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D. Little Girl and Maximum XOR(贪心)

时间:2015-04-10 09:40:40      阅读:147      评论:0      收藏:0      [点我收藏+]

标签:贪心

D. Little Girl and Maximum XOR

A little girl loves problems on bitwise operations very much. Here‘s one of them.

You are given two integers l and r. Let‘s consider the values of 技术分享 for all pairs of integers a and b (l?≤?a?≤?b?≤?r). Your task is to find the maximum value among all considered ones.

Expression 技术分享 means applying bitwise excluding or operation to integers x and y. The given operation exists in all modern programming languages, for example, in languages C++ and Java it is represented as "^", in Pascal — as ?xor?.

Input

The single line contains space-separated integers l and r (1?≤?l?≤?r?≤?1018).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

In a single line print a single integer — the maximum value of 技术分享 for all pairs of integers a, b (l?≤?a?≤?b?≤?r).

Sample test(s)
Input
1 2
Output
3
Input
8 16
Output
31
Input
1 1
Output
0

题意: 在区间[l,r]中找出两个数a,b(a <= b),使得a ^ b达到最大;

题解:(1) 首先有这样一个现象,当2 ^ n <= r的n达到最大时,且2 ^ n - 1 >= l ,答案是(2 ^ n + 2 ^ n - 1),即其二进制数全部为一,且为异或的最大值,没法再大,因为2 ^ n已达到
极限; 另一种情况是当2^n < l 时就贪心处理. 从高位往低位枚举,对于当前为如果二进制数为1,比l还小的话,则置为1,如果当前值大于r的话,则置为0; 否则则后面的位符合
(1)说法;

AC代码:
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <bitset>
#include <algorithm>
#include <vector>

#define lson l,mid,u << 1
#define rson mid + 1,r,u << 1 | 1
#define ls u << 1
#define rs u << 1 | 1
#define exp 1e-8

using namespace std;
typedef long long ll;

int main() {
    ll l,r;
    while(cin>>l>>r) {
        ll maxn = 0;
        if(l == r) {
            puts("0");
            continue;
        }
        ll i = 0,ans;
        while(true) {
            ans = 1LL << i;
            if(ans > r) {
                ans = 1LL << (i - 1);
                break;
            }
            i++;
        }
        i--;
        if(ans >= l && ans - 1 >= l) {
            cout<<ans + ans - 1<<endl;
        } else {
            while(true) {
                ll res = ans + (1LL << (i - 1));
                if(res <= l) ans += 1LL << (i - 1);
                else if(res <= r){
                    ans = 0;
                    for(ll j = 0; j < i; j++) {
                        ans += 1LL << j;
                    }
                    break;
                }
                i--;
            }
            cout<<ans<<endl;
        }
    }
    return 0;
}


D. Little Girl and Maximum XOR(贪心)

标签:贪心

原文地址:http://blog.csdn.net/zsgg_acm/article/details/44967663

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