分治问题CodeForces768B大数

xiaoxiao2021-02-28  3

分治的思想,二分法,采用BigInteger解决大数 Jon fought bravely to rescue the wildlings who were attacked by the white-walkers at Hardhome. On his arrival, Sam tells him that he wants to go to Oldtown to train at the Citadel to become a maester, so he can return and take the deceased Aemon’s place as maester of Castle Black. Jon agrees to Sam’s proposal and Sam sets off his journey to the Citadel. However becoming a trainee at the Citadel is not a cakewalk and hence the maesters at the Citadel gave Sam a problem to test his eligibility.

Initially Sam has a list with a single element n. Then he has to perform certain operations on this list. In each operation Sam must remove any element x, such that x > 1, from the list and insert at the same position , , sequentially. He must continue with these operations until all the elements in the list are either 0 or 1.

Now the masters want the total number of 1s in the range l to r (1-indexed). Sam wants to become a maester but unfortunately he cannot solve this problem. Can you help Sam to pass the eligibility test?

Input

The first line contains three integers n, l, r (0 ≤ n < 250, 0 ≤ r - l ≤ 105, r ≥ 1, l ≥ 1) – initial element and the range l to r.

It is guaranteed that r is not greater than the length of the final list.

Output

Output the total number of 1s in the range l to r in the final sequence.

Example

Input 7 2 5 Output 4 Input 10 3 10 Output 5

import java.math.BigInteger; import java.util.Scanner; import java.util.regex.Matcher; /** * Created by 95112 on 10/21/2017. */ public class TwoPoint { private static long sum = 1; private static BigInteger ans; static BigInteger two; public static void main(String[] args) { Scanner scanner = new Scanner(System.in); ans = new BigInteger("0"); BigInteger n = new BigInteger(scanner.next()); BigInteger l = new BigInteger(scanner.next()); BigInteger r = new BigInteger(scanner.next()); BigInteger x = new BigInteger("1"); BigInteger y = new BigInteger("1"); BigInteger tmp = n.add(new BigInteger("0")); two = new BigInteger("2"); while (tmp.compareTo(x) == 1) { tmp = tmp.divide(two); y = y.multiply(two).add(x); } solve(x,y,l,r,n); System.out.println(ans.toString()); } private static void solve(BigInteger x,BigInteger y , BigInteger l , BigInteger r , BigInteger n){ if (x.compareTo(y) == 1 || l.compareTo(r) == 1) return; BigInteger mid = x.add(y).divide(two); if ( mid.compareTo(l) == -1 ) solve(mid.add(BigInteger.ONE),y,l,r,n.divide(two)); else if (mid.compareTo(r) == 1) solve(x,mid.subtract(BigInteger.ONE),l,r,n.divide(two)); else { ans = ans.add(n.mod(two)); solve(mid.add(BigInteger.ONE),y,mid.add(BigInteger.ONE),r,n.divide(two)); solve(x,mid.subtract(BigInteger.ONE),l,mid.subtract(BigInteger.ONE),n.divide(two)); } } }
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