結果
| 問題 |
No.409 ダイエット
|
| コンテスト | |
| ユーザー |
 Grenache
|
| 提出日時 | 2018-03-03 00:49:45 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 745 ms / 2,000 ms |
| コード長 | 9,024 bytes |
| コンパイル時間 | 4,174 ms |
| コンパイル使用メモリ | 92,584 KB |
| 実行使用メモリ | 78,240 KB |
| 最終ジャッジ日時 | 2024-06-26 10:32:25 |
| 合計ジャッジ時間 | 32,860 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 92 |
ソースコード
import java.io.*;
import java.util.*;
public class Main_yukicoder409 {
private static Scanner sc;
private static Printer pr;
private static void solve() {
int n = sc.nextInt();
long a = sc.nextInt();
long b = sc.nextInt();
long w = sc.nextInt();
int[] d = new int[n];
for (int i = 0; i < n; i++) {
d[i] = sc.nextInt();
}
long[] dp = new long[n + 1];
ConvexHullTrick cht = new ConvexHullTrick(n);
for (int i = 1; i <= n; i++) {
int j = i - 1;
cht.add(-b * j, dp[j] + a * j + b * j * (j + 1) / 2);
dp[i] = cht.query(i) + d[i - 1] - a * (i - 1) + b * i * (i - 1) / 2;
}
long ans = Long.MAX_VALUE;
for (int i = 0; i <= n; i++) {
long tmp = dp[i] - a * (n - i) + b * (n - i) * (n - i + 1) / 2;
// pr.printf("%d %d %d\n", i, tmp, ans);
ans = Math.min(ans, tmp);
}
pr.println(ans + w);
}
private static class ConvexHullTrick {
// int n;
int cnt;
long[] aa;
long[] bb;
long[] left;
NavigableSet<Integer> f;
// NavigableSet<Integer> d;
// TreeSet で利用する Comparator 内で利用する。直線の傾きなら true、左端の座標なら false
boolean cmpf;
// add, query ともに特別な条件がない一般 ConvexHullTrick
// 追加できる直線は n 本まで。
ConvexHullTrick(int n) {
// this.n = n;
cnt = 0;
aa = new long[n];
bb = new long[n];
// i番目の直線と1つ前の直線との交点のx座標。0番目は-INF
left = new long[n + 1];
cmpf = true;
// 必要な直線を傾きの降順に保持する
// cmpf によって、直線の左端のx座標の昇順で探索する
f = new TreeSet<>((x, y) -> {
if (cmpf) return aa[x] == aa[y] ? Long.compare(bb[x], bb[y]) : Long.compare(aa[y], aa[x]);
else return left[x] == left[y] ? Integer.compare(x, y) : Long.compare(left[x], left[y]);
});
}
// ax+b を追加。
private void add(long a, long b) {
aa[cnt] = a;
bb[cnt] = b;
int curr = cnt++;
if (f.contains(curr)) {
return;
}
Integer prev = f.lower(curr);
Integer next = f.higher(curr);
if (!check(prev, curr, next)) {
return;
}
while (prev != null) {
Integer pprev = f.lower(prev);
if (check(pprev, prev, curr)) {
break;
}
f.remove(prev);
prev = pprev;
}
while (next != null) {
Integer nnext = f.higher(next);
if (check(curr, next, nnext)) {
break;
}
f.remove(next);
next = nnext;
}
if (prev == null) {
left[curr] = Long.MIN_VALUE;
f.add(curr);
} else {
long bbb = bb[curr] - bb[prev];
long aaa = aa[prev] - aa[curr];
left[curr] = bbb >= 0 ? (bbb + aaa - 1) / aaa : bbb / aaa;
f.add(curr);
}
if (next != null) {
long bbb = bb[next] - bb[curr];
long aaa = aa[curr] - aa[next];
left[next] = bbb >= 0 ? (bbb + aaa - 1) / aaa : bbb / aaa;
}
}
// f(x)の最小値。
private long query(long x) {
left[cnt] = x;
cmpf = false;
Integer mini = f.lower(cnt);
cmpf = true;
// if (mini == null) {
// pr.printf("%d %f\n", x, dd[cnt]);
// pr.flush();
// }
return fx(mini, x);
}
// i 番目の直線を使った時の f(x) の値
private long fx(int i, long x) {
return aa[i] * x + bb[i];
}
// curr の直線が必要な場合 true
private boolean check(Integer prev, Integer curr, Integer next) {
// Comparator で aは降順、bは昇順なので
if (prev == null) {
return true;
} else {
if (aa[prev] == aa[curr]) {
return false;
}
}
if (next == null) {
return true;
}
double b32 = bb[next] - bb[curr];
double a21 = aa[curr] - aa[prev];
double b21 = bb[curr] - bb[prev];
double a32 = aa[next] - aa[curr];
// if (Math.abs(b32 * a21) > (double)Long.MAX_VALUE || Math.abs(b21 * a32) > (double)Long.MAX_VALUE) {
// throw new RuntimeException();
// }
return b32 * a21 < b21 * a32;
// long でいける場合
// return (bb[next] - bb[curr]) * (aa[curr] - aa[prev]) < (bb[curr] - bb[prev]) * (aa[next] - aa[curr]);
/*
BigInteger a1 = BigInteger.valueOf(aa[prev]);
BigInteger a2 = BigInteger.valueOf(aa[curr]);
BigInteger a3 = BigInteger.valueOf(aa[next]);
BigInteger b1 = BigInteger.valueOf(bb[prev]);
BigInteger b2 = BigInteger.valueOf(bb[curr]);
BigInteger b3 = BigInteger.valueOf(bb[next]);
// BigInteger LMAX = BigInteger.valueOf(Long.MAX_VALUE);
// if (b3.multiply(a1).abs().compareTo(LMAX) > 0) {
// pr.printf("Overflow : %s %s\n", b3, a1);
// }
// if (b1.multiply(a3).abs().compareTo(LMAX) > 0) {
// pr.printf("Overflow : %s %s\n", b1, a3);
// }
// if (a2.multiply(b3).abs().compareTo(LMAX) > 0) {
// pr.printf("Overflow : %s %s\n", a2, b3);
// }
// if (a2.multiply(b1).abs().compareTo(LMAX) > 0) {
// pr.printf("Overflow : %s %s\n", a2, b1);
// }
// if (b2.multiply(a1).abs().compareTo(LMAX) > 0) {
// pr.printf("Overflow : %s %s\n", b2, a1);
// }
// if (b2.multiply(a3).abs().compareTo(LMAX) > 0) {
// pr.printf("Overflow : %s %s\n", b2, a3);
// }
return b3.multiply(a1).subtract(b1.multiply(a3)).compareTo(a2.multiply(b3).subtract(a2.multiply(b1)).add(b2.multiply(a1)).subtract(b2.multiply(a3))) > 0;
// */
}
}
// ---------------------------------------------------
public static void main(String[] args) {
sc = new Scanner(INPUT == null ? System.in : new ByteArrayInputStream(INPUT.getBytes()));
pr = new Printer(System.out);
solve();
// pr.close();
pr.flush();
// sc.close();
}
static String INPUT = null;
@SuppressWarnings("unused")
private static class Scanner {
BufferedReader br;
Scanner (InputStream in) {
br = new BufferedReader(new InputStreamReader(in));
}
private boolean isPrintable(int ch) {
return ch >= '!' && ch <= '~';
}
private boolean isCRLF(int ch) {
return ch == '\n' || ch == '\r' || ch == -1;
}
private int nextPrintable() {
try {
int ch;
while (!isPrintable(ch = br.read())) {
if (ch == -1) {
throw new NoSuchElementException();
}
}
return ch;
} catch (IOException e) {
throw new NoSuchElementException();
}
}
String next() {
try {
int ch = nextPrintable();
StringBuilder sb = new StringBuilder();
do {
sb.appendCodePoint(ch);
} while (isPrintable(ch = br.read()));
return sb.toString();
} catch (IOException e) {
throw new NoSuchElementException();
}
}
int nextInt() {
try {
// parseInt from Integer.parseInt()
boolean negative = false;
int res = 0;
int limit = -Integer.MAX_VALUE;
int radix = 10;
int fc = nextPrintable();
if (fc < '0') {
if (fc == '-') {
negative = true;
limit = Integer.MIN_VALUE;
} else if (fc != '+') {
throw new NumberFormatException();
}
fc = br.read();
}
int multmin = limit / radix;
int ch = fc;
do {
int digit = ch - '0';
if (digit < 0 || digit >= radix) {
throw new NumberFormatException();
}
if (res < multmin) {
throw new NumberFormatException();
}
res *= radix;
if (res < limit + digit) {
throw new NumberFormatException();
}
res -= digit;
} while (isPrintable(ch = br.read()));
return negative ? res : -res;
} catch (IOException e) {
throw new NoSuchElementException();
}
}
long nextLong() {
try {
// parseLong from Long.parseLong()
boolean negative = false;
long res = 0;
long limit = -Long.MAX_VALUE;
int radix = 10;
int fc = nextPrintable();
if (fc < '0') {
if (fc == '-') {
negative = true;
limit = Long.MIN_VALUE;
} else if (fc != '+') {
throw new NumberFormatException();
}
fc = br.read();
}
long multmin = limit / radix;
int ch = fc;
do {
int digit = ch - '0';
if (digit < 0 || digit >= radix) {
throw new NumberFormatException();
}
if (res < multmin) {
throw new NumberFormatException();
}
res *= radix;
if (res < limit + digit) {
throw new NumberFormatException();
}
res -= digit;
} while (isPrintable(ch = br.read()));
return negative ? res : -res;
} catch (IOException e) {
throw new NoSuchElementException();
}
}
float nextFloat() {
return Float.parseFloat(next());
}
double nextDouble() {
return Double.parseDouble(next());
}
String nextLine() {
try {
int ch;
while (isCRLF(ch = br.read())) {
if (ch == -1) {
throw new NoSuchElementException();
}
}
StringBuilder sb = new StringBuilder();
do {
sb.appendCodePoint(ch);
} while (!isCRLF(ch = br.read()));
return sb.toString();
} catch (IOException e) {
throw new NoSuchElementException();
}
}
void close() {
try {
br.close();
} catch (IOException e) {
// throw new NoSuchElementException();
}
}
}
private static class Printer extends PrintWriter {
Printer(OutputStream out) {
super(out);
}
}
}