Acdreamoj1115(数学思维称号)

意甲冠军:1,3是完美的数,假定a,b是完美的数,然后,2+a*b+2*a+2*b,结论认为,n无论是完美的数字。


解法:開始仅仅看出来2+a*b+2*a+2*b=(a+2)*(b+2)-2,没推出很多其它结论,囧。没办法,仅仅能暴力将全部的完美数求出来然后查表。正解是c+2=(a+2)*(b+2);完美数都是有质因子3或5组成的(5本身除外);


自己暴力代码:

/******************************************************
* author:xiefubao
*******************************************************/
#pragma comment(linker, "/STACK:102400000,102400000")
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <queue>
#include <vector>
#include <algorithm>
#include <cmath>
#include <map>
#include <set>
#include <stack>
#include <string.h>
//freopen ("in.txt" , "r" , stdin);
using namespace std;

#define eps 1e-8
#define zero(_) (abs(_)<=eps)
const double pi=acos(-1.0);
typedef long long LL;
const int Max=1010;
const int INF=1000000000;

LL num[Max];
int help[Max];
LL get(int l,int r)
{
    return 2*(num[l]+1)*(num[r]+1)-num[l]*num[r];
}
struct point
{
    LL ans;
    int h;
};
bool operator<(const point& a,const point& b)
{
    return a.ans>b.ans;
}
priority_queue<point> pri;
int main()
{
    num[0]=1;
    num[1]=3;
    point p;
    p.ans=7;
    p.h=0;
    pri.push(p);
    p.ans=23;
    p.h=1;
    pri.push(p);
    for(int i=0; i<Max; i++)
        help[i]=i;
    help[0]=1;
    help[1]=2;
    int po=2;
    while(pri.top().ans<=INF)
    {
        point ptop=pri.top();
        pri.pop();
        if(num[po-1]==ptop.ans)
        {
            point p;
            p.ans=get(ptop.h,help[ptop.h]);
            p.h=ptop.h;
            pri.push(p);
            help[ptop.h]++;
            continue;
        }
        point p;
        p.ans=get(ptop.h,help[ptop.h]);
        p.h=ptop.h;
        pri.push(p);
        help[ptop.h]++;
       // cout<<ptop.ans<<" ";
        num[po++]=ptop.ans;

        p.ans=get(po-1,po-1);
        p.h=po-1;
        pri.push(p);
        help[po-1]=po;
    }
    int t;
    while(scanf("%d",&t)==1)
    {
        if(binary_search(num,num+po,t))
            puts("Yes");
        else
            puts("No");
    }
    return 0;
}

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posted @ 2015-10-17 12:27  zfyouxi  阅读(206)  评论(0编辑  收藏  举报