#include<bits/stdc++.h>
using namespace std;
#define fwd(i, a, b) for(int i=(a);i<(int)(b);i++)
#define rep(i, n) for(int i=0;i<(int)(n);i++)
#define all(X) (X).begin(), (X).end()
#define sz(X) ((int)(X).size())
#define mp make_pair
#define st first
#define nd second
typedef long long ll;
typedef pair<int,int> pii;
typedef vector<int> vi;
template <int32_t _MODD>
struct modint {
int32_t value;
modint() = default;
modint(int32_t value_) : value(value_) {}
inline modint<_MODD> operator + (modint<_MODD> other) const { int32_t c = this->value + other.value; return modint<_MODD>(c >= _MODD ? c - _MODD : c); }
inline modint<_MODD> operator - (modint<_MODD> other) const { int32_t c = this->value - other.value; return modint<_MODD>(c < 0 ? c + _MODD : c); }
inline modint<_MODD> operator * (modint<_MODD> other) const { int32_t c = (int64_t)this->value * other.value % _MODD; return modint<_MODD>(c < 0 ? c + _MODD : c); }
inline modint<_MODD> & operator += (modint<_MODD> other) { this->value += other.value; if (this->value >= _MODD) this->value -= _MODD; return *this; }
inline modint<_MODD> & operator -= (modint<_MODD> other) { this->value -= other.value; if (this->value < 0) this->value += _MODD; return *this; }
inline modint<_MODD> & operator *= (modint<_MODD> other) { this->value = (int64_t)this->value * other.value % _MODD; if (this->value < 0) this->value += _MODD; return *this; }
inline modint<_MODD> operator - () const { return modint<_MODD>(this->value ? _MODD - this->value : 0); }
modint<_MODD> pow(uint64_t k) const {
modint<_MODD> x = *this, y = 1;
for (; k; k >>= 1) {
if (k & 1) y *= x;
x *= x;
}
return y;
}
modint<_MODD> inv() const { return pow(_MODD - 2); } // _MODD must be a prime
inline modint<_MODD> operator / (modint<_MODD> other) const { return *this * other.inv(); }
inline modint<_MODD> operator /= (modint<_MODD> other) { return *this *= other.inv(); }
inline bool operator == (modint<_MODD> other) const { return value == other.value; }
inline bool operator != (modint<_MODD> other) const { return value != other.value; }
inline bool operator < (modint<_MODD> other) const { return value < other.value; }
inline bool operator > (modint<_MODD> other) const { return value > other.value; }
};
template <int32_t _MODD> modint<_MODD> operator * (int64_t value, modint<_MODD> n) { return modint<_MODD>(value) * n; }
template <int32_t _MODD> modint<_MODD> operator * (int32_t value, modint<_MODD> n) { return modint<_MODD>(value % _MODD) * n; }
template <int32_t _MODD> istream & operator >> (istream & in, modint<_MODD> &n) { return in >> n.value; }
template <int32_t _MODD> ostream & operator << (ostream & out, modint<_MODD> n) { return out << n.value; }
typedef modint<(int)(1e9+7)> mint;
mint numberOfSeqsOfLengthNOverPlusMinus1HavingSumMod3DifferentThanR(int n, int r) {
mint res = (mint(2).pow(n)-mint(n%2 == 0 ? 1 : 2))/mint(3);
static const vector<vi> lookup = {
{1,0,0},
{1,1,0},
{0,1,0},
{0,1,1},
{0,0,1},
{1,0,1}
};
return mint(2).pow(n) - (res + mint(lookup[n%6][r]));
}
int cntC[2], cntZ[2], cntN;
void update(char c, int pos, int v) {
if(c == 'C')
cntC[pos&1] += v;
else if(c == 'Z')
cntZ[pos&1] += v;
else
cntN += v;
}
bool czczPossible() {
return cntC[1] == 0 && cntZ[0] == 0;
}
bool zczcPossible() {
return cntC[0] == 0 && cntZ[1] == 0;
}
int n;
void ans() {
int sum = (cntC[0]+cntC[1]-cntZ[0]-cntZ[1]);
int badR = 2*(cntN-sum);
badR = (badR%3+3)%3;
mint res = numberOfSeqsOfLengthNOverPlusMinus1HavingSumMod3DifferentThanR(cntN, badR);
if(czczPossible() && n%2 == 1)
res -= 1;
if(zczcPossible() && n%2 == 1)
res -= 1;
if(n == 1)
res = mint(cntN == 0 ? 1 : 2);
cout<<res<<"\n";
}
int32_t main(){
ios::sync_with_stdio(false);
cin.tie(0);
int q;
cin >> n >> q;
string s;
cin >> s;
rep(i,n)
update(s[i],i,1);
ans();
while(q--) {
int pos; char c;
cin >> pos >> c;
pos--;
update(s[pos], pos, -1);
s[pos] = c;
update(s[pos], pos, 1);
ans();
}
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 | #include<bits/stdc++.h> using namespace std; #define fwd(i, a, b) for(int i=(a);i<(int)(b);i++) #define rep(i, n) for(int i=0;i<(int)(n);i++) #define all(X) (X).begin(), (X).end() #define sz(X) ((int)(X).size()) #define mp make_pair #define st first #define nd second typedef long long ll; typedef pair<int,int> pii; typedef vector<int> vi; template <int32_t _MODD> struct modint { int32_t value; modint() = default; modint(int32_t value_) : value(value_) {} inline modint<_MODD> operator + (modint<_MODD> other) const { int32_t c = this->value + other.value; return modint<_MODD>(c >= _MODD ? c - _MODD : c); } inline modint<_MODD> operator - (modint<_MODD> other) const { int32_t c = this->value - other.value; return modint<_MODD>(c < 0 ? c + _MODD : c); } inline modint<_MODD> operator * (modint<_MODD> other) const { int32_t c = (int64_t)this->value * other.value % _MODD; return modint<_MODD>(c < 0 ? c + _MODD : c); } inline modint<_MODD> & operator += (modint<_MODD> other) { this->value += other.value; if (this->value >= _MODD) this->value -= _MODD; return *this; } inline modint<_MODD> & operator -= (modint<_MODD> other) { this->value -= other.value; if (this->value < 0) this->value += _MODD; return *this; } inline modint<_MODD> & operator *= (modint<_MODD> other) { this->value = (int64_t)this->value * other.value % _MODD; if (this->value < 0) this->value += _MODD; return *this; } inline modint<_MODD> operator - () const { return modint<_MODD>(this->value ? _MODD - this->value : 0); } modint<_MODD> pow(uint64_t k) const { modint<_MODD> x = *this, y = 1; for (; k; k >>= 1) { if (k & 1) y *= x; x *= x; } return y; } modint<_MODD> inv() const { return pow(_MODD - 2); } // _MODD must be a prime inline modint<_MODD> operator / (modint<_MODD> other) const { return *this * other.inv(); } inline modint<_MODD> operator /= (modint<_MODD> other) { return *this *= other.inv(); } inline bool operator == (modint<_MODD> other) const { return value == other.value; } inline bool operator != (modint<_MODD> other) const { return value != other.value; } inline bool operator < (modint<_MODD> other) const { return value < other.value; } inline bool operator > (modint<_MODD> other) const { return value > other.value; } }; template <int32_t _MODD> modint<_MODD> operator * (int64_t value, modint<_MODD> n) { return modint<_MODD>(value) * n; } template <int32_t _MODD> modint<_MODD> operator * (int32_t value, modint<_MODD> n) { return modint<_MODD>(value % _MODD) * n; } template <int32_t _MODD> istream & operator >> (istream & in, modint<_MODD> &n) { return in >> n.value; } template <int32_t _MODD> ostream & operator << (ostream & out, modint<_MODD> n) { return out << n.value; } typedef modint<(int)(1e9+7)> mint; mint numberOfSeqsOfLengthNOverPlusMinus1HavingSumMod3DifferentThanR(int n, int r) { mint res = (mint(2).pow(n)-mint(n%2 == 0 ? 1 : 2))/mint(3); static const vector<vi> lookup = { {1,0,0}, {1,1,0}, {0,1,0}, {0,1,1}, {0,0,1}, {1,0,1} }; return mint(2).pow(n) - (res + mint(lookup[n%6][r])); } int cntC[2], cntZ[2], cntN; void update(char c, int pos, int v) { if(c == 'C') cntC[pos&1] += v; else if(c == 'Z') cntZ[pos&1] += v; else cntN += v; } bool czczPossible() { return cntC[1] == 0 && cntZ[0] == 0; } bool zczcPossible() { return cntC[0] == 0 && cntZ[1] == 0; } int n; void ans() { int sum = (cntC[0]+cntC[1]-cntZ[0]-cntZ[1]); int badR = 2*(cntN-sum); badR = (badR%3+3)%3; mint res = numberOfSeqsOfLengthNOverPlusMinus1HavingSumMod3DifferentThanR(cntN, badR); if(czczPossible() && n%2 == 1) res -= 1; if(zczcPossible() && n%2 == 1) res -= 1; if(n == 1) res = mint(cntN == 0 ? 1 : 2); cout<<res<<"\n"; } int32_t main(){ ios::sync_with_stdio(false); cin.tie(0); int q; cin >> n >> q; string s; cin >> s; rep(i,n) update(s[i],i,1); ans(); while(q--) { int pos; char c; cin >> pos >> c; pos--; update(s[pos], pos, -1); s[pos] = c; update(s[pos], pos, 1); ans(); } } |
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