CF959E Mahmoud and Ehab and the xor-MST 思维
Ehab is interested in the bitwise-xor operation and the special graphs. Mahmoud gave him a problem that combines both. He has a complete graph consisting of n vertices numbered from 0 to n - 1. For all 0 ≤ u < v < n, vertex u and vertex v are connected with an undirected edge that has weight (where
is the bitwise-xor operation). Can you find the weight of the minimum spanning tree of that graph?
You can read about complete graphs in https://en.wikipedia.org/wiki/Complete_graph
You can read about the minimum spanning tree in https://en.wikipedia.org/wiki/Minimum_spanning_tree
The weight of the minimum spanning tree is the sum of the weights on the edges included in it.
The only line contains an integer n (2 ≤ n ≤ 1012), the number of vertices in the graph.
The only line contains an integer x, the weight of the graph's minimum spanning tree.
4
4
In the first sample: The weight of the minimum spanning tree is 1+2+1=4.
题意翻译
n个点的完全图标号(0-n-1),i和j连边权值为i^j,求MST的值
不妨先手算几项,可以发现每一位上的贡献为当前n 的一半;
#include<iostream> #include<cstdio> #include<algorithm> #include<cstdlib> #include<cstring> #include<string> #include<cmath> #include<map> #include<set> #include<vector> #include<queue> #include<bitset> #include<ctime> #include<deque> #include<stack> #include<functional> #include<sstream> //#include<cctype> //#pragma GCC optimize("O3") using namespace std; #define maxn 300005 #define inf 0x3f3f3f3f #define INF 9999999999 #define rdint(x) scanf("%d",&x) #define rdllt(x) scanf("%lld",&x) #define rdult(x) scanf("%lu",&x) #define rdlf(x) scanf("%lf",&x) #define rdstr(x) scanf("%s",x) typedef long long ll; typedef unsigned long long ull; typedef unsigned int U; #define ms(x) memset((x),0,sizeof(x)) const long long int mod = 1e9 + 7; #define Mod 1000000000 #define sq(x) (x)*(x) #define eps 1e-3 typedef pair<int, int> pii; #define pi acos(-1.0) //const int N = 1005; #define REP(i,n) for(int i=0;i<(n);i++) inline ll rd() { ll x = 0; char c = getchar(); bool f = false; while (!isdigit(c)) { if (c == '-') f = true; c = getchar(); } while (isdigit(c)) { x = (x << 1) + (x << 3) + (c ^ 48); c = getchar(); } return f ? -x : x; } ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a%b); } ll sqr(ll x) { return x * x; } /*ll ans; ll exgcd(ll a, ll b, ll &x, ll &y) { if (!b) { x = 1; y = 0; return a; } ans = exgcd(b, a%b, x, y); ll t = x; x = y; y = t - a / b * y; return ans; } */ ll qpow(ll a, ll b, ll c) { ll ans = 1; a = a % c; while (b) { if (b % 2)ans = ans * a%c; b /= 2; a = a * a%c; } return ans; } int main() { //ios::sync_with_stdio(0); ll n; rdllt(n); ll ans = 0; ll tmp = 1; while (n>1) { ans += tmp * (n >> 1); tmp <<= 1; n -= (n >> 1); // cout << n<<' '<<ans << endl; } cout << ans << endl; return 0; }