結果
| 問題 |
No.409 ダイエット
|
| ユーザー |
 Grenache
|
| 提出日時 | 2018-03-02 14:59:11 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 292 ms / 2,000 ms |
| コード長 | 5,960 bytes |
| コンパイル時間 | 3,985 ms |
| コンパイル使用メモリ | 80,840 KB |
| 実行使用メモリ | 59,784 KB |
| 最終ジャッジ日時 | 2024-06-26 10:30:02 |
| 合計ジャッジ時間 | 19,291 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
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| 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_4 {
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];
ConvexHullTrickOpt cht = new ConvexHullTrickOpt(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 ConvexHullTrickOpt {
LinkedList<Pair> q;
// add における a が単調非増加、query における x が単調非減少である場合
// add O(n), query O(n + q)
ConvexHullTrickOpt(int n) {
q = new LinkedList<>();
}
// ax+b を追加。a は単調非増加とする
private void add(long a, long b) {
Pair next = new Pair(a, b);
while (q.size() >= 2) {
Pair curr = q.get(q.size() - 1);
Pair prev = q.get(q.size() - 2);
if (check(prev, curr, next)) {
break;
}
q.removeLast();
}
q.add(next);
}
// f(x)の最小値。x は単調非減少とする
private long query(long x) {
long fx0 = fx(q.get(0), x);
while (q.size() > 1) {
long fx1 = fx(q.get(1), x);
if (fx0 < fx1) {
return fx0;
}
q.removeFirst();
fx0 = fx1;
}
return fx0;
}
// i 番目の直線を使った時の f(x) の値
private long fx(Pair i, long x) {
return i.a * x + i.b;
}
// curr の直線が必要な場合 true
private boolean check(Pair prev, Pair curr, Pair next) {
return (next.b - curr.b) * (curr.a - prev.a) < (curr.b - prev.b) * (next.a - curr.a);
}
private static class Pair {
long a;
long b;
Pair(long a, long b) {
this.a = a;
this.b = b;
}
}
}
// ---------------------------------------------------
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);
}
}
}