B. Make Array Good【二进制构造】

B. Make Array Good

https://codeforces.com/problemset/problem/1762/B

思路

将不是 $2^{n} (n > 0)$ 的数构造成最小的一个大于 $a [i]$ 的 $2^{n}$ ，
证明：

a [i]_{n e w} = 2^{n} = a [i] + x (0 \leq x \leq a [i])

a [i] > 2^{n - 1}

x = 2^{n} - a [i] < 2^{n} - 2^{n - 1} = 2^{n - 1} < a [i]

代码

点击查看代码

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<vector>
#include<queue>
#include<cctype>
using namespace std;

#define X first
#define Y second

typedef pair<int,int> pii;
typedef long long LL;
const char nl = '\n';
const int N = 1e5+10;
const int M = 2e5+10;
int a[N];

void solve(){
	int t;
	cin >> t;
	while(t -- ){
		int n;
		cin >> n;
		vector<pair<int,LL>> v;
		for(int i = 1; i <= n; i ++ ){
			cin >> a[i];
			if(__builtin_popcount(a[i]) != 1 && a[i] != 1){
				v.push_back({i,(1ll << (32 - __builtin_clz(a[i]))) - a[i]});
			}
		}
		cout << v.size() << nl;
		for(auto u:v){
			cout << u.X << " " << u.Y << nl;
		}
	}
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0),cout.tie(0);

	solve();
}