UVA 1587 Box

题目链接：https://vjudge.net/problem/UVA-1587

题目翻译摘自《算法禁赛入门经典》

题目大意

　　给定 6 个矩形的长和宽，判断他们能否构成长方体。

分析

　　设不同的矩形有 a 种，不同的长或宽有 b 种。

　　首先每一种矩形只能出现偶数次；其次，a == b 且 a <= 3。

　　然后就可以分情况讨论了。

1. a == 1，一定可以。
2. a == 2，只要这两种矩形不全是正方形即可。
3. a == 3，三种矩形中不能有正方形。

代码如下

#include <bits/stdc++.h>
using namespace std;
 
#define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define Rep(i,n) for (int i = 0; i < (n); ++i)
#define For(i,s,t) for (int i = (s); i <= (t); ++i)
#define rFor(i,t,s) for (int i = (t); i >= (s); --i)
#define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
#define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
#define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
#define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 
#define pr(x) cout << #x << " = " << x << "  "
#define prln(x) cout << #x << " = " << x << endl
 
#define LOWBIT(x) ((x)&(-x))
 
#define ALL(x) x.begin(),x.end()
#define INS(x) inserter(x,x.begin())
 
#define ms0(a) memset(a,0,sizeof(a))
#define msI(a) memset(a,inf,sizeof(a))
#define msM(a) memset(a,-1,sizeof(a))

#define MP make_pair
#define PB push_back
#define ft first
#define sd second
 
template<typename T1, typename T2>
istream &operator>>(istream &in, pair<T1, T2> &p) {
    in >> p.first >> p.second;
    return in;
}
 
template<typename T>
istream &operator>>(istream &in, vector<T> &v) {
    for (auto &x: v)
        in >> x;
    return in;
}
 
template<typename T1, typename T2>
ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
    out << "[" << p.first << ", " << p.second << "]" << "
";
    return out;
}

inline int gc(){
    static const int BUF = 1e7;
    static char buf[BUF], *bg = buf + BUF, *ed = bg;
    
    if(bg == ed) fread(bg = buf, 1, BUF, stdin);
    return *bg++;
} 

inline int ri(){
    int x = 0, f = 1, c = gc();
    for(; c<48||c>57; f = c=='-'?-1:f, c=gc());
    for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
    return x*f;
}
 
typedef long long LL;
typedef unsigned long long uLL;
typedef pair< double, double > PDD;
typedef pair< int, int > PII;
typedef pair< int, PII > PIPII;
typedef pair< string, int > PSI;
typedef pair< int, PSI > PIPSI;
typedef set< int > SI;
typedef set< PII > SPII;
typedef vector< int > VI;
typedef vector< VI > VVI;
typedef vector< PII > VPII;
typedef map< int, int > MII;
typedef map< int, PII > MIPII;
typedef map< PII, int > MPIII;
typedef map< string, int > MSI;
typedef multimap< int, int > MMII;
//typedef unordered_map< int, int > uMII;
typedef pair< LL, LL > PLL;
typedef vector< LL > VL;
typedef vector< VL > VVL;
typedef priority_queue< int > PQIMax;
typedef priority_queue< int, VI, greater< int > > PQIMin;
const double EPS = 1e-10;
const LL inf = 0x7fffffff;
const LL infLL = 0x7fffffffffffffffLL;
const LL mod = 1e9 + 7;
const int maxN = 1e4 + 7;
const LL ONE = 1;
const LL evenBits = 0xaaaaaaaaaaaaaaaa;
const LL oddBits = 0x5555555555555555;

int T, ans;
int x, y;

int main(){
    //freopen("MyOutput.txt","w",stdout);
    //freopen("input.txt","r",stdin);
    INIT();
    while(cin >> x >> y) {
        MPIII mpiii;
        SI si;
        ans = 0;
        
        Rep(i, 6) {
            if(i) cin >> x >> y;
            si.insert(x);
            si.insert(y);
            if(x > y) swap(x, y);
            ++mpiii[MP(x, y)];
        }
        
        if(si.size() <= 3 && si.size() == mpiii.size()) {
            if(si.size() == 1) ans = 1;
            if(si.size() == 2) foreach(i, mpiii) if(i->ft.ft != i->ft.sd) ans = 1;
            if(si.size() == 3) {
                ans = 1;
                foreach(i, mpiii) if(i->ft.ft == i->ft.sd) ans = 0;
            }
            foreach(i, mpiii) if(i->sd % 2) ans = 0; // 每个矩形必须出现偶数次 
        }
        if(ans) cout << "POSSIBLE" << endl;
        else cout << "IMPOSSIBLE" << endl;
    }
    return 0;
}