結果

問題 No.913 木の燃やし方
ユーザー uwiuwi
提出日時 2019-10-18 23:16:27
言語 Java21
(openjdk 21)
結果
AC  
実行時間 2,252 ms / 3,000 ms
コード長 7,623 bytes
コンパイル時間 4,104 ms
コンパイル使用メモリ 78,804 KB
実行使用メモリ 86,920 KB
最終ジャッジ日時 2023-09-08 02:23:15
合計ジャッジ時間 42,152 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge15
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 41 ms
49,424 KB
testcase_01 AC 41 ms
49,348 KB
testcase_02 AC 40 ms
49,560 KB
testcase_03 AC 94 ms
55,156 KB
testcase_04 AC 99 ms
54,764 KB
testcase_05 AC 103 ms
54,988 KB
testcase_06 AC 93 ms
53,284 KB
testcase_07 AC 81 ms
52,088 KB
testcase_08 AC 1,201 ms
77,720 KB
testcase_09 AC 930 ms
79,340 KB
testcase_10 AC 1,009 ms
81,836 KB
testcase_11 AC 1,067 ms
85,468 KB
testcase_12 AC 1,322 ms
80,848 KB
testcase_13 AC 925 ms
80,888 KB
testcase_14 AC 867 ms
78,612 KB
testcase_15 AC 848 ms
78,184 KB
testcase_16 AC 942 ms
76,204 KB
testcase_17 AC 863 ms
71,884 KB
testcase_18 AC 1,034 ms
73,324 KB
testcase_19 AC 988 ms
81,972 KB
testcase_20 AC 923 ms
78,532 KB
testcase_21 AC 896 ms
82,624 KB
testcase_22 AC 847 ms
81,620 KB
testcase_23 AC 1,141 ms
86,508 KB
testcase_24 AC 911 ms
80,128 KB
testcase_25 AC 1,039 ms
84,456 KB
testcase_26 AC 1,750 ms
82,060 KB
testcase_27 AC 2,252 ms
86,920 KB
testcase_28 AC 1,061 ms
80,044 KB
testcase_29 AC 972 ms
79,624 KB
testcase_30 AC 1,134 ms
83,360 KB
testcase_31 AC 1,145 ms
82,488 KB
testcase_32 AC 1,057 ms
80,380 KB
testcase_33 AC 912 ms
80,616 KB
testcase_34 AC 1,140 ms
80,648 KB
testcase_35 AC 1,149 ms
80,588 KB
testcase_36 AC 951 ms
82,344 KB
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ソースコード

diff # 

package contest191018;
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 F {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		// 左a, 右b
		// (a+b+1)^2 + sa+sb+mine
		// a^2+b^2+1+2a+2b+2ab+sa+sb+mine
		// a^2+1+2a+sa+mine + b^2+2b + 2ab + sb
		
		int n = ni();
		long[] a = new long[n];
		for(int i = 0;i < n;i++) {
			a[i] = nl();
		}
		ans = new long[n];
		vals = new long[n];
		Arrays.fill(ans, Long.MAX_VALUE);
		
		dfs(0, n, a);
		
		for(long v : ans) {
			out.println(v);
		}
	}
	
	long[] ans;
	long[] vals;
	
	void dfs(int l, int r, long[] a)
	{
		if(r-l == 1) {
			ans[l] = Math.min(ans[l], a[l]+1);
			return;
		}
		
		int h = l+r>>1;
		{
			long sum = 0;
//			EnvelopeLinear el = new EnvelopeLinear(r-h+1);
			EnvelopeLinearDeque el = new EnvelopeLinearDeque(r-h+1);
			long[][] si = new long[r-h][];
			int p = 0;
			for(int i = h;i < r;i++) {
				sum += a[i];
				si[p++] = new long[] {2L*(i-h+1), (long)(i-h+1)*(i-h+1) + sum};
			}
			for(int i = p-1;i >= 0;i--) {
				el.add(si[i][0], si[i][1]);
			}
			// (l+r)^2 + sl + sr
			// r^2 + 2lr + l^2
			
			sum = 0;
			for(int i = h-1;i >= l;i--) {
				sum += a[i];
				long val = sum + (long)(h-i)*(h-i) + el.get(h-i);
				vals[i] = val;
			}
			for(int i = l+1;i < h;i++) {
				vals[i] = Math.min(vals[i], vals[i-1]);
			}
			for(int i = l;i < h;i++) {
				ans[i] = Math.min(ans[i], vals[i]);
			}
		}
		{
			long sum = 0;
//			EnvelopeLinear el = new EnvelopeLinear(h-l);
			EnvelopeLinearDeque el = new EnvelopeLinearDeque(h-l);
			long[][] si = new long[h-l][];
			int p = 0;
			for(int i = h-1;i >= l;i--) {
				sum += a[i];
				si[p++] = new long[] {2L*(h-i), (long)(h-i)*(h-i) + sum};
			}
			for(int i = p-1;i >= 0;i--) {
				el.add(si[i][0], si[i][1]);
			}
			// (l+r)^2 + sl + sr
			// r^2 + 2lr + l^2
			
			sum = 0;
			for(int i = h;i < r;i++) {
				sum += a[i];
				long val = sum + (long)(i-h+1)*(i-h+1) + el.get(i-h+1);
				vals[i] = val;
			}
			for(int i = r-2;i >= h;i--) {
				vals[i] = Math.min(vals[i], vals[i+1]);
			}
			for(int i = r-1;i >= h;i--) {
				ans[i] = Math.min(ans[i], vals[i]);
			}
		}
		dfs(l, h, a);
		dfs(h, r, a);
	}
	
	public static class EnvelopeLinearDeque {
		public long[] slopes, intercepts;
		public int f, b;
		
		public EnvelopeLinearDeque(int n)
		{
			slopes = new long[n];
			intercepts = new long[n];
			f = b = 0;
		}
		
		public long f(long x, int ind)
		{
			return slopes[ind]*x+intercepts[ind];
		}
		
		public double f(double x, int ind)
		{
			return slopes[ind]*x+intercepts[ind];
		}
		
		public boolean strictLesser(int a, int b, long num, long den)
		{
			double x = (double)num/den;
			double cha = f(x, a) - f(x, b);
			if(Math.abs(cha) < 1e-9){
				return (slopes[a]*num+intercepts[a]*den) - (slopes[b]*num+intercepts[b]*den) < 0;
			}else{
				return cha < 0;
			}
		}
		
		public long get(long x)
		{
			while(f-b > 1 && f(x, b) > f(x, b+1))b++;
			return f(x, b);
		}
			
		public void add(long slope, long intercept)
		{
			if(f-b > 0)assert slope <= slopes[f-1];
			if(f-b > 0 && slope == slopes[f-1] && intercept >= intercepts[f-1])return;
			
			// sl*x+in = lsl*x+lin
			// (sl-lsl)*x = lin-in
			while(f-1-b > 0 && strictLesser(f-2, f-1, intercept-intercepts[f-1], slopes[f-1] - slope)){
				f--;
			}
			slopes[f] = slope;
			intercepts[f] = intercept;
			f++;
		}
	}

	
	public static class EnvelopeLinear {
		public static final long INF = Long.MIN_VALUE;
		
		public long[] xs;
		public long[] intercepts, slopes;
		public int p;
		
		public EnvelopeLinear(int n)
		{
			xs = new long[n];
			intercepts = new long[n];
			slopes = new long[n];
			p = 0;
		}
		
		public void clear()
		{
			p = 0;
		}
		
		public void add(long slope, long intercept)
		{
			assert p == 0 || slopes[p-1] >= slope;
			while(p > 0){
				int i = p-1;
				if(p > 1 && intercept+xs[i]*slope <= intercepts[i]+xs[i]*slopes[i]){ // x=xs[i]
					p--;
					continue;
				}
				if(slope == slopes[i]){
					if(intercept >= intercepts[i]){
						return;
					}else{
						p--;
						continue;
					}
				}
				// y=sx+i vs y=Sx+I
				// sx+i=Sx+I
				// x=(i-I)/(S-s)
				long num = intercept-intercepts[i];
				long den = slopes[i]-slope;
				long nx = num < 0 ? num/den : (num+den-1)/den;
				xs[p] = nx;
				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 slopes[ind]*x + 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 F().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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