CF 702B Powers of Two（暴力）

题目链接: 传送门

Devu and Partitioning of the Array

time limit per test:3 second     memory limit per test:256 megabytes

Description

You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2^x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 10^5) — the number of integers.
The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 10^9).

Output

Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.

Sample Input

4
7 3 2 1

3
1 1 1

Sample Output

2

3

解题思路

注意到2^31次方就能达到10^9级别，所以枚举的时候枚举2的幂次方而不是枚举N，枚举N果断超时。

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<map>
using namespace std;
typedef __int64 LL;
int main()
{
    int N;
    while (~scanf("%d",&N))
    {
        LL tmp,res = 0;
        map<LL,LL>mp;
        for (int i = 0;i < N;i++)
        {
            scanf("%I64d",&tmp);
            for (int j = 1;j < 32;j++)
            {
                if (mp.find((1<<j)-tmp) != mp.end())
                {
                    res += mp[(1<<j)-tmp];
                }
            }
            mp[tmp]++;
        }
        printf("%I64d\n",res);
    }
    return 0;
}