#266103 (Java21) No.705 ゴミ拾い Hard

• 問題: No.705 ゴミ拾い Hard
• ユーザー: uwi
• 提出日時: 2018-06-15 23:21:16
• 言語: Java21 (openjdk 21)
• 結果: AC
• 実行時間: 282 ms / 1,500 ms
• コード長: 4,993 bytes
• コンパイル時間: 3,780 ms
• コンパイル使用メモリ: 82,368 KB
• 実行使用メモリ: 65,848 KB
• 最終ジャッジ日時: 2023-09-13 05:17:24
• 合計ジャッジ時間: 12,007 ms
• ジャッジサーバーID （参考情報）: judge12 / judge15

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	41 ms; 49,544 KB
testcase_01	AC	42 ms; 49,380 KB
testcase_02	AC	41 ms; 49,380 KB
testcase_03	AC	41 ms; 49,384 KB
testcase_04	AC	42 ms; 49,328 KB
testcase_05	AC	40 ms; 47,420 KB
testcase_06	AC	41 ms; 49,356 KB
testcase_07	AC	39 ms; 49,308 KB
testcase_08	AC	41 ms; 49,476 KB
testcase_09	AC	42 ms; 49,468 KB
testcase_10	AC	41 ms; 49,452 KB
testcase_11	AC	41 ms; 49,392 KB
testcase_12	AC	41 ms; 49,380 KB
testcase_13	AC	42 ms; 49,560 KB
testcase_14	AC	53 ms; 50,308 KB
testcase_15	AC	55 ms; 50,436 KB
testcase_16	AC	52 ms; 50,584 KB
testcase_17	AC	56 ms; 50,308 KB
testcase_18	AC	53 ms; 50,400 KB
testcase_19	AC	53 ms; 50,480 KB
testcase_20	AC	53 ms; 50,404 KB
testcase_21	AC	53 ms; 50,236 KB
testcase_22	AC	54 ms; 50,884 KB
testcase_23	AC	55 ms; 50,836 KB
testcase_24	AC	274 ms; 65,396 KB
testcase_25	AC	280 ms; 65,272 KB
testcase_26	AC	269 ms; 65,488 KB
testcase_27	AC	282 ms; 65,560 KB
testcase_28	AC	282 ms; 65,328 KB
testcase_29	AC	274 ms; 65,848 KB
testcase_30	AC	274 ms; 65,480 KB
testcase_31	AC	256 ms; 65,740 KB
testcase_32	AC	279 ms; 65,732 KB
testcase_33	AC	211 ms; 65,572 KB
testcase_34	AC	207 ms; 65,800 KB
testcase_35	AC	270 ms; 65,392 KB
testcase_36	AC	282 ms; 65,660 KB
testcase_37	AC	213 ms; 65,836 KB
testcase_38	AC	234 ms; 65,524 KB
testcase_39	AC	275 ms; 65,556 KB
testcase_40	AC	41 ms; 49,352 KB
testcase_41	AC	40 ms; 49,356 KB
testcase_42	AC	39 ms; 49,448 KB
testcase_43	AC	222 ms; 65,484 KB

ソースコード

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)); }
}