結果
| 問題 |
No.907 Continuous Kadomatu
|
| ユーザー |
 uwi
|
| 提出日時 | 2019-10-11 22:30:43 |
| 言語 | Java (openjdk 23) |
| 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 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 25 |
ソースコード
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)); }
}