#include<bits/stdc++.h> using namespace std; using LL=long long; #define FOR(i,l,r)for(int i=(l);i<=(r);++i) #define REP(i,n)FOR(i,0,(n)-1) #define ssize(x)int(x.size()) #ifdef DEBUG auto operator<<(auto&o,auto x)->decltype(x.end(),o); auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";} auto&operator<<(auto&o,tuple<auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<")";} auto&operator<<(auto&o,tuple<auto,auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<", "<<get<3>(t)<<")";} auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";} #define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X) #else #define debug(...){} #endif template<typename T> void self_max(T& x, T y) { if (x < y) x = y; } template<typename T> void self_min(T& x, T y) { if (x > y) x = y; } constexpr int mod = int(1e9) + 7; int add(int a, int b) { a += b; return a >= mod ? a - mod : a; } void self_add(int& a, int b) { a += b; if (a >= mod) a -= mod; } int sub(int a, int b) { return add(a, mod - b); } int mul(int a, int b) { return int(a * LL(b) % mod); } int powi(int a, int b) { for(int ret = 1;; b /= 2) { if(b == 0) return ret; if(b & 1) ret = mul(ret, a); a = mul(a, a); } } int inv(int x) { return powi(x, mod - 2); } struct BinomCoeff { vector<int> fac, rev; BinomCoeff(int n) { fac = rev = vector(n + 1, 1); FOR(i, 1, n) fac[i] = mul(fac[i - 1], i); rev[n] = inv(fac[n]); for(int i = n; i > 0; --i) rev[i - 1] = mul(rev[i], i); } int operator()(int n, int k) { return mul(fac[n], mul(rev[n - k], rev[k])); } }; int main() { cin.tie(0)->sync_with_stdio(0); int n, m; cin >> n >> m; vector<LL> ans(n + m + 1); vector<int> a(n), b(m); REP(i, n) cin >> a[i]; REP(i, m) cin >> b[i]; debug(n, m, a, b); FOR(len, 1, min(n, m)) { ans[2] += mul(n - len + 1, m - len + 1); } REP(iter, 2) { swap(n, m); swap(a, b); // prep(i, j, dir) - pierwsze r, że na [j-1,r] jest co najmniej wynik i gdzie elem i-1 ma daje dir, a przy dir=2 rozważamy [j,r] // all values in prep were decremented by 1 vector prep(n + 3, vector (n, vector (3, n - 1))); REP(j, n) { REP(dir, 3) { int last_dir = dir; int last = 1 + (last_dir != 2), val = last; int i = 2; if (last == 2) { prep[i][j][dir] = j - 1; ++i; } FOR(r, j + 1, n - 1) { int new_dir = a[r] < a[r - 1]; if (new_dir != last_dir) { last_dir = new_dir; last = 1; } ++last; if (last > val) { val = last; prep[i][j][dir] = r - 1; ++i; } } } } debug(iter, a, b, prep); // dp(i, rb) - największe takie ra, że splot [la, ra] z [lb, rb] ma wynik <= i vector dp(n + 2, vector (m, n - 1)); // dzięki tej kolejności rozważania lb, niedotknięte wartości dp będą ustawione na n - 1 REP(la, n) { for (auto& v : dp) fill(v.begin(), v.end(), n - 1); for (int lb = m - 1; lb >= 0; --lb) { { int pos = prep[3][la][2]; int rb = lb; while (rb < m and pos != n - 1) { int new_pos = prep[3][pos][b[rb] > a[pos]]; if (not pos or (b[rb] < a[pos]) != (a[pos] < a[pos - 1])) { const int val = prep[3][pos + 1][a[pos + 1] < b[rb]]; self_max(new_pos, val); } dp[2][rb] = pos = new_pos; ++rb; } } FOR(rb, lb, m - 1) { ans[2] += max(0, (dp[2][rb] - la + 1) - (rb - lb + 1)); } FOR(i, 3, n) { int pos = prep[i + 1][la][2]; int rb = lb; while (rb < m and pos != n - 1) { int new_pos = prep[i + 1][pos][b[rb] > a[pos]]; if (not pos or (b[rb] < a[pos]) != (a[pos] < a[pos - 1])) { const int val = prep[i + 1][pos + 1][a[pos + 1] < b[rb]]; self_max(new_pos, val); } dp[i][rb] = pos = new_pos; ans[i] += dp[i][rb] - dp[i - 1][rb]; ++rb; } while (rb < m and dp[i - 1][rb] != n - 1) { ans[i] += dp[i][rb] - dp[i - 1][rb]; ++rb; } if (dp[i][lb] == n - 1) break; } } } } FOR(i, 1, n + m) cout << ans[i] % mod << (i == n + m ? '\n' : ' '); }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 | #include<bits/stdc++.h> using namespace std; using LL=long long; #define FOR(i,l,r)for(int i=(l);i<=(r);++i) #define REP(i,n)FOR(i,0,(n)-1) #define ssize(x)int(x.size()) #ifdef DEBUG auto operator<<(auto&o,auto x)->decltype(x.end(),o); auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";} auto&operator<<(auto&o,tuple<auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<")";} auto&operator<<(auto&o,tuple<auto,auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<", "<<get<3>(t)<<")";} auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";} #define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X) #else #define debug(...){} #endif template<typename T> void self_max(T& x, T y) { if (x < y) x = y; } template<typename T> void self_min(T& x, T y) { if (x > y) x = y; } constexpr int mod = int(1e9) + 7; int add(int a, int b) { a += b; return a >= mod ? a - mod : a; } void self_add(int& a, int b) { a += b; if (a >= mod) a -= mod; } int sub(int a, int b) { return add(a, mod - b); } int mul(int a, int b) { return int(a * LL(b) % mod); } int powi(int a, int b) { for(int ret = 1;; b /= 2) { if(b == 0) return ret; if(b & 1) ret = mul(ret, a); a = mul(a, a); } } int inv(int x) { return powi(x, mod - 2); } struct BinomCoeff { vector<int> fac, rev; BinomCoeff(int n) { fac = rev = vector(n + 1, 1); FOR(i, 1, n) fac[i] = mul(fac[i - 1], i); rev[n] = inv(fac[n]); for(int i = n; i > 0; --i) rev[i - 1] = mul(rev[i], i); } int operator()(int n, int k) { return mul(fac[n], mul(rev[n - k], rev[k])); } }; int main() { cin.tie(0)->sync_with_stdio(0); int n, m; cin >> n >> m; vector<LL> ans(n + m + 1); vector<int> a(n), b(m); REP(i, n) cin >> a[i]; REP(i, m) cin >> b[i]; debug(n, m, a, b); FOR(len, 1, min(n, m)) { ans[2] += mul(n - len + 1, m - len + 1); } REP(iter, 2) { swap(n, m); swap(a, b); // prep(i, j, dir) - pierwsze r, że na [j-1,r] jest co najmniej wynik i gdzie elem i-1 ma daje dir, a przy dir=2 rozważamy [j,r] // all values in prep were decremented by 1 vector prep(n + 3, vector (n, vector (3, n - 1))); REP(j, n) { REP(dir, 3) { int last_dir = dir; int last = 1 + (last_dir != 2), val = last; int i = 2; if (last == 2) { prep[i][j][dir] = j - 1; ++i; } FOR(r, j + 1, n - 1) { int new_dir = a[r] < a[r - 1]; if (new_dir != last_dir) { last_dir = new_dir; last = 1; } ++last; if (last > val) { val = last; prep[i][j][dir] = r - 1; ++i; } } } } debug(iter, a, b, prep); // dp(i, rb) - największe takie ra, że splot [la, ra] z [lb, rb] ma wynik <= i vector dp(n + 2, vector (m, n - 1)); // dzięki tej kolejności rozważania lb, niedotknięte wartości dp będą ustawione na n - 1 REP(la, n) { for (auto& v : dp) fill(v.begin(), v.end(), n - 1); for (int lb = m - 1; lb >= 0; --lb) { { int pos = prep[3][la][2]; int rb = lb; while (rb < m and pos != n - 1) { int new_pos = prep[3][pos][b[rb] > a[pos]]; if (not pos or (b[rb] < a[pos]) != (a[pos] < a[pos - 1])) { const int val = prep[3][pos + 1][a[pos + 1] < b[rb]]; self_max(new_pos, val); } dp[2][rb] = pos = new_pos; ++rb; } } FOR(rb, lb, m - 1) { ans[2] += max(0, (dp[2][rb] - la + 1) - (rb - lb + 1)); } FOR(i, 3, n) { int pos = prep[i + 1][la][2]; int rb = lb; while (rb < m and pos != n - 1) { int new_pos = prep[i + 1][pos][b[rb] > a[pos]]; if (not pos or (b[rb] < a[pos]) != (a[pos] < a[pos - 1])) { const int val = prep[i + 1][pos + 1][a[pos + 1] < b[rb]]; self_max(new_pos, val); } dp[i][rb] = pos = new_pos; ans[i] += dp[i][rb] - dp[i - 1][rb]; ++rb; } while (rb < m and dp[i - 1][rb] != n - 1) { ans[i] += dp[i][rb] - dp[i - 1][rb]; ++rb; } if (dp[i][lb] == n - 1) break; } } } } FOR(i, 1, n + m) cout << ans[i] % mod << (i == n + m ? '\n' : ' '); } |