Codeforces Round #144 (Div. 2) C. Cycles

http://codeforces.com/contest/233/problem/C

题意：求一个具有k个三元环的无向图。

分析：先一个i个节点的无向完全图，其中C(i,3)<=k,剩下k-C(i,3)个三元环未构成，再加j条边（C(j,2)<=未构成的环）直到满足条件。

/*
Author:Zhaofa Fang
Lang:C++
*/
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <string>
#include <utility>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
using namespace std;
typedef long long ll;
#define pii pair<int,int>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define lowbit(x) (x&(-x))
#define INF (1<<30)

int maz[105][105];
int main()
{
    #ifndef ONLINE_JUDGE
    freopen("in","r",stdin);
    #endif
    int K;
    while(cin>>K)
    {
        memset(maz,0,sizeof(maz));
        int i;
        for(i=3;i*(i-1)*(i-2)/6<=K;i++);
        i--;
        K -= i*(i-1)*(i-2)/6;
        for(int j=0;j<i;j++)
            for(int k=0;k<i;k++)
                maz[j][k] = (j != k);
        int n=i;
        while(K)
        {
            int j;
            for(j=2;j*(j-1)/2<=K;j++);
            j--;
            for(int k=0;k<j;k++)maz[n][k] = maz[k][n] = 1;
            K -= (j-1)*j/2;
            n++;
        }
        cout<<n<<endl;
        for(int x=0;x<n;x++)
        {
            for(int y=0;y<n;y++)
            printf("%d",maz[x][y]);
            puts("");
        }
    }
    return 0;
}