結果

問題 No.705 ゴミ拾い Hard
ユーザー uwiuwi
提出日時 2018-06-15 23:21:16
言語 Java21
(openjdk 21)
結果
AC  
実行時間 280 ms / 1,500 ms
コード長 4,993 bytes
コンパイル時間 4,104 ms
コンパイル使用メモリ 92,340 KB
実行使用メモリ 64,924 KB
最終ジャッジ日時 2024-06-30 15:27:38
合計ジャッジ時間 11,680 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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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 50 ms
50,264 KB
testcase_01 AC 49 ms
50,220 KB
testcase_02 AC 47 ms
50,240 KB
testcase_03 AC 47 ms
50,284 KB
testcase_04 AC 49 ms
50,304 KB
testcase_05 AC 51 ms
50,248 KB
testcase_06 AC 50 ms
50,300 KB
testcase_07 AC 53 ms
50,376 KB
testcase_08 AC 50 ms
50,096 KB
testcase_09 AC 51 ms
50,316 KB
testcase_10 AC 51 ms
49,744 KB
testcase_11 AC 52 ms
49,868 KB
testcase_12 AC 52 ms
49,760 KB
testcase_13 AC 51 ms
49,860 KB
testcase_14 AC 75 ms
50,528 KB
testcase_15 AC 63 ms
49,812 KB
testcase_16 AC 58 ms
50,372 KB
testcase_17 AC 60 ms
50,808 KB
testcase_18 AC 69 ms
50,532 KB
testcase_19 AC 69 ms
50,272 KB
testcase_20 AC 60 ms
50,272 KB
testcase_21 AC 58 ms
50,328 KB
testcase_22 AC 63 ms
50,540 KB
testcase_23 AC 57 ms
49,944 KB
testcase_24 AC 268 ms
64,432 KB
testcase_25 AC 278 ms
64,436 KB
testcase_26 AC 263 ms
64,704 KB
testcase_27 AC 280 ms
64,708 KB
testcase_28 AC 279 ms
64,704 KB
testcase_29 AC 266 ms
64,724 KB
testcase_30 AC 269 ms
64,456 KB
testcase_31 AC 254 ms
64,924 KB
testcase_32 AC 260 ms
64,856 KB
testcase_33 AC 204 ms
64,748 KB
testcase_34 AC 199 ms
64,776 KB
testcase_35 AC 252 ms
64,588 KB
testcase_36 AC 266 ms
64,828 KB
testcase_37 AC 217 ms
64,664 KB
testcase_38 AC 239 ms
64,472 KB
testcase_39 AC 275 ms
64,380 KB
testcase_40 AC 52 ms
50,304 KB
testcase_41 AC 51 ms
50,272 KB
testcase_42 AC 49 ms
50,240 KB
testcase_43 AC 236 ms
64,728 KB
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ソースコード

diff # 

package contest180615;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class F2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] a = na(n);
		int[] x = na(n);
		int[] y = na(n);
		
		// dp[i] = dp[j] + d(j+1,i+1)
		// dp[i] = min(dp[j] + (a[i]-x[j+1])^2+y[j+1]^2)
		// dp[i] = min(dp[j] + a[i]^2-2x[j+1]a[i]+x[j+1]^2+y[j+1]^2)
		
		long[] dp = new long[n+1];
		Arrays.fill(dp, Long.MAX_VALUE);
		dp[0] = 0;
		EnvelopeL3 el = new EnvelopeL3(n);
		for(int i = 0;i < n;i++){
			el.add(x[i], Math.abs((long)y[i]*y[i]*y[i])+dp[i]);
			dp[i+1] = el.min(a[i]);
		}
		out.println(dp[n]);
	}
	
	public class EnvelopeL3 {
		public static final long INF = Long.MIN_VALUE;
		
		public long[] xs;
		public long[] intercepts, slopes;
		public int p;
		
		public EnvelopeL3(int n)
		{
			xs = new long[n];
			intercepts = new long[n];
			slopes = new long[n];
			p = 0;
		}
		
		public void clear()
		{
			p = 0;
		}
		
		public long f(long x, long a, long b)
		{
			return Math.abs((x-a)*(x-a)*(x-a))+b;
		}
		
		long intersection(long a, long b, long c, long d)
		{
			long low = -10, high = 1000000;
			while(high - low > 1){
				long h = high+low>>1;
				if(f(h, a, b) - f(h, c, d) > 0){
					high = h;
				}else{
					low = h;
				}
			}
			return high;
		}
		
		public void add(long slope, long intercept)
		{
			assert p == 0 || slopes[p-1] <= slope;
			while(p > 0){
				int i = p-1;
				if(p > 1 && intersection(slopes[i], intercepts[i], slope, intercept) <= xs[i]){
					p--;
					continue;
				}
				
				xs[p] = intersection(slopes[i], intercepts[i], slope, intercept);
				intercepts[p] = intercept;
				slopes[p] = slope;
				p++;
				return;
			}
			
			xs[p] = INF;
			intercepts[p] = intercept;
			slopes[p] = slope;
			p++;
		}
		
		public int argmin(int x)
		{
			if(p <= 0)return -1;
			int ind = Arrays.binarySearch(xs, 0, p, x);
			if(ind < 0)ind = -ind-2;
			return ind;
		}
		
		public long min(long x)
		{
			if(p <= 0)return Long.MIN_VALUE;
			int ind = Arrays.binarySearch(xs, 0, p, x);
			if(ind < 0)ind = -ind-2;
			return f(x, slopes[ind], intercepts[ind]);
		}
	}
	
	
	
	void run() throws Exception
	{
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//		Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
//			@Override
//			public void run() {
//				long s = System.currentTimeMillis();
//				solve();
//				out.flush();
//				if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
//			}
//		};
//		t.start();
//		t.join();
	}
	
	public static void main(String[] args) throws Exception { new F2().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}
	
	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}
	
	private int ni() { return (int)nl(); }
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}
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