結果

問題 No.1297 銅像
ユーザー 👑 hos.lyric
提出日時 2020-11-24 12:22:38
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 200 ms / 2,000 ms
コード長 5,929 bytes
コンパイル時間 891 ms
コンパイル使用メモリ 125,104 KB
実行使用メモリ 22,876 KB
最終ジャッジ日時 2024-06-22 10:02:06
合計ジャッジ時間 4,352 ms
ジャッジサーバーID
(参考情報)
judge1 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 21
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

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)); }
// class Func = TX -> TY
// for any f, g: Func, x -> sgn(g(x) - f(x)) must be monotone
class LiChaoTree(Func) {
import std.algorithm : swap;
alias TX = Func.TX;
alias TY = Func.TY;
const(TX) L, R;
class Tree {
Tree l, r;
Func f;
this(Func f) {
this.f = f;
}
}
Tree root;
// [L, R)
this(TX L, TX R) {
assert(L < R, "LiChaoTree: L < R must hold");
this.L = L;
this.R = R;
}
// Add g to the whole [L, R)
void add(Func g) {
root = add(root, L, R, g);
}
// Add g to [a, b)
void add(TX a, TX b, Func g) {
root = add(root, L, R, a, b, g);
}
// Get max at a
TY opCall(TX a) {
TY mx = TY.min;
TX l = L, r = R;
for (Tree u = root; u; ) {
if (u.f) {
const fX = u.f(a);
if (mx < fX) mx = fX;
}
const mid = l + (r - l) / 2;
if (a < mid) {
u = u.l; r = mid;
} else {
u = u.r; l = mid;
}
}
return mx;
}
private:
Tree add(Tree u0, TX l, TX r, Func g) {
if (!u0) return new Tree(g);
TY gL = g(l), gR = g(r);
for (Tree u = u0; ; ) {
TY fL = u.f ? u.f(l) : TY.min, fR = u.f ? u.f(r) : TY.min;
if (fL >= gL && fR >= gR) return u0;
if (fL <= gL && fR <= gR) { u.f = g; return u0; }
if (r - l == 1) { if (fL <= gL) { u.f = g; } return u0; }
const mid = l + (r - l) / 2;
TY fMid = u.f(mid), gMid = g(mid);
if (fMid < gMid) {
swap(u.f, g);
if (!g) return u0;
if (gL < fL) {
if (!u.l) { u.l = new Tree(g); return u0; }
u = u.l; r = mid; gL = fL; gR = fMid;
} else {
if (!u.r) { u.r = new Tree(g); return u0; }
u = u.r; l = mid; gL = fMid; gR = fR;
}
} else {
if (fL < gL) {
if (!u.l) { u.l = new Tree(g); return u0; }
u = u.l; r = mid; gR = gMid;
} else {
if (!u.r) { u.r = new Tree(g); return u0; }
u = u.r; l = mid; gL = gMid;
}
}
}
}
Tree add(Tree u, TX l, TX r, TX a, TX b, Func g) {
if (b <= l || r <= a) return u;
if (a <= l && r <= b) return add(u, l, r, g);
if (u && u.f && u.f(l) >= g(l) && u.f(r) >= g(r)) return u;
if (!u) u = new Tree(null);
const mid = l + (r - l) / 2;
u.l = add(u.l, l, mid, a, b, g);
u.r = add(u.r, mid, r, a, b, g);
return u;
}
}
// y = p x + q
class Line {
alias TX = long;
alias TY = long;
long p, q;
this(long p, long q) {
this.p = p;
this.q = q;
}
TY opCall(TX x) {
return p * x + q;
}
}
enum INF = 10L^^18;
enum LIM_CN = 10L^^12 + 10L^^11 + 10;
void main() {
try {
for (; ; ) {
const N = readInt();
const C = readLong();
auto A = new long[N];
auto B = new long[N];
foreach (i; 0 .. N) {
A[i] = readLong();
B[i] = readLong();
}
/*
min_{j<=i} (dp[j] + A[i] (i - j) + C (i - j) (i - j + 1) / 2)
= min_{j<=i} ((dp[j] + C j (j - 1) / 2) - j (A[i] + C i))
+ A[i] i + C i (i + 1) / 2
min_i (DP[i] + A[i] (j - i - 1) + C (j - i - 1) (j - i) / 2)
= min_i ((DP[i] - A[i] (i + 1) + C i (i + 1) / 2) + (A[i] - C i) j)
+ C j (j - 1) / 2
*/
auto lct = new LiChaoTree!Line(-LIM_CN, LIM_CN);
auto LCT = new LiChaoTree!Line(0, N + 1);
void add(int j, long val) {
lct.add(new Line(-(-j), -(val + C * j * (j - 1) / 2)));
}
void ADD(int i, long val) {
LCT.add(new Line(-(A[i] - C * i), -(val - A[i] * (i + 1) + C * i * (i + 1) / 2)));
}
auto dp = new long[N + 1];
dp[] = INF;
foreach (i; 0 .. N + 1) {
dp[i] = (i == 0) ? 0 : (-LCT(i) + C * i * (i - 1) / 2);
add(i, dp[i]);
if (i == N) {
break;
}
long mn = -lct(A[i] + C * i) + A[i] * i + C * i * (i + 1) / 2;
debug {
writeln(i, ": ", mn, " ", mn + A[i] + B[i]);
}
ADD(i, mn + A[i] + B[i]);
}
debug {
writeln("dp = ", dp);
}
writeln(dp[N]);
debug {
auto brt = new long[N + 1];
brt[] = INF;
brt[0] = 0;
foreach (i; 0 .. N) {
long mn = INF;
foreach (j; 0 .. i + 1) {
// [j, i)
const long l = i - j;
chmin(mn, brt[j] + A[i] * l + C * (l * (l + 1) / 2));
}
writeln(i, ": ", mn, " ", mn + A[i] + B[i]);
mn += A[i] + B[i];
foreach (j; i + 1 .. N + 1) {
// [i + 1, j)
const long l = j - (i + 1);
chmin(brt[j], mn + A[i] * l + C * (l * (l + 1) / 2));
}
}
writeln("brt = ", brt);
}
}
} catch (EOFException e) {
}
}
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