Topic links: https://atcoder.jp/contests/abc129/tasks/abc129_e
Subject to the effect
For a given number of L binary representation, asked how many of the natural numbers (a, b) satisfies $ a + b \ leq L and a + b = a \ oplus b $.
analysis
Since the exclusive OR sum with no carry, so $ a + b = a \ oplus b $ and b is equivalent to a bit corresponding to each bit 1 will not be two.
L 1 is provided with n. L is sequentially numbered n ~ 1.
Provided L (i) is the number of sub-string at the end i to 1 L formed.
Provided Ans (i) of L (i) contains a natural number logarithm.
a + b the following two cases:
- a + b most significant bit and L (i) are the same as the highest bit 1: then a and b are numbers 1 and I i + 1 corresponding to a position between the upper bound are all 0, so the answer depends Ans ( i - 1), and because a and b can be interchanged, so that part of its contribution to 2 * Ans (i - 1), may be provided to facilitate the calculation Ans (0) = 1.
- a + b is the most significant bit 0 (with respect to L (i) the most significant bit): a and b, then the remaining bits not limit, each a, b can have binary bits (0, 0) , (0, 1), (1, 0) three cases, therefore, the total contribution of $ 3 ^ {L (i) .size () - 1} $.
code show as below
1 #include <bits/stdc++.h> 2 using namespace std; 3 4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); 5 #define Rep(i,n) for (int i = 0; i < (n); ++i) 6 #define For(i,s,t) for (int i = (s); i <= (t); ++i) 7 #define rFor(i,t,s) for (int i = (t); i >= (s); --i) 8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i) 9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i) 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i) 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i) 12 13 #define pr(x) cout << #x << " = " << x << " " 14 #define prln(x) cout << #x << " = " << x << endl 15 16 #define LOWBIT(x) ((x)&(-x)) 17 18 #define ALL(x) x.begin(),x.end() 19 #define INS(x) inserter(x,x.begin()) 20 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end()) 21 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end());22deleting all x c// #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower); 23 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper); 24 25 #define ms0(a) memset(a,0,sizeof(a)) 26 #define msI(a) memset(a,inf,sizeof(a)) 27 #define msM(a) memset(a,-1,sizeof(a)) 28 29 #define MP make_pair 30 #define PB push_back 31 #define ft first 32 #define sd second 33 34 template<typename T1, typename T2> 35 istream &operator>>(istream &in, pair<T1, T2> &p) { 36 in >> p.first >> p.second; 37 return in; 38 } 39 40 template<typename T> 41 istream &operator>>(istream &in, vector<T> &v) { 42 for (auto &x: v) 43 in >> x; 44 return in; 45 } 46 47 template<typename T1, typename T2> 48 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) { 49 out << "[" << p.first << ", " << p.second << "]" << "\n"; 50 return out; 51 } 52 53 inline int gc(){ 54 static const int BUF = 1e7; 55 static char buf[BUF], *bg = buf + BUF, *ed = bg; 56 57 if(bg == ed) fread(bg = buf, 1, BUF, stdin); 58 return *bg++; 59 } 60 61 inline int ri(){ 62 int x = 0, f = 1, c = gc(); 63 for(; c<48||c>57; f = c=='-'?-1:f, c=gc()); 64 for(; c>47&&c<58; x = x*10 + c - 48, c=gc()); 65 return x*f; 66 } 67 68 template<class T> 69 inline string toString(T x) { 70 ostringstream sout; 71 sout << x; 72 return sout.str(); 73 } 74 75 inline int toInt(string s) { 76 int v; 77 istringstream sin(s); 78 sin >> v; 79 return v; 80 } 81 82 //min <= aim <= max 83 template<typename T> 84 inline bool BETWEEN(const T aim, const T min, const T max) { 85 return min <= aim && aim <= max; 86 } 87 88 typedef long long LL; 89 typedef unsigned long long uLL; 90 typedef pair< double, double > PDD; 91 typedef pair< int, int > PII; 92 typedef pair< int, PII > PIPII; 93 typedef pair< string, int > PSI; 94 typedef pair< int, PSI > PIPSI; 95 typedef set< int > SI; 96 typedef set< PII > SPII; 97 typedef vector< int > VI; 98 typedef vector< double > VD; 99 typedef vector< VI > VVI; 100 typedef vector< SI > VSI; 101 typedef vector< PII > VPII; 102 typedef map< int, int > MII; 103 typedef map< int, string > MIS; 104 typedef map< int, PII > MIPII; 105 typedef map< PII, int > MPIII; 106 typedef map< string, int > MSI; 107 typedef map< string, string > MSS; 108 typedef map< PII, string > MPIIS; 109 typedef map< PII, PII > MPIIPII; 110 typedef multimap< int, int > MMII; 111 typedef multimap< string, int > MMSI; 112 //typedef unordered_map< int, int > uMII; 113 typedef pair< LL, LL > PLL; 114 typedef vector< LL > VL; 115 typedef vector< VL > VVL; 116 typedef priority_queue< int > PQIMax; 117 typedef priority_queue< int, VI, greater< int > > PQIMin; 118 const double EPS = 1e-8; 119 const LL inf = 0x7fffffff; 120 const LL infLL = 0x7fffffffffffffffLL; 121 const LL mod = 1e9 + 7; 122 const int maxN = 1e5 + 7; 123 const LL ONE = 1; 124 const LL evenBits = 0xaaaaaaaaaaaaaaaa; 125 const LL oddBits = 0x5555555555555555; 126 127 string L; 128 LL ans = 1; 129 130 void mul_mod(LL &x, LL y) { 131 x = (x * y) % mod; 132 } 133 134 void add_mod(LL &x, LL y) { 135 x = (x + y) % mod; 136 } 137 138 LL pow_mod(LL x, LL y) { 139 LL ret = 1; 140 while(y) { 141 if(y & 1) mul_mod(ret, x); 142 mul_mod(x, x); 143 y >>= 1; 144 } 145 return ret; 146 } 147 148 int main(){ 149 //freopen("MyOutput.txt","w",stdout); 150 //freopen("input.txt","r",stdin); 151 //INIT(); 152 cin >> L; 153 rFor(i, L.size() - 1, 0) { 154 if(L[i] == '1') { 155 mul_mod(ans, 2); 156 add_mod(ans, pow_mod(3, L.size() - i - 1)); 157 } 158 } 159 cout << ans << endl; 160 return 0; 161 }