結果

問題 No.409 ダイエット
ユーザー tutuztutuz
提出日時 2019-02-18 16:21:29
言語 Java19
(openjdk 21)
結果
AC  
実行時間 223 ms / 2,000 ms
コード長 6,216 bytes
コンパイル時間 3,554 ms
コンパイル使用メモリ 81,704 KB
実行使用メモリ 63,068 KB
最終ジャッジ日時 2023-07-29 03:20:16
合計ジャッジ時間 16,369 ms
ジャッジサーバーID
(参考情報)
judge11 / judge12
このコードへのチャレンジ(β)

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 42 ms
49,532 KB
testcase_01 AC 44 ms
49,612 KB
testcase_02 AC 44 ms
49,624 KB
testcase_03 AC 43 ms
49,380 KB
testcase_04 AC 43 ms
49,528 KB
testcase_05 AC 43 ms
49,504 KB
testcase_06 AC 42 ms
49,700 KB
testcase_07 AC 43 ms
49,468 KB
testcase_08 AC 43 ms
49,488 KB
testcase_09 AC 43 ms
49,420 KB
testcase_10 AC 43 ms
49,384 KB
testcase_11 AC 43 ms
49,612 KB
testcase_12 AC 44 ms
47,600 KB
testcase_13 AC 44 ms
49,448 KB
testcase_14 AC 43 ms
49,472 KB
testcase_15 AC 42 ms
49,436 KB
testcase_16 AC 42 ms
49,464 KB
testcase_17 AC 43 ms
49,656 KB
testcase_18 AC 44 ms
49,380 KB
testcase_19 AC 44 ms
49,472 KB
testcase_20 AC 44 ms
49,484 KB
testcase_21 AC 44 ms
49,624 KB
testcase_22 AC 44 ms
49,740 KB
testcase_23 AC 44 ms
49,992 KB
testcase_24 AC 45 ms
49,828 KB
testcase_25 AC 42 ms
49,448 KB
testcase_26 AC 45 ms
49,352 KB
testcase_27 AC 45 ms
49,496 KB
testcase_28 AC 42 ms
49,552 KB
testcase_29 AC 43 ms
49,440 KB
testcase_30 AC 43 ms
49,384 KB
testcase_31 AC 43 ms
49,560 KB
testcase_32 AC 44 ms
49,520 KB
testcase_33 AC 43 ms
49,380 KB
testcase_34 AC 42 ms
49,588 KB
testcase_35 AC 51 ms
49,756 KB
testcase_36 AC 51 ms
49,768 KB
testcase_37 AC 52 ms
49,664 KB
testcase_38 AC 52 ms
49,676 KB
testcase_39 AC 52 ms
49,664 KB
testcase_40 AC 52 ms
49,540 KB
testcase_41 AC 55 ms
50,704 KB
testcase_42 AC 52 ms
49,668 KB
testcase_43 AC 50 ms
49,560 KB
testcase_44 AC 54 ms
51,172 KB
testcase_45 AC 53 ms
49,620 KB
testcase_46 AC 54 ms
50,972 KB
testcase_47 AC 55 ms
50,900 KB
testcase_48 AC 52 ms
49,564 KB
testcase_49 AC 54 ms
50,744 KB
testcase_50 AC 54 ms
51,644 KB
testcase_51 AC 51 ms
49,460 KB
testcase_52 AC 51 ms
49,896 KB
testcase_53 AC 51 ms
50,004 KB
testcase_54 AC 51 ms
49,764 KB
testcase_55 AC 145 ms
56,736 KB
testcase_56 AC 177 ms
61,416 KB
testcase_57 AC 196 ms
61,200 KB
testcase_58 AC 149 ms
56,788 KB
testcase_59 AC 172 ms
57,040 KB
testcase_60 AC 145 ms
54,908 KB
testcase_61 AC 194 ms
61,168 KB
testcase_62 AC 190 ms
61,068 KB
testcase_63 AC 193 ms
61,088 KB
testcase_64 AC 141 ms
56,940 KB
testcase_65 AC 197 ms
61,344 KB
testcase_66 AC 199 ms
60,588 KB
testcase_67 AC 178 ms
56,864 KB
testcase_68 AC 168 ms
56,776 KB
testcase_69 AC 194 ms
58,928 KB
testcase_70 AC 212 ms
60,572 KB
testcase_71 AC 166 ms
56,908 KB
testcase_72 AC 223 ms
63,068 KB
testcase_73 AC 215 ms
61,988 KB
testcase_74 AC 201 ms
57,260 KB
testcase_75 AC 214 ms
62,572 KB
testcase_76 AC 195 ms
57,348 KB
testcase_77 AC 164 ms
56,728 KB
testcase_78 AC 178 ms
57,240 KB
testcase_79 AC 152 ms
57,020 KB
testcase_80 AC 217 ms
62,080 KB
testcase_81 AC 214 ms
62,492 KB
testcase_82 AC 194 ms
57,656 KB
testcase_83 AC 199 ms
57,172 KB
testcase_84 AC 198 ms
57,212 KB
testcase_85 AC 92 ms
52,160 KB
testcase_86 AC 196 ms
57,716 KB
testcase_87 AC 210 ms
59,544 KB
testcase_88 AC 137 ms
54,860 KB
testcase_89 AC 202 ms
57,092 KB
testcase_90 AC 128 ms
54,796 KB
testcase_91 AC 199 ms
57,300 KB
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 #

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;

public class Main {

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		MyInput in = new MyInput(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 30;
	static long LINF = 1L << 55;
	static int MOD = 1000000007;
	static int[] mh4 = { 0, -1, 1, 0 };
	static int[] mw4 = { -1, 0, 0, 1 };
	static int[] mh8 = { -1, -1, -1, 0, 0, 1, 1, 1 };
	static int[] mw8 = { -1, 0, 1, -1, 1, -1, 0, 1 };

	static class TaskX {

		public void solve(int testNumber, MyInput in, PrintWriter out) {

			int n = in.nextInt();
			long a = in.nextLong(), b = in.nextLong(), w = in.nextLong();
			long[] d = in.nextLongArray(n);

			ConvexHullTrick cht = new ConvexHullTrick(n + 100);
			long[] dp = new long[n+1];
			dp[0] = 0;

			for (int i = 1; i < n+1; i++) {
				int j = i -1;
				cht.addLine(-j * b, dp[j] + j * a + (long)(j + 1) * j / 2 * b);
				dp[i] = cht.query(i) - (i-1) * a + (long)(i-1) * i / 2 * b + d[i-1];
			}

			long ans = Long.MAX_VALUE;
			for (int i = 0; i < n+1; i++) {
				ans = Math.min(ans, dp[i] - (n - i) * a + (long)(n - i) * (n - i + 1) / 2 * b);
			}

			out.println(w + ans);

		}

		/**
		 * 追加クエリの直線の傾きが単調減少の場合
		 * - insert (a, b): add y = ax + b
		 * - query (x)    : min_i{a[i]x + b}
		 * */
		class ConvexHullTrick {
			long[] A, B;
			int len;

			public ConvexHullTrick(int n) {
				A = new long[n];
				B = new long[n];
			}

			private boolean check(long a, long b) {
				return (B[len - 2] - B[len - 1]) * (a - A[len - 1]) >= (B[len - 1] - b) * (A[len - 1] - A[len - 2]);
			}

			public void addLine(long a, long b) {
				while (len >= 2 && check(a, b)) {
					len--;
				}
				A[len] = a;
				B[len] = b;
				len++;
			}

			public long query(long x) {
				int l = -1, r = len;
				while (r - l > 1) {
					int mid = (r + l) / 2;
					if (get(mid, x) >= get(mid + 1, x)) {
						l = mid;
					} else {
						r = mid;
					}
				}
				return get(r, x);
			}

			private long get(int k, long x) {
				return A[k] * x + B[k];
			}
		}
	}

	static class MyInput {
		private final BufferedReader in;
		private static int pos;
		private static int readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500 * 8 * 2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static {
			for (int i = 0; i < 10; i++) {
				isDigit['0' + i] = true;
			}
			isDigit['-'] = true;
			isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
			isLineSep['\r'] = isLineSep['\n'] = true;
		}

		public MyInput(InputStream is) {
			in = new BufferedReader(new InputStreamReader(is));
		}

		public int read() {
			if (pos >= readLen) {
				pos = 0;
				try {
					readLen = in.read(buffer);
				} catch (IOException e) {
					throw new RuntimeException();
				}
				if (readLen <= 0) {
					throw new MyInput.EndOfFileRuntimeException();
				}
			}
			return buffer[pos++];
		}

		public int nextInt() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			int i = 0;
			int ret = 0;
			if (str[0] == '-') {
				i = 1;
			}
			for (; i < len; i++)
				ret = ret * 10 + str[i] - '0';
			if (str[0] == '-') {
				ret = -ret;
			}
			return ret;
		}

		public long nextLong() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			int i = 0;
			long ret = 0;
			if (str[0] == '-') {
				i = 1;
			}
			for (; i < len; i++)
				ret = ret * 10 + str[i] - '0';
			if (str[0] == '-') {
				ret = -ret;
			}
			return ret;
		}

		public char nextChar() {
			while (true) {
				final int c = read();
				if (!isSpace[c]) {
					return (char) c;
				}
			}
		}

		public String nextString() {
			return new String(nextChars());
		}

		public char[] nextChars() {
			int len = 0;
			str[len++] = nextChar();
			len = reads(len, isSpace);
			return Arrays.copyOf(str, len);
		}

		public char[][] next2DChars(int h, int w) {
			char[][] s = new char[h][w];
			for (int i = 0; i < h; i++) {
				s[i] = nextChars();
			}
			return s;
		}

		int reads(int len, boolean[] accept) {
			try {
				while (true) {
					final int c = read();
					if (accept[c]) {
						break;
					}
					if (str.length == len) {
						char[] rep = new char[str.length * 3 / 2];
						System.arraycopy(str, 0, rep, 0, str.length);
						str = rep;
					}
					str[len++] = (char) c;
				}
			} catch (MyInput.EndOfFileRuntimeException e) {
			}
			return len;
		}

		public int[] nextIntArray(final int n) {
			final int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public int[] nextIntArray1Index(final int n) {
			final int[] res = new int[n + 1];
			for (int i = 1; i < n + 1; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public int[] nextIntArrayDec(final int n) {
			final int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt() - 1;
			}
			return res;
		}

		public long[] nextLongArray(final int n) {
			final long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public long[] nextLongArray1Index(final int n) {
			final long[] res = new long[n + 1];
			for (int i = 1; i < n + 1; i++) {
				res[i] = nextLong();
			}
			return res;
		}

		public long[] nextLongArrayDec(final int n) {
			final long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong() - 1;
			}
			return res;
		}

		public double nextDouble() {
			return Double.parseDouble(nextString());
		}

		public double[] nextDoubleArray(int n) {
			double[] res = new double[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextDouble();
			}
			return res;
		}

		static class EndOfFileRuntimeException extends RuntimeException {
		}

	}

}
0