USACO 1.4.3 —— 暴搜
An arithmetic progression is a sequence of the form a, a+b, a+2b, ..., a+nb where n=0,1,2,3,... . For this problem, a is a non-negative integer and b is a positive integer.
Write a program that finds all arithmetic progressions of length n in the set S of bisquares. The set of bisquares is defined as the set of all integers of the form p2 + q2 (where p and q are non-negative integers).
TIME LIMIT: 5 secs
PROGRAM NAME: ariprog
INPUT FORMAT
| Line 1: | N (3 <= N <= 25), the length of progressions for which to search |
| Line 2: | M (1 <= M <= 250), an upper bound to limit the search to the bisquares with 0 <= p,q <= M. |
SAMPLE INPUT (file ariprog.in)
5 7
OUTPUT FORMAT
If no sequence is found, a singe line reading `NONE'. Otherwise, output one or more lines, each with two integers: the first element in a found sequence and the difference between consecutive elements in the same sequence. The lines should be ordered with smallest-difference sequences first and smallest starting number within those sequences first.
There will be no more than 10,000 sequences.
SAMPLE OUTPUT (file ariprog.out)
1 4 37 4 2 8 29 8 1 12 5 12 13 12 17 12 5 20 2 24
/*
ID: XMzhou
LANG: C++
TASK: ariprog
*/
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <map>
#include <string>
#include <stack>
#include <cctype>
#include <vector>
#include <queue>
#include <set>
#include <utility>
#include <cassert>
using namespace std;
#define Online_Judge
#define outstars cout << "***********************" << endl;
#define clr(a,b) memset(a,b,sizeof(a))
#define lson l , mid , rt << 1
#define rson mid + 1 , r , rt << 1 | 1
#define mk make_pair
#define FOR(i , x , n) for(int i = (x) ; i < (n) ; i++)
#define FORR(i , x , n) for(int i = (x) ; i <= (n) ; i++)
#define REP(i , x , n) for(int i = (x) ; i > (n) ; i--)
#define REPP(i ,x , n) for(int i = (x) ; i >= (n) ; i--)
const int MAXN = 250 + 50;
const int MAXS = 10000 + 50;
const int sigma_size = 26;
const long long LLMAX = 0x7fffffffffffffffLL;
const long long LLMIN = 0x8000000000000000LL;
const int INF = 0x7fffffff;
const int IMIN = 0x80000000;
const int inf = 1 << 30;
#define eps 1e-10
const long long MOD = 1000000000 + 7;
const int mod = 10007;
typedef long long LL;
const double PI = acos(-1.0);
typedef double D;
typedef pair<int , int> pii;
typedef vector<int> vec;
typedef vector<vec> mat;
#define Bug(s) cout << "s = " << s << endl;
///#pragma comment(linker, "/STACK:102400000,102400000")
int bisquares[2 * MAXN * MAXN];
int a[2 * MAXN *MAXN];
int n , m;
vector <pair <int, int > > path;
void creat_bisquares()
{
for(int i = 0; i <= m ; i++)
{
for(int j = i ; j <= m ; j++)
{
bisquares[i * i + j * j] = 1;
}
}
}
int main()
{
//ios::sync_with_stdio(false);
#ifdef Online_Judge
freopen("ariprog.in","r",stdin);
freopen("ariprog.out","w",stdout);
#endif // Online_Judge
while(~scanf("%d%d" , &n , &m))
{
clr(bisquares , 0);
creat_bisquares();
int num = 0;
for(int i = 0 ; i <= 2 * m * m ; i++)
{
if(bisquares[i])a[num++] = i;
}
// for(int i = 0 ; i < num ; i++)cout << "a[i] = " << a[i] << endl;
for(int i = 0 ; i < num ; i++)
{
for(int j = i + 1; j < num ; j++)
{
int d = a[j] - a[i];
if(a[i] + (n - 1) * d > 2 * m * m)break;
int ok = 1;
for(int k = 2 ; k < n ; k++)
{
if(!bisquares[a[i] + k * d])
{
ok = 0;
break;
}
}
if(ok)path.push_back(mk(d , a[i]));
}
}
sort(path.begin() , path.end());
if(path.size() == 0)puts("NONE");
else for(int i = 0 ; i < path.size() ; i++)
{
printf("%d %d\n" , path[i].second , path[i].first);
}
}
return 0;
}