106 lines
3.8 KiB
C++
106 lines
3.8 KiB
C++
#include<cstdio>
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#include<cstdlib>
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#include<iostream>
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#include<algorithm>
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#include<vector>
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#include<map>
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#include<set>
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#include<utility>
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using namespace std;
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map<int,int> tmp;
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set<map<int,int> > ans[1010];
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int a[1010],b[1010],c[1010];
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bool cmp(vector<pair<int,int> > A,vector<pair<int,int> > B)
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{
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vector<pair<int,int> >::reverse_iterator pA=A.rbegin(),pB=B.rbegin();
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while (1)
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{
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if (pA->first<pB->first) return true;
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if (pA->first>pB->first) return false;
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if (abs(pA->second)<abs(pB->second)) return true;
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if (abs(pA->second)>abs(pB->second)) return false;
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if (pA->second<pB->second) return true;
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if (pA->second>pB->second) return false;
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++pA;++pB;
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}
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}
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void init()
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{
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tmp[1]=1;
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tmp[0]=-1;
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ans[1].insert(tmp);
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for (int i=2;i<=1001;++i)
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{
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for (int j=1;j<i;++j)
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if (i%j==0)
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for (set<map<int,int> >::iterator p=ans[j].begin();p!=ans[j].end();++p)
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ans[i].insert(*p);
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for (int j=0;j<=i;++j) a[j]=0;
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a[i]=1;
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a[0]=-1;
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for (set<map<int,int> >::iterator p=ans[i].begin();p!=ans[i].end();++p)
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{
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for (int j=0;j<=i;++j) b[j]=c[j]=0;
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for (std::_Rb_tree_const_iterator<std::pair<const int, int> > it=p->begin();it!=p->end();++it)
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b[it->first]=it->second;
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int get=0;
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for (int j=0;j<=i;++j) if (b[j]) get=j;
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for (int j=i;j>=0;--j)
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if (a[j])
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{
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c[j-get]=a[j];
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for (int k=get;k>=0;--k)
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a[j-get+k]-=c[j-get]*b[k];
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}
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for (int j=i;j>=0;--j) a[j]=c[j];
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}
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tmp.clear();
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for (int j=i;j>=0;--j)
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if (a[j]) tmp[j]=a[j];
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ans[i].insert(tmp);
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}
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}
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void work()
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{
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while (1)
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{
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int n;
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scanf("%d",&n);
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if (!n) return;
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vector<vector<pair<int,int> > > v;
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v.clear();
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vector<pair<int,int> > w;
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for (set<map<int,int> >::iterator p=ans[n].begin();p!=ans[n].end();++p)
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{
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w.clear();
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for (std::_Rb_tree_const_iterator<std::pair<const int, int> > it=p->begin();it!=p->end();++it)
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w.push_back(make_pair(it->first,it->second));
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v.push_back(w);
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}
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sort(v.begin(),v.end(),cmp);
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for (vector<vector<pair<int,int> > >::iterator p=v.begin();p!=v.end();++p)
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{
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w=*p;
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putchar('(');
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int flag=0;
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for (vector<pair<int,int> >::reverse_iterator it=w.rbegin();it!=w.rend();++it)
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{
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if (flag) putchar((it->second>0)?'+':'-');
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it->second=abs(it->second);
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if (it->first==0) printf("%d",it->second);
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else if (it->first==1) (it->second==1)?putchar('x'):printf("%dx",it->second);
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else (it->second==1)?printf("x^%d",it->first):printf("%dx^%d",it->second,it->first);
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flag=1;
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}
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putchar(')');
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}
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puts("");
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}
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}
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int main()
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{
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init();
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work();
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return 0;
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}
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