题目
题意:
x & y = a
x + y = s
判断是否存在非负整数x、y满足条件
思路: 首先考虑到两个数至少都是a,s >= 2 *a.
先假定x和y都是a,然后去凑s-2 * a剩余位置。如果剩余位置在a中出现过,那寄了,因为这一位用过。
s >= 2 * a and ( (s-2 *a) & a) == 0
或者特殊一点,x = a,y = s-a. x & y == a
时间复杂度: O(1)
代码:
// Problem: D - AND and SUM // Contest: AtCoder - Monoxer Programming Contest 2022(AtCoder Beginner Contest 238) // URL: https://atcoder.jp/contests/abc238/tasks/abc238_d // Memory Limit: 1024 MB // Time Limit: 2000 ms // // Powered by CP Editor (https://cpeditor.org) #include<iostream> #include<cstdio> #include<algorithm> #include<complex> #include<cstring> #include<cmath> #include<vector> #include<map> #include<unordered_map> #include<list> #include<set> #include<queue> #include<stack> #define OldTomato ios::sync_with_stdio(false),cin.tie(nullptr),cout.tie(nullptr) #define fir(i,a,b) for(int i=a;i<=b;++i) #define mem(a,x) memset(a,x,sizeof(a)) #define p_ priority_queue // round() 四舍五入 ceil() 向上取整 floor() 向下取整 // lower_bound(a.begin(),a.end(),tmp,greater<ll>()) 第一个小于等于的 // #define int long long //QAQ using namespace std; typedef complex<double> CP; typedef pair<int,int> PII; typedef long long ll; // typedef __int128 it; const double pi = acos(-1.0); const int INF = 0x3f3f3f3f; const ll inf = 1e18; const int N = 2e5+10; const int M = 1e6+10; const int mod = 1e9+7; const double eps = 1e-6; inline int lowbit(int x){ return x&(-x);} template<typename T>void write(T x) { if(x<0) { putchar('-'); x=-x; } if(x>9) { write(x/10); } putchar(x%10+'0'); } template<typename T> void read(T &x) { x = 0;char ch = getchar();ll f = 1; while(!isdigit(ch)){if(ch == '-')f*=-1;ch=getchar();} while(isdigit(ch)){x = x*10+ch-48;ch=getchar();}x*=f; } int n,m,k,T; void solve() { ll a,s; read(a),read(s); if(s >= 2*a && ( ((s-2*a)&a) == 0) ) puts("Yes"); else puts("No"); // if(((s-a)&a) == a) puts("Yes"); // else puts("No"); } signed main(void) { // T = 1; // OldTomato; cin>>T; read(T); while(T--) { solve(); } return 0; }