] = '0';
      }
      auto perm = iota(2 * n).array;
      do {
        int h;
        foreach (i; 0 .. n) {
          if (perm[i] < perm[n + i]) {
            h |= 1 << i;
          }
        }
        const a = lis(perm[0 .. n]);
        const b = lis(perm[n .. 2 * n]);
        can[h][a][b] = '1';
      } while (perm.nextPermutation);
      foreach (h; 0 .. 1 << n) {
        const string pat = iota(n).map!(i => "ab"[h >> i & 1]).array;
        writeln(pat, " ", can[h]);
      }
      stdout.flush;
      foreach (h; 0 .. 1 << n) {
        const string pat = iota(n).map!(i => "ab"[h >> i & 1]).array;
        foreach (a; 1 .. n + 1) foreach (b; 1 .. n + 1) {
          const res = solve(n, a, b, pat);
          if (can[h][a][b] == '1') {
            judge(n, a, b, pat, res.xs, res.ys);
          } else {
            assert(!res.xs);
          }
        }
      }
      writeln("DONE n = ", n);
      stdout.flush;
    }
    return;
  }
  //*/
  
  try {
    for (; ; ) {
      const numCases = readInt;
      foreach (caseId; 0 .. numCases) {
        const N = readInt;
        const A = readInt;
        const B = readInt;
        const S = readToken;
        
        const ans = solve(N, A, B, S);
        if (ans.xs) {
          writeln("Yes");
          foreach (i; 0 .. N) {
            if (i) write(" ");
            write(ans.xs[i] + 1);
          }
          writeln;
          foreach (i; 0 .. N) {
            if (i) write(" ");
            write(ans.ys[i] + 1);
          }
          writeln;
          debug {
            writeln(N, " ", A, " ", B, " ", S, ": ", ans.xs, " ", ans.ys);
            stdout.flush;
            judge(N, A, B, S, ans.xs, ans.ys);
          }
        } else {
          writeln("No");
        }
      }
    }
  } catch (EOFException e) {
  }
}

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結果

テストケース

ソースコード