結果
問題 | No.1193 Penguin Sequence |
ユーザー | 👑 hos.lyric |
提出日時 | 2020-08-22 13:40:35 |
言語 | D (dmd 2.107.1) |
結果 |
AC
|
実行時間 | 155 ms / 2,000 ms |
コード長 | 5,547 bytes |
コンパイル時間 | 2,323 ms |
コンパイル使用メモリ | 159,456 KB |
実行使用メモリ | 18,804 KB |
最終ジャッジ日時 | 2023-09-04 09:07:30 |
合計ジャッジ時間 | 10,679 ms |
ジャッジサーバーID (参考情報) |
judge13 / judge11 |
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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 | 103 ms
18,080 KB |
testcase_01 | AC | 154 ms
17,508 KB |
testcase_02 | AC | 153 ms
17,616 KB |
testcase_03 | AC | 154 ms
18,804 KB |
testcase_04 | AC | 154 ms
16,988 KB |
testcase_05 | AC | 154 ms
16,680 KB |
testcase_06 | AC | 153 ms
17,160 KB |
testcase_07 | AC | 155 ms
16,716 KB |
testcase_08 | AC | 154 ms
16,948 KB |
testcase_09 | AC | 154 ms
17,696 KB |
testcase_10 | AC | 153 ms
18,544 KB |
testcase_11 | AC | 90 ms
13,440 KB |
testcase_12 | AC | 91 ms
14,092 KB |
testcase_13 | AC | 132 ms
17,268 KB |
testcase_14 | AC | 125 ms
16,204 KB |
testcase_15 | AC | 147 ms
16,640 KB |
testcase_16 | AC | 77 ms
16,460 KB |
testcase_17 | AC | 14 ms
8,064 KB |
testcase_18 | AC | 24 ms
8,712 KB |
testcase_19 | AC | 154 ms
16,704 KB |
testcase_20 | AC | 122 ms
16,196 KB |
testcase_21 | AC | 99 ms
16,300 KB |
testcase_22 | AC | 26 ms
8,928 KB |
testcase_23 | AC | 85 ms
13,836 KB |
testcase_24 | AC | 75 ms
14,196 KB |
testcase_25 | AC | 42 ms
9,808 KB |
testcase_26 | AC | 20 ms
8,516 KB |
testcase_27 | AC | 132 ms
16,436 KB |
testcase_28 | AC | 94 ms
13,896 KB |
testcase_29 | AC | 134 ms
16,352 KB |
testcase_30 | AC | 54 ms
11,548 KB |
testcase_31 | AC | 46 ms
9,872 KB |
testcase_32 | AC | 108 ms
13,912 KB |
testcase_33 | AC | 77 ms
14,352 KB |
testcase_34 | AC | 65 ms
12,924 KB |
testcase_35 | AC | 78 ms
12,088 KB |
testcase_36 | AC | 64 ms
12,536 KB |
testcase_37 | AC | 128 ms
15,892 KB |
testcase_38 | AC | 13 ms
7,972 KB |
testcase_39 | AC | 13 ms
8,108 KB |
testcase_40 | AC | 14 ms
7,968 KB |
ソースコード
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)); } struct ModInt(int M_) { import std.conv : to; alias M = M_; int x; this(ModInt a) { x = a.x; } this(long a) { x = cast(int)(a % M); if (x < 0) x += M; } ref ModInt opAssign(long a) { return (this = ModInt(a)); } ref ModInt opOpAssign(string op)(ModInt a) { static if (op == "+") { x += a.x; if (x >= M) x -= M; } else static if (op == "-") { x -= a.x; if (x < 0) x += M; } else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } ref ModInt opOpAssign(string op)(long a) { static if (op == "^^") { if (a < 0) return (this = inv()^^(-a)); ModInt t2 = this, te = ModInt(1); for (long e = a; e > 0; e >>= 1) { if (e & 1) te *= t2; t2 *= t2; } x = cast(int)(te.x); return this; } else return mixin("this " ~ op ~ "= ModInt(a)"); } ModInt inv() const { int a = x, b = M, y = 1, z = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1); return ModInt(b * z); } y -= t * z; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1); return ModInt(a * y); } z -= t * y; } } ModInt opUnary(string op: "-")() const { return ModInt(-x); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op)(long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0); } string toString() const { return x.to!string; } } enum MO = 998244353; alias Mint = ModInt!MO; enum LIM = 4 * 10^^5 + 10; Mint[] inv, fac, invFac; void prepare() { inv = new Mint[LIM]; fac = new Mint[LIM]; invFac = new Mint[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = -(Mint.M / i) * inv[cast(size_t)(Mint.M % i)]; } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(long n, long k) { if (0 <= k && k <= n) { assert(n < LIM); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)]; } else { return Mint(0); } } void bAdd(T)(T[] bit, int pos, T val) in { assert(0 <= pos && pos < bit.length, "bAdd: 0 <= pos < |bit| must hold"); } do { for (int x = pos; x < bit.length; x |= x + 1) { bit[x] += val; } } // sum of [0, pos) T bSum(T)(T[] bit, int pos) in { assert(0 <= pos && pos <= bit.length, "bSum: 0 <= pos <= |bit| must hold"); } do { T ret = 0; for (int x = pos - 1; x >= 0; x = (x & (x + 1)) - 1) { ret += bit[x]; } return ret; } void main() { prepare; try { for (; ; ) { const N = readInt(); auto A = new int[N]; foreach (i; 0 .. N) { A[i] = readInt(); } auto as = A.dup; as = as.sort.uniq.array; const asLen = cast(int)(as.length); auto bit = new int[asLen]; long num0, num1; foreach (i; 0 .. N) { const pos = as.lowerBound(A[i]); num0 += bit.bSum(pos); num1 += i - bit.bSum(pos + 1); bit.bAdd(pos, 1); } debug { writeln("num0 = ", num0); writeln("num1 = ", num1); } Mint ans; Mint prod = 1; foreach (i; 1 .. N + 1) { prod *= binom(N, i); } // i Mint sum1; foreach (i; 2 .. N + 1) { sum1 += Mint(i) * Mint(i - 1) * inv[N] * inv[N - 1]; } sum1 *= prod; ans += num1 * sum1; // i < j Mint sum2; foreach (i; 1 .. N + 1) { sum2 += Mint(i) * inv[N]; } sum2 = sum2^^2; foreach (i; 1 .. N + 1) { sum2 -= (Mint(i) * inv[N])^^2; } sum2 /= 2; sum2 *= prod; ans += (num0 + num1) * sum2; debug { Mint brt; foreach (i; 1 .. N + 1) foreach (j; i + 1 .. N + 1) { Mint tmp = binom(N - 1, i - 1) * binom(N - 1, j - 1); foreach (k; 1 .. N + 1) { if (k != i && k != j) { tmp *= binom(N, k); } } brt += tmp; } writeln("brt = ", brt, ", sum2 = ", sum2); } writeln(ans); } } catch (EOFException e) { } }