4fd800b3a8 2011-02-23 kinaba: #include <iostream> 4fd800b3a8 2011-02-23 kinaba: #include <sstream> 4fd800b3a8 2011-02-23 kinaba: #include <iomanip> 4fd800b3a8 2011-02-23 kinaba: #include <vector> 4fd800b3a8 2011-02-23 kinaba: #include <string> 4fd800b3a8 2011-02-23 kinaba: #include <map> 4fd800b3a8 2011-02-23 kinaba: #include <set> 4fd800b3a8 2011-02-23 kinaba: #include <algorithm> 4fd800b3a8 2011-02-23 kinaba: #include <numeric> 4fd800b3a8 2011-02-23 kinaba: #include <iterator> 4fd800b3a8 2011-02-23 kinaba: #include <functional> 4fd800b3a8 2011-02-23 kinaba: #include <complex> 4fd800b3a8 2011-02-23 kinaba: #include <queue> 4fd800b3a8 2011-02-23 kinaba: #include <stack> 4fd800b3a8 2011-02-23 kinaba: #include <cmath> 4fd800b3a8 2011-02-23 kinaba: #include <cassert> 4fd800b3a8 2011-02-23 kinaba: #include <cstring> 4fd800b3a8 2011-02-23 kinaba: using namespace std; 4fd800b3a8 2011-02-23 kinaba: typedef long long LL; 4fd800b3a8 2011-02-23 kinaba: typedef complex<double> CMP; 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: static const LL MODVAL = 1000000007LL; 4fd800b3a8 2011-02-23 kinaba: LL ADD(LL x, LL y) { return (x+y)%MODVAL; } 4fd800b3a8 2011-02-23 kinaba: LL MUL(LL x, LL y) { return (x*y)%MODVAL; } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: class MegaSum { public: 4fd800b3a8 2011-02-23 kinaba: int calculate(long long N) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: LL nth = sq(N); 4fd800b3a8 2011-02-23 kinaba: pair<LL,LL> p = position_of(N); 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: LL cnt = 0; 4fd800b3a8 2011-02-23 kinaba: for(LL lane=1; lane<=nth; ++lane) 4fd800b3a8 2011-02-23 kinaba: cnt = ADD(cnt, sum_in_the_lane(p, lane)); 4fd800b3a8 2011-02-23 kinaba: return cnt; 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: LL sq( LL N ) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: LL nth=1; 4fd800b3a8 2011-02-23 kinaba: while( !(N <= nth*nth) ) 4fd800b3a8 2011-02-23 kinaba: ++nth; 4fd800b3a8 2011-02-23 kinaba: return nth; 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: pair<LL,LL> position_of( LL N ) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: // in which lane? 4fd800b3a8 2011-02-23 kinaba: LL nth = sq(N); 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: // position 4fd800b3a8 2011-02-23 kinaba: LL dif = N - (nth-1)*(nth-1); 4fd800b3a8 2011-02-23 kinaba: LL y = (dif<=nth ? dif : nth); 4fd800b3a8 2011-02-23 kinaba: LL x = (dif<=nth ? nth : nth+nth-dif); 4fd800b3a8 2011-02-23 kinaba: if( nth%2 == 1 ) swap(x, y); 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: return make_pair(y,x); 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: LL sum_in_the_lane(pair<LL,LL> p, LL lane) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: LL y = p.first; 4fd800b3a8 2011-02-23 kinaba: LL x = p.second; 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: if( lane%2 == 0 ) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: // V 4fd800b3a8 2011-02-23 kinaba: // V 4fd800b3a8 2011-02-23 kinaba: //<<<<<< 4fd800b3a8 2011-02-23 kinaba: LL s = lane<=x ? sumV( 1, lane, min(y,lane), lane, y, x ) : 0; 4fd800b3a8 2011-02-23 kinaba: s = ADD(s, lane<=y ? sumH(lane,min(x,lane-1),lane,1,y,x) : 0); 4fd800b3a8 2011-02-23 kinaba: return s; 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: else 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: // A 4fd800b3a8 2011-02-23 kinaba: // A 4fd800b3a8 2011-02-23 kinaba: //>>>>>> 4fd800b3a8 2011-02-23 kinaba: LL s = lane<=y ? sumH( lane, 1, lane, min(x,lane), y, x ) : 0; 4fd800b3a8 2011-02-23 kinaba: s = ADD(s, lane<=x ? sumV(min(y,lane-1),lane,1,lane,y,x) : 0); 4fd800b3a8 2011-02-23 kinaba: return s; 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: LL value_of(LL y, LL x) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: LL lane = max(x, y); 4fd800b3a8 2011-02-23 kinaba: return (lane-1)*(lane-1) + (lane%2==0 ? (y<lane ? y : lane+lane-x) 4fd800b3a8 2011-02-23 kinaba: : (x<lane ? x : lane+lane-y)); 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: LL sumH(LL y0, LL x, LL y1, LL _, LL Y, LL X) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: // \Sigma value_of(y0+i,x) * (X-x+1)*(Y-(y0+i)+1) 4fd800b3a8 2011-02-23 kinaba: //= 4fd800b3a8 2011-02-23 kinaba: // \Sigma (value_of(y0,x)+i) * (X-x+1)*(Y-(y0+i)+1) 4fd800b3a8 2011-02-23 kinaba: //= 4fd800b3a8 2011-02-23 kinaba: // \Sigma (V0 +i) * XX *(YY-i) 4fd800b3a8 2011-02-23 kinaba: //= 4fd800b3a8 2011-02-23 kinaba: // ... 4fd800b3a8 2011-02-23 kinaba: assert(false); 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: LL sumV(LL y, LL x0, LL _, LL x1, LL Y, LL X) 4fd800b3a8 2011-02-23 kinaba: { 4fd800b3a8 2011-02-23 kinaba: assert(false); 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: }; 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: // BEGIN CUT HERE 4fd800b3a8 2011-02-23 kinaba: #include <ctime> 4fd800b3a8 2011-02-23 kinaba: double start_time; string timer() 4fd800b3a8 2011-02-23 kinaba: { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); } 4fd800b3a8 2011-02-23 kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v) 4fd800b3a8 2011-02-23 kinaba: { os << "{ "; 4fd800b3a8 2011-02-23 kinaba: for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it) 4fd800b3a8 2011-02-23 kinaba: os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; } 4fd800b3a8 2011-02-23 kinaba: void verify_case(const int& Expected, const int& Received) { 4fd800b3a8 2011-02-23 kinaba: bool ok = (Expected == Received); 4fd800b3a8 2011-02-23 kinaba: if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; 4fd800b3a8 2011-02-23 kinaba: cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } } 4fd800b3a8 2011-02-23 kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock(); 4fd800b3a8 2011-02-23 kinaba: #define END verify_case(_, MegaSum().calculate(N));} 4fd800b3a8 2011-02-23 kinaba: int main(){ 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: CASE(0) 4fd800b3a8 2011-02-23 kinaba: long long N = 8LL; 4fd800b3a8 2011-02-23 kinaba: int _ = 58; 4fd800b3a8 2011-02-23 kinaba: END 4fd800b3a8 2011-02-23 kinaba: CASE(1) 4fd800b3a8 2011-02-23 kinaba: long long N = 12LL; 4fd800b3a8 2011-02-23 kinaba: int _ = 282; 4fd800b3a8 2011-02-23 kinaba: END 4fd800b3a8 2011-02-23 kinaba: CASE(2) 4fd800b3a8 2011-02-23 kinaba: long long N = 11LL; 4fd800b3a8 2011-02-23 kinaba: int _ = 128; 4fd800b3a8 2011-02-23 kinaba: END 4fd800b3a8 2011-02-23 kinaba: CASE(3) 4fd800b3a8 2011-02-23 kinaba: long long N = 6LL; 4fd800b3a8 2011-02-23 kinaba: int _ = 50; 4fd800b3a8 2011-02-23 kinaba: END 4fd800b3a8 2011-02-23 kinaba: CASE(4) 4fd800b3a8 2011-02-23 kinaba: long long N = 34539LL; 4fd800b3a8 2011-02-23 kinaba: int _ = 437909839; 4fd800b3a8 2011-02-23 kinaba: END 4fd800b3a8 2011-02-23 kinaba: CASE(5) 4fd800b3a8 2011-02-23 kinaba: long long N = 10000000000LL; 4fd800b3a8 2011-02-23 kinaba: int _ = -1; 4fd800b3a8 2011-02-23 kinaba: END 4fd800b3a8 2011-02-23 kinaba: CASE(6) 4fd800b3a8 2011-02-23 kinaba: long long N = 123456789LL; 4fd800b3a8 2011-02-23 kinaba: int _ = -1; 4fd800b3a8 2011-02-23 kinaba: END 4fd800b3a8 2011-02-23 kinaba: 4fd800b3a8 2011-02-23 kinaba: } 4fd800b3a8 2011-02-23 kinaba: // END CUT HERE