結果

問題 No.907 Continuous Kadomatu
ユーザー uwiuwi
提出日時 2019-10-11 22:30:43
言語 Java21
(openjdk 21)
結果
AC  
実行時間 1,455 ms / 2,000 ms
コード長 6,108 bytes
コンパイル時間 4,059 ms
コンパイル使用メモリ 83,092 KB
実行使用メモリ 304,912 KB
最終ジャッジ日時 2024-11-25 08:22:19
合計ジャッジ時間 19,374 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
このコードへのチャレンジ
（要ログイン）

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 53 ms
38,944 KB
testcase_01 AC 53 ms
38,716 KB
testcase_02 AC 51 ms
38,468 KB
testcase_03 AC 51 ms
38,912 KB
testcase_04 AC 52 ms
38,688 KB
testcase_05 AC 273 ms
65,732 KB
testcase_06 AC 54 ms
39,124 KB
testcase_07 AC 128 ms
47,556 KB
testcase_08 AC 215 ms
56,580 KB
testcase_09 AC 153 ms
50,928 KB
testcase_10 AC 389 ms
81,552 KB
testcase_11 AC 470 ms
107,264 KB
testcase_12 AC 939 ms
195,560 KB
testcase_13 AC 1,054 ms
201,892 KB
testcase_14 AC 1,193 ms
255,820 KB
testcase_15 AC 1,104 ms
225,904 KB
testcase_16 AC 1,164 ms
251,332 KB
testcase_17 AC 1,248 ms
270,664 KB
testcase_18 AC 1,177 ms
253,076 KB
testcase_19 AC 1,182 ms
268,788 KB
testcase_20 AC 58 ms
38,064 KB
testcase_21 AC 71 ms
39,876 KB
testcase_22 AC 75 ms
40,100 KB
testcase_23 AC 1,297 ms
304,912 KB
testcase_24 AC 1,455 ms
287,888 KB
testcase_25 AC 51 ms
36,896 KB
testcase_26 AC 53 ms
36,852 KB
testcase_27 AC 52 ms
37,168 KB
testcase_28 AC 51 ms
37,064 KB
testcase_29 AC 53 ms
36,724 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 # 

package contest1910;
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 E {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	int mod = 1000000007;

	void solve()
	{
		// a1 b1
		// a3 b3
		// \int_{a2^b2} (x-a1)/(b1-a1)*(x-a3)*(b3-a3) dx
		//  = abx-ax^2/2-bx^2/2+x^3/3
		// (x-1)/3*(x-1)/2 7/18*(7/18+5/6)/2
		
		// (\int_{a2^min(b1,b2)} (x-a1)/(b1-a1) dx
		//  + \int_{min(b1,b2)^b2} 1 dx) / (b2-a2)
		
		// \int_{ } p(x)dx
		
		int n = ni();
		int[] a = new int[n];
		int[] b = new int[n];
		for(int i = 0;i < n;i++) {
			a[i] = ni();
			b[i] = ni();
		}
		
		int[] ys = new int[2*n];
		for(int i = 0;i < n;i++) {
			ys[i] = a[i];
			ys[i+n] = b[i];
		}
		Arrays.sort(ys);
		ys = uniq(ys);
		
		int m = ys.length-1;
		long[][][] dp = new long[n][m][n+1];
		for(int j = 0;j < m;j++) {
			if(a[0] <= ys[j] && ys[j+1] <= b[0]) {
				dp[0][j][0] = invl(b[0] - a[0], mod);
			}
		}
		
		// 1/4*x-1/4
		// 3/8 - (1/8*x^2-1/4*x)
		// -1/8*x^2 + 1/4*x + 3/8
		for(int i = 1;i < n;i++) {
			if(i % 2 == 1) {
				long cum = 0;
				long il = invl(b[i]-a[i], mod);
				for(int j = 0;j < m;j++) {
					// \int_{inf^y} p(x)dx
					long[] ip = i(dp[i-1][j]);
					for(int k = 0;k < ip.length;k++) {
						ip[k] = ip[k] * il % mod;
					}
					long ipinf = sub(ip, ys[j]);
					long ipsup = sub(ip, ys[j+1]);
					ip[0] += mod - ipinf;
					ip[0] += cum;
					ip[0] %= mod;
					if(a[i] <= ys[j] && ys[j+1] <= b[i]) {
						dp[i][j] = ip;
					}
					
					cum += ipsup - ipinf;
					cum %= mod;
					if(cum < 0)cum += mod;
				}
			}else {
				long cum = 0;
				long il = invl(b[i]-a[i], mod);
				for(int j = m-1;j >= 0;j--) {
					// \int_{y^sup} p(x)dx
					long[] ip = i(dp[i-1][j]);
					for(int k = 0;k < ip.length;k++) {
						ip[k] = ip[k] * il % mod;
					}
					long ipinf = sub(ip, ys[j]);
					long ipsup = sub(ip, ys[j+1]);
					for(int k = 0;k < n+1;k++) {
						ip[k] = mod-ip[k];
					}
					ip[0] += ipsup;
					ip[0] += cum;
					ip[0] %= mod;
					if(a[i] <= ys[j] && ys[j+1] <= b[i]) {
						dp[i][j] = ip;
					}
					
					cum += ipsup - ipinf;
					cum %= mod;
					if(cum < 0)cum += mod;
				}
			}
		}
		
		long ans = 0;
		for(int j = 0;j < m;j++) {
			ans += sub(i(dp[n-1][j]), ys[j+1]);
			ans += mod - sub(i(dp[n-1][j]), ys[j]);
		}
		out.println(ans%mod);
	}
	
	int[] invs = enumInvs(1000, mod);
	
	long[] i(long[] a)
	{
		long[] b = new long[a.length];
		for(int i = 1;i < a.length;i++) {
			b[i] = a[i-1] * invs[i] % mod;
		}
		return b;
	}
	
	long sub(long[] a, long x)
	{
		long v = 0;
		for(int i = a.length-1;i >= 0;i--) {
			v = v * x + a[i];
			v %= mod;
		}
		return v;
	}
	
	public static int[] enumInvs(int n, int mod) {
		int[] inv = new int[n + 1];
		inv[1] = 1;
		for (int i = 2; i <= n; i++) {
			inv[i] = (int) (inv[mod % i] * (long) (mod - mod / i) % mod);
		}
		return inv;
	}

	
	public static int[] uniq(int[] a)
	{
		int n = a.length;
		int p = 0;
		for(int i = 0;i < n;i++) {
			if(i == 0 || a[i] != a[i-1])a[p++] = a[i];
		}
		return Arrays.copyOf(a, p);
	}

	
	public static long invl(long a, long mod) {
		long b = mod;
		long p = 1, q = 0;
		while (b > 0) {
			long c = a / b;
			long d;
			d = a;
			a = b;
			b = d % b;
			d = p;
			p = q;
			q = d - c * q;
		}
		return p < 0 ? p + mod : p;
	}

	
	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 E().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)); }
}
0