#include<iostream> #include<vector> #include<algorithm> #include<complex> using namespace std; const double PI = acos(-1); const int MAX_FFT = 1 << 24; complex<double> vvt[MAX_FFT]; complex<double> vvvt[MAX_FFT]; int calc_size(int a, int b) { long long n = 1; while (n < a + b) n <<= 1; return n; } int reverse(int num, int lg_n) { int res = 0; for (int i = 0; i < lg_n; i++) { if (num & (1 << i)) res |= 1 << (lg_n - 1 - i); } return res; } void fft(complex<double> a[], int n, bool invert) { for (int i = 1, j = 0; i < n; i++) { int bit = n >> 1; for (; j & bit; bit >>= 1) j ^= bit; j ^= bit; if (i < j) swap(a[i], a[j]); } for (int len = 2; len <= n; len <<= 1) { double ang = 2 * PI / len * (invert ? -1 : 1); complex<double> wlen(cos(ang), sin(ang)); for (int i = 0; i < n; i += len) { complex<double> w(1); for (int j = 0; j < len / 2; j++) { complex<double> u = a[i+j], v = a[i+j+len/2] * w; a[i+j] = u + v; a[i+j+len/2] = u - v; w *= wlen; } } } if (invert) { for (int i = 0; i < n; i++) { a[i] /= n; } } } void multiply(vector<short> &freq, int sizea, int sizeb) { long long n = calc_size(sizea, sizeb); for (int i = 0; i < sizea; i++) { vvvt[i] = vvt[i]; } for (int i = 0; i < n; i++) vvt[i] = 0; for (int i = 0; i < freq.size(); i++) { vvt[i] = freq[i]; } fft(vvvt, n, false); fft(vvt, n, false); for (int i = 0; i < n; i++) { vvvt[i] *= vvt[i]; } fft(vvvt, n, true); } int multiply_ffq(int sizea) { long long n = calc_size(sizea, sizea); fft(vvt, n, false); for (int i = 0; i < n; i++) { vvt[i] *= vvt[i]; } fft(vvt, n, true); return n; } const int MAX = 500 * 500 + 5; long long bicoff[MAX][4]; vector<short> count(vector<long long> &v, int N) { int n = v.size(); vector<short> res(2 * N + 1); for (int i = 0; i < n; i++) { res[v[i]]++; } return res; } long long get_freq(vector<short> &freq, int k) { return k >= freq.size() || k < 0 ? 0 : freq[k]; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n; cin >> n; vector<long long> tmp(n); for (int i = 0; i < n; i++) { cin >> tmp[i]; } if (n == 1) { cout << 0 << endl; return 0; } // create BUC long long minn = 0; long long maxx = 0; vector<long long> v(n * (n + 1) / 2); for (int i = 0, k = 0; i < n; i++) { long long acc = 0; for (int j = i; j < n; j++) { acc += tmp[j]; v[k++] = acc; minn = min(minn, acc); maxx = max(maxx, acc); } } sort(v.begin(), v.end()); long long N = max(abs(minn), maxx); if (N > 4'000'000) { long long ret = 0; for (int i = 0; i < v.size() - 2; i++) { long long a = i + 1, b = v.size() - 1; while (a < b) { int acc = v[i] + v[a] + v[b]; if (acc == 0) { if (v[a] == v[b]) { ret += (b - a) * (b - a + 1) / 2; break; } else { long long ac = 1; while (v[a + 1] == v[a]) { ac++; a++; } a++; long long bc = 1; while (v[b - 1] == v[b]) { bc++; b--; } b--; ret += ac * bc; } } else if (acc < 0) a++; else b--; } } cout << ret << endl; return 0; } // compute binomial coefficients bicoff[0][0] = 1; bicoff[0][1] = 0; bicoff[0][2] = 0; bicoff[0][3] = 0; for (int i = 1; i < MAX; i++) { bicoff[i][0] = 1; bicoff[i][1] = bicoff[i - 1][1] + bicoff[i - 1][0]; bicoff[i][2] = bicoff[i - 1][2] + bicoff[i - 1][1]; bicoff[i][3] = bicoff[i - 1][3] + bicoff[i - 1][2]; } // shift BUC for (int i = 0; i < v.size(); i++) { v[i] += N; } // compute fft vector<short> freq = count(v, N); for (int i = 0; i < freq.size(); i++) { vvt[i] = freq[i]; } int sizevvt = multiply_ffq(freq.size()); multiply(freq, sizevvt, freq.size()); // remove duples and triples long long wyn = round(vvvt[3 * N].real()); for (int l = 0; l < N; l++) { long long sub = 3ll * get_freq(freq, l) * get_freq(freq, l) * get_freq(freq, 3 * N - 2 * l); wyn -= sub; int k = 3 * N - l; if (k % 2 == 0) { sub = 3ll * get_freq(freq, l) * get_freq(freq, k / 2) * get_freq(freq, k / 2); wyn -= sub; } } wyn -= get_freq(freq, N) * get_freq(freq, N) * get_freq(freq, N); wyn /= 6; // add dupples and triples for (int l = 0; l < N; l++) { long long add = get_freq(freq, l) * (get_freq(freq, l) - 1) / 2 * get_freq(freq, 3 * N - 2 * l); wyn += add; int k = 3 * N - l; if (k % 2 == 0) { add = get_freq(freq, l) * (get_freq(freq, k / 2) * (get_freq(freq, k / 2) - 1) / 2); wyn += add; } } if (get_freq(freq, N) >= 3) { wyn += bicoff[get_freq(freq, N)][3]; } cout << wyn << endl; return 0; }
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 | #include<iostream> #include<vector> #include<algorithm> #include<complex> using namespace std; const double PI = acos(-1); const int MAX_FFT = 1 << 24; complex<double> vvt[MAX_FFT]; complex<double> vvvt[MAX_FFT]; int calc_size(int a, int b) { long long n = 1; while (n < a + b) n <<= 1; return n; } int reverse(int num, int lg_n) { int res = 0; for (int i = 0; i < lg_n; i++) { if (num & (1 << i)) res |= 1 << (lg_n - 1 - i); } return res; } void fft(complex<double> a[], int n, bool invert) { for (int i = 1, j = 0; i < n; i++) { int bit = n >> 1; for (; j & bit; bit >>= 1) j ^= bit; j ^= bit; if (i < j) swap(a[i], a[j]); } for (int len = 2; len <= n; len <<= 1) { double ang = 2 * PI / len * (invert ? -1 : 1); complex<double> wlen(cos(ang), sin(ang)); for (int i = 0; i < n; i += len) { complex<double> w(1); for (int j = 0; j < len / 2; j++) { complex<double> u = a[i+j], v = a[i+j+len/2] * w; a[i+j] = u + v; a[i+j+len/2] = u - v; w *= wlen; } } } if (invert) { for (int i = 0; i < n; i++) { a[i] /= n; } } } void multiply(vector<short> &freq, int sizea, int sizeb) { long long n = calc_size(sizea, sizeb); for (int i = 0; i < sizea; i++) { vvvt[i] = vvt[i]; } for (int i = 0; i < n; i++) vvt[i] = 0; for (int i = 0; i < freq.size(); i++) { vvt[i] = freq[i]; } fft(vvvt, n, false); fft(vvt, n, false); for (int i = 0; i < n; i++) { vvvt[i] *= vvt[i]; } fft(vvvt, n, true); } int multiply_ffq(int sizea) { long long n = calc_size(sizea, sizea); fft(vvt, n, false); for (int i = 0; i < n; i++) { vvt[i] *= vvt[i]; } fft(vvt, n, true); return n; } const int MAX = 500 * 500 + 5; long long bicoff[MAX][4]; vector<short> count(vector<long long> &v, int N) { int n = v.size(); vector<short> res(2 * N + 1); for (int i = 0; i < n; i++) { res[v[i]]++; } return res; } long long get_freq(vector<short> &freq, int k) { return k >= freq.size() || k < 0 ? 0 : freq[k]; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); int n; cin >> n; vector<long long> tmp(n); for (int i = 0; i < n; i++) { cin >> tmp[i]; } if (n == 1) { cout << 0 << endl; return 0; } // create BUC long long minn = 0; long long maxx = 0; vector<long long> v(n * (n + 1) / 2); for (int i = 0, k = 0; i < n; i++) { long long acc = 0; for (int j = i; j < n; j++) { acc += tmp[j]; v[k++] = acc; minn = min(minn, acc); maxx = max(maxx, acc); } } sort(v.begin(), v.end()); long long N = max(abs(minn), maxx); if (N > 4'000'000) { long long ret = 0; for (int i = 0; i < v.size() - 2; i++) { long long a = i + 1, b = v.size() - 1; while (a < b) { int acc = v[i] + v[a] + v[b]; if (acc == 0) { if (v[a] == v[b]) { ret += (b - a) * (b - a + 1) / 2; break; } else { long long ac = 1; while (v[a + 1] == v[a]) { ac++; a++; } a++; long long bc = 1; while (v[b - 1] == v[b]) { bc++; b--; } b--; ret += ac * bc; } } else if (acc < 0) a++; else b--; } } cout << ret << endl; return 0; } // compute binomial coefficients bicoff[0][0] = 1; bicoff[0][1] = 0; bicoff[0][2] = 0; bicoff[0][3] = 0; for (int i = 1; i < MAX; i++) { bicoff[i][0] = 1; bicoff[i][1] = bicoff[i - 1][1] + bicoff[i - 1][0]; bicoff[i][2] = bicoff[i - 1][2] + bicoff[i - 1][1]; bicoff[i][3] = bicoff[i - 1][3] + bicoff[i - 1][2]; } // shift BUC for (int i = 0; i < v.size(); i++) { v[i] += N; } // compute fft vector<short> freq = count(v, N); for (int i = 0; i < freq.size(); i++) { vvt[i] = freq[i]; } int sizevvt = multiply_ffq(freq.size()); multiply(freq, sizevvt, freq.size()); // remove duples and triples long long wyn = round(vvvt[3 * N].real()); for (int l = 0; l < N; l++) { long long sub = 3ll * get_freq(freq, l) * get_freq(freq, l) * get_freq(freq, 3 * N - 2 * l); wyn -= sub; int k = 3 * N - l; if (k % 2 == 0) { sub = 3ll * get_freq(freq, l) * get_freq(freq, k / 2) * get_freq(freq, k / 2); wyn -= sub; } } wyn -= get_freq(freq, N) * get_freq(freq, N) * get_freq(freq, N); wyn /= 6; // add dupples and triples for (int l = 0; l < N; l++) { long long add = get_freq(freq, l) * (get_freq(freq, l) - 1) / 2 * get_freq(freq, 3 * N - 2 * l); wyn += add; int k = 3 * N - l; if (k % 2 == 0) { add = get_freq(freq, l) * (get_freq(freq, k / 2) * (get_freq(freq, k / 2) - 1) / 2); wyn += add; } } if (get_freq(freq, N) >= 3) { wyn += bicoff[get_freq(freq, N)][3]; } cout << wyn << endl; return 0; } |