CF 1583F(Defender of Childhood Dreams-构造)

Posted 2021-11-07 nike0good

给一个$n\le 1000$个点有向完全图($i$向$j$连边,$i<j$)
求一个合法边染色使得所有长度为$k$的路径存在至少$2$种颜色。

把所有点分成若干大小为$k$的集合，每个集合连同一种颜色边，则其余边必须连除此以外的颜色

考虑把所有点按$0,\cdots ,n-1$编号，2个点之间连它们$k$进制下第一个相同的位置

#include<bits/stdc++.h> 
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define ForkD(i,k,n) for(int i=n;i>=k;i--)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i>0;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])  
#define Lson (o<<1)
#define Rson ((o<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,0x3f,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define MEMx(a,b) memset(a,b,sizeof(a));
#define INF (0x3f3f3f3f)
#define F (1000000007)
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define vi vector<int> 
#define pi pair<int,int>
#define SI(a) ((a).size())
#define Pr(kcase,ans) printf("Case #%d: %lld\\n",kcase,ans);
#define PRi(a,n) For(i,n-1) cout<<a[i]<<' '; cout<<a[n]<<endl;
#define PRi2D(a,n,m) For(i,n) { \\
						For(j,m-1) cout<<a[i][j]<<' ';\\
						cout<<a[i][m]<<endl; \\
						} 
#pragma comment(linker, "/STACK:102400000,102400000")
#define ALL(x) (x).begin(),(x).end()
#define gmax(a,b) a=max(a,b);
#define gmin(a,b) a=min(a,b);
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return ((a-b)%F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
inline int read()
{
	int x=0,f=1; char ch=getchar();
	while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}
	while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();}
	return x*f;
} 
#define MAXN (312345)
int n,k;
int lowbit(int i,int j) {
	int ans=0; 
	while(i!=j)i/=k,j/=k,++ans;
	return ans;
}
int main()
{
//	freopen("f.in","r",stdin);
//	freopen(".out","w",stdout);
//  cin.tie(0)->sync_with_stdio(0); 
	n=read(),k=read();
	vi v;
	For(i,n) {
		Fork(j,i+1,n) {
			v.pb(lowbit(i-1,j-1));
		}
	}
	cout<<*max_element(v.begin(),v.end())<<endl;
	for(int i:v) cout<<i<<' ';
	return 0;
}