ADDED SRM/566-U/1A.cpp
Index: SRM/566-U/1A.cpp
==================================================================
--- SRM/566-U/1A.cpp
+++ SRM/566-U/1A.cpp
@@ -0,0 +1,159 @@
+#include <iostream>
+#include <sstream>
+#include <iomanip>
+#include <vector>
+#include <string>
+#include <map>
+#include <set>
+#include <algorithm>
+#include <numeric>
+#include <iterator>
+#include <functional>
+#include <complex>
+#include <queue>
+#include <stack>
+#include <cmath>
+#include <cassert>
+using namespace std;
+typedef long long LL;
+typedef long double LD;
+typedef complex<LD> CMP;
+
+LL comb(LL n, LL k)
+{
+ k = min(k, n-k);
+
+ LL c = 1;
+ for(LL i=0; i<k; ++i)
+ c *= n-i, c /= i+1;
+ return c;
+}
+
+class PenguinSledding { public:
+ long long countDesigns(int numCheckpoints, vector <int> checkpoint1, vector <int> checkpoint2)
+ {
+ LL zero = 1;
+ LL one = checkpoint1.size();
+ LL star = 0;
+ LL triangle = 0;
+
+ for(int center=1; center<=numCheckpoints; ++center) {
+ int leaf = 0;
+ for(int i=0; i<checkpoint1.size(); ++i)
+ if(checkpoint1[i] == center)
+ ++leaf;
+ else if(checkpoint2[i] == center)
+ ++leaf;
+ for(int k=2; k<=leaf; ++k)
+ star += comb(leaf, k);
+ }
+
+ set< pair<int,int> > conn;
+ for(int i=0; i<checkpoint1.size(); ++i) {
+ conn.insert(make_pair(checkpoint1[i], checkpoint2[i]));
+ conn.insert(make_pair(checkpoint2[i], checkpoint1[i]));
+ }
+ for(int a=1; a<=numCheckpoints; ++a)
+ for(int b=a+1; b<=numCheckpoints; ++b)
+ for(int c=b+1; c<=numCheckpoints; ++c)
+ if(conn.count(make_pair(a,b)) && conn.count(make_pair(b,c)) && conn.count(make_pair(c,a)))
+ ++triangle;
+
+ return zero + one + star + triangle;
+ }
+};
+
+// BEGIN CUT HERE
+#include <ctime>
+double start_time; string timer()
+ { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
+template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
+ { os << "{ ";
+ for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
+ os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
+void verify_case(const long long& Expected, const long long& Received) {
+ bool ok = (Expected == Received);
+ if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
+ cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
+#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
+#define END verify_case(_, PenguinSledding().countDesigns(numCheckpoints, checkpoint1, checkpoint2));}
+int main(){
+
+CASE(0)
+ int numCheckpoints = 2;
+ int checkpoint1_[] = {1};
+ vector <int> checkpoint1(checkpoint1_, checkpoint1_+sizeof(checkpoint1_)/sizeof(*checkpoint1_));
+ int checkpoint2_[] = {2};
+ vector <int> checkpoint2(checkpoint2_, checkpoint2_+sizeof(checkpoint2_)/sizeof(*checkpoint2_));
+ long long _ = 2LL;
+END
+CASE(1)
+ int numCheckpoints = 4;
+ int checkpoint1_[] = {1,2,3};
+ vector <int> checkpoint1(checkpoint1_, checkpoint1_+sizeof(checkpoint1_)/sizeof(*checkpoint1_));
+ int checkpoint2_[] = {2,3,4};
+ vector <int> checkpoint2(checkpoint2_, checkpoint2_+sizeof(checkpoint2_)/sizeof(*checkpoint2_));
+ long long _ = 6LL;
+END
+CASE(2)
+ int numCheckpoints = 6;
+ int checkpoint1_[] = {1,3,6};
+ vector <int> checkpoint1(checkpoint1_, checkpoint1_+sizeof(checkpoint1_)/sizeof(*checkpoint1_));
+ int checkpoint2_[] = {2,4,4};
+ vector <int> checkpoint2(checkpoint2_, checkpoint2_+sizeof(checkpoint2_)/sizeof(*checkpoint2_));
+ long long _ = 5LL;
+END
+CASE(3)
+ int numCheckpoints = 50;
+ int checkpoint1_[] = {40, 40, 40, 40, 40, 40, 40, 40,
+ 40, 40, 40, 40, 50, 40, 40, 40,
+ 23, 4, 24, 40, 22, 40, 8, 40, 40,
+ 40, 34, 21, 40, 40, 38, 40, 40,
+ 40, 40, 40, 28, 40, 40, 40, 40,
+ 46, 13, 40, 40, 40, 47, 40, 40};
+ vector <int> checkpoint1(checkpoint1_, checkpoint1_+sizeof(checkpoint1_)/sizeof(*checkpoint1_));
+ int checkpoint2_[] = {45, 42, 20, 48, 12, 32, 25, 10,
+ 26, 39, 16, 2, 19, 43, 37, 17,
+ 19, 19, 19, 18, 19, 27, 19, 29,
+ 11, 36, 19, 19, 1, 41, 19, 35,
+ 14, 33, 49, 3, 19, 7, 5, 19, 31,
+ 19, 19, 6, 9, 15, 19, 44, 30};
+ vector <int> checkpoint2(checkpoint2_, checkpoint2_+sizeof(checkpoint2_)/sizeof(*checkpoint2_));
+ long long _ = 68719493118LL;
+END
+CASE(4)
+ int numCheckpoints = 36;
+ int checkpoint1_[] = {13, 24, 24, 20, 31, 16, 10, 36, 34, 32,
+ 28, 5, 20, 29, 23, 2, 14, 4, 9, 5, 19,
+ 21, 8, 1, 26, 27, 25, 15, 22, 30, 30,
+ 6, 11, 7, 2, 35, 13, 29, 4, 12, 33, 18,
+ 13, 14, 17, 35, 3};
+ vector <int> checkpoint1(checkpoint1_, checkpoint1_+sizeof(checkpoint1_)/sizeof(*checkpoint1_));
+ int checkpoint2_[] = {10, 15, 27, 1, 29, 11, 5, 18, 33, 1, 9,
+ 2, 31, 6, 19, 10, 33, 18, 6, 27, 3, 22,
+ 4, 12, 31, 30, 34, 16, 7, 24, 3, 28, 15,
+ 21, 22, 8, 26, 20, 14, 32, 25, 17, 35,
+ 8, 36, 26, 23};
+ vector <int> checkpoint2(checkpoint2_, checkpoint2_+sizeof(checkpoint2_)/sizeof(*checkpoint2_));
+ long long _ = 162LL;
+END
+/*
+CASE(5)
+ int numCheckpoints = ;
+ int checkpoint1_[] = ;
+ vector <int> checkpoint1(checkpoint1_, checkpoint1_+sizeof(checkpoint1_)/sizeof(*checkpoint1_));
+ int checkpoint2_[] = ;
+ vector <int> checkpoint2(checkpoint2_, checkpoint2_+sizeof(checkpoint2_)/sizeof(*checkpoint2_));
+ long long _ = LL;
+END
+CASE(6)
+ int numCheckpoints = ;
+ int checkpoint1_[] = ;
+ vector <int> checkpoint1(checkpoint1_, checkpoint1_+sizeof(checkpoint1_)/sizeof(*checkpoint1_));
+ int checkpoint2_[] = ;
+ vector <int> checkpoint2(checkpoint2_, checkpoint2_+sizeof(checkpoint2_)/sizeof(*checkpoint2_));
+ long long _ = LL;
+END
+*/
+}
+// END CUT HERE
ADDED SRM/566-U/1B.cpp
Index: SRM/566-U/1B.cpp
==================================================================
--- SRM/566-U/1B.cpp
+++ SRM/566-U/1B.cpp
@@ -0,0 +1,155 @@
+#include <iostream>
+#include <sstream>
+#include <iomanip>
+#include <vector>
+#include <string>
+#include <map>
+#include <set>
+#include <algorithm>
+#include <numeric>
+#include <iterator>
+#include <functional>
+#include <complex>
+#include <queue>
+#include <stack>
+#include <cmath>
+#include <cassert>
+using namespace std;
+typedef long long LL;
+typedef long double LD;
+typedef complex<LD> CMP;
+
+static const unsigned MODVAL = 1000000007;
+struct mint
+{
+ unsigned val;
+ mint():val(0){}
+ mint(int x):val(x%MODVAL) {}
+ mint(unsigned x):val(x%MODVAL) {}
+ mint(LL x):val(x%MODVAL) {}
+};
+mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
+mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
+mint operator+(mint x, mint y) { return x+=y; }
+mint operator*(mint x, mint y) { return x*=y; }
+
+template<typename T>
+vector<T> MATMULxx(const vector<T>& a, const vector<T>& v)
+{
+ int N = a.size();
+ vector<T> u(N);
+ for(int i=0; i<N; ++i)
+ for(int j=0; j<N; ++j)
+ u[i] += a[(j-i+N)%N]*v[j];
+ return u;
+}
+
+template<typename T>
+vector<T> MATMULxx(const vector<T>& a)
+{
+ int N = a.size();
+ vector<T> c(N);
+ for(int j=0; j<N; ++j)
+ for(int k=0; k<N; ++k)
+ c[j] += a[k]*a[(j-k+N)%N];
+ return c;
+}
+
+template<typename T>
+vector<T> MATPOWMULxx(vector<T> a, LL e, vector<T> v)
+{
+ for(; e; e>>=1, a=MATMULxx(a))
+ if(e&1)
+ v = MATMULxx(a, v);
+ return v;
+}
+
+class PenguinEmperor { public:
+ int countJourneys(int N, long long daysPassed)
+ {
+ vector<mint> v(N), u(N);
+ u[0] = 1;
+ for(int i=0; i<N; ++i) {
+ if(i == daysPassed % N)
+ v = u;
+ vector<mint> uu(N);
+ for(int x=0; x<N; ++x) {
+ int f = (x+i+1)%N;
+ int b = (x-i-1+N)%N;
+ uu[x] += u[f];
+ if(f!=b)
+ uu[x] += u[b];
+ }
+ u = uu;
+ }
+
+ v = MATPOWMULxx(u, daysPassed/N, v);
+ return v[0].val;
+ }
+};
+
+// BEGIN CUT HERE
+#include <ctime>
+double start_time; string timer()
+ { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
+template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
+ { os << "{ ";
+ for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
+ os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
+void verify_case(const int& Expected, const int& Received) {
+ bool ok = (Expected == Received);
+ if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
+ cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
+#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
+#define END verify_case(_, PenguinEmperor().countJourneys(numCities, daysPassed));}
+int main(){
+
+CASE(0)
+ int numCities = 3;
+ long long daysPassed = 2LL;
+ int _ = 2;
+END
+CASE(1)
+ int numCities = 4;
+ long long daysPassed = 3LL;
+ int _ = 2;
+END
+CASE(2)
+ int numCities = 5;
+ long long daysPassed = 36LL;
+ int _ = 107374182;
+END
+CASE(3)
+ int numCities = 300;
+ long long daysPassed = 751LL;
+ int _ = 413521250;
+END
+CASE(4)
+ int numCities = 300;
+ long long daysPassed = 750LL;
+ int _ = 0;
+END
+CASE(5)
+ int numCities = 350;
+ long long daysPassed = 1000000000000000000LL;
+ int _ = 667009739;
+END
+CASE(6)
+ int numCities = 5;
+ long long daysPassed = 7LL;
+ int _ = 12;
+END
+/*
+CASE(7)
+ int numCities = ;
+ long long daysPassed = LL;
+ int _ = ;
+END
+CASE(8)
+ int numCities = ;
+ long long daysPassed = LL;
+ int _ = ;
+END
+*/
+}
+// END CUT HERE
Index: lib/doc/nim.txt
==================================================================
--- lib/doc/nim.txt
+++ lib/doc/nim.txt
@@ -58,11 +58,16 @@
- *n1 + *n2 = *(n1 xor n2)
- より一般的に G1≡*n1, G2≡*n2 ならば、G1 + G2 ≡ *(n1 xor n2)
証明
- *n1 + *n2 + *(n1 xor n2) が必敗であることを言えば良い。
-
+ - (n1 xor n2 xor (n1 xor n2)) は 0 である
+ - 一手動かすと 0 じゃなくなる
+ >> n1 と n2 と n1^n2 のどれか一個だけビットが変わるので絶対xorが変わるから
+ - 相手は一手動かして 0 に戻せる
+ >> 常に
+ - よって最終局面"全部 0"になるのは絶対に自分のターン
-------------------------------------------------------------------------------------------
定理【ゲームの状態遷移はmex】
- {*n1, ..., *nk} ≡ *mex(n1,...,nk)