結果
| 問題 |
No.1214 Market
|
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2020-08-30 13:38:32 |
| 言語 | D (dmd 2.109.1) |
| 結果 |
AC
|
| 実行時間 | 1,484 ms / 2,000 ms |
| コード長 | 6,295 bytes |
| コンパイル時間 | 1,937 ms |
| コンパイル使用メモリ | 162,464 KB |
| 実行使用メモリ | 56,524 KB |
| 最終ジャッジ日時 | 2024-06-22 08:41:42 |
| 合計ジャッジ時間 | 20,291 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 39 |
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 = 10^^9 + 7;
alias Mint = ModInt!MO;
enum LIM = 110;
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 main() {
prepare;
try {
for (; ; ) {
const N = readInt();
const M = readInt();
const K = readInt();
auto A = new long[M];
auto B = new long[M];
foreach (i; 0 .. M) {
A[i] = readLong();
B[i] = readLong();
}
auto as = A.dup;
as ~= 0;
as ~= K + 1;
as.sort;
as = as.uniq.array;
const asLen = cast(int)(as.length) - 1;
auto bss = new long[][asLen];
foreach (i; 0 .. M) {
const e = as.upperBound(A[i]) - 1;
bss[e] ~= B[i];
}
debug {
writeln("as = ", as);
writeln("bss = ", bss);
}
auto coef = new Mint[][](asLen, N + 1);
auto coefGoal = new Mint[][](asLen, N + 1);
foreach (e; 0 .. asLen) {
foreach (dj; 0 .. N + 1) {
coef[e][dj] = invFac[dj] * Mint(as[e + 1] - as[e])^^dj;
coefGoal[e][dj] = invFac[dj] * Mint(K + 1 - as[e + 1])^^dj;
}
}
Mint ans;
foreach (b0; B) {
debug {
long counter;
writeln("b0 = ", b0);
}
const numLarge = cast(int)(B.count!(b => (b > b0)));
const numSmall = cast(int)(B.count!(b => (b < b0)));
// processed poss, # of customers, stock (+, 0, -)
auto dp = new Mint[][][][][](asLen + 1, N + 1, numLarge + 1, 2, numSmall + 1);
dp[0][0][0][0][0] = 1;
foreach (e; 0 .. asLen) {
int dx, dy, dz;
foreach (b; bss[e]) {
if (b > b0) ++dx;
if (b == b0) ++dy;
if (b < b0) ++dz;
}
foreach (j; 0 .. N + 1) {
foreach (x; 0 .. numLarge + 1) foreach (y; 0 .. 2) foreach (z; 0 .. numSmall + 1) {
if (dp[e][j][x][y][z]) {
int xx = x + dx, yy = y + dy, zz = z + dz;
foreach (dj; 0 .. N - j + 1) {
debug{
++counter;
}
// dp[e + 1][j + dj][xx][yy][zz] += dp[e][j][x][y][z] * coef[e][dj];
if (y + dy > 0 && yy == 0) {
// goal
dp[asLen][N][0][0][0] += dp[e][j][x][y][z] * coef[e][dj] * coefGoal[e][N - (j + dj)];
} else {
dp[e + 1][j + dj][xx][yy][zz] += dp[e][j][x][y][z] * coef[e][dj];
}
(xx > 0) ? --xx : (yy > 0) ? --yy : (zz > 0) ? --zz : 0;
}
}
}
}
}
Mint sum;
foreach (x; 0 .. numLarge + 1) foreach (z; 0 .. numSmall + 1) {
sum += dp[asLen][N][x][0][z];
}
sum *= fac[N];
debug {
writeln("counter = ",counter);
writeln(" sum = ", sum);
stdout.flush;
}
ans += sum * b0;
}
ans /= Mint(K + 1)^^N;
writeln(ans);
}
} catch (EOFException e) {
}
}