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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,4 +1,4 @@ | ||
| \section{FFT封装} | ||
| \section{多项式算法封装}\label{Module} | ||
| 牛顿迭代法/分治FFT时使用。 | ||
|
|
||
| 使用vector存储多项式。 | ||
|
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||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,77 @@ | ||
| #include <algorithm> | ||
| #include <cstdio> | ||
| #include <cstring> | ||
| #include <vector> | ||
| const int size = 100005; | ||
| struct Edge { | ||
| int u, v, w; | ||
| } E[size]; | ||
| bool cmp(int a, int b) { | ||
| return E[a].w < E[b].w; | ||
| } | ||
| typedef std::vector<int> ES; | ||
| int n, fa[105]; | ||
| int find(int x) { | ||
| return fa[x] ? fa[x] = find(fa[x]) : x; | ||
| } | ||
| ES merge(const ES& A, const ES& B) { | ||
| ES X(A.size() + B.size()); | ||
| std::merge(A.begin(), A.end(), B.begin(), B.end(), | ||
| X.begin(), cmp); | ||
| ES Y; | ||
| memset(fa + 1, 0, sizeof(int) * n); | ||
| for(int i = 0, ecnt = n - 1; i < X.size(); ++i) { | ||
| Edge& e = E[X[i]]; | ||
| int u = find(e.u), v = find(e.v); | ||
| if(u != v) { | ||
| Y.push_back(X[i]); | ||
| fa[u] = v; | ||
| if(--ecnt == 0) | ||
| break; | ||
| } | ||
| } | ||
| return Y; | ||
| } | ||
| ES G[size << 2]; | ||
| #define ls l, m, id << 1 | ||
| #define rs m + 1, r, id << 1 | 1 | ||
| void build(int l, int r, int id) { | ||
| if(l == r) | ||
| G[id].push_back(l); | ||
| else { | ||
| int m = (l + r) >> 1; | ||
| build(ls); | ||
| build(rs); | ||
| G[id] = merge(G[id << 1], G[id << 1 | 1]); | ||
| } | ||
| } | ||
| ES query(int l, int r, int id, int nl, int nr) { | ||
| if(nl <= l && r <= nr) | ||
| return G[id]; | ||
| else { | ||
| int m = (l + r) >> 1; | ||
| if(nl <= m && m < nr) | ||
| return merge(query(ls, nl, nr), | ||
| query(rs, nl, nr)); | ||
| if(nl <= m) | ||
| return query(ls, nl, nr); | ||
| return query(rs, nl, nr); | ||
| } | ||
| } | ||
| int main() { | ||
| int m, q; | ||
| scanf("%d%d%d", &n, &m, &q); | ||
| for(int i = 1; i <= m; ++i) | ||
| scanf("%d%d%d", &E[i].u, &E[i].v, &E[i].w); | ||
| build(1, m, 1); | ||
| for(int i = 1; i <= q; ++i) { | ||
| int l, r; | ||
| scanf("%d%d", &l, &r); | ||
| ES res = query(1, m, 1, l, r); | ||
| int ans = 0; | ||
| for(int j = 0; j < res.size(); ++j) | ||
| ans += E[res[j]].w; | ||
| printf("%d\n", ans); | ||
| } | ||
| return 0; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,142 @@ | ||
| #include <algorithm> | ||
| #include <cmath> | ||
| #include <complex> | ||
| #include <cstdio> | ||
| #include <cstring> | ||
| const int size = 1 << 20; | ||
| typedef double FT; | ||
| typedef std::complex<FT> Complex; | ||
| Complex root[size], invR[size]; | ||
| int tot; | ||
| void init(int n) { | ||
| tot = n; | ||
| FT base = 2.0 * acos(-1.0) / n; | ||
| for(int i = 0; i < n; ++i) { | ||
| root[i] = | ||
| Complex(cos(base * i), sin(base * i)); | ||
| invR[i] = std::conj(root[i]); | ||
| } | ||
| } | ||
| void FFT(int n, Complex* A, const Complex* w) { | ||
| for(int i = 0, j = 0; i < n; ++i) { | ||
| if(i < j) | ||
| std::swap(A[i], A[j]); | ||
| for(int l = n >> 1; (j ^= l) < l; l >>= 1) | ||
| ; | ||
| } | ||
| for(int i = 2; i <= n; i <<= 1) { | ||
| int m = i >> 1, fac = tot / i; | ||
| for(int j = 0; j < n; j += i) | ||
| for(int k = 0; k < m; ++k) { | ||
| Complex &x = A[j + k], | ||
| &y = A[j + m + k]; | ||
| Complex t = y * w[k * fac]; | ||
| y = x - t; | ||
| x += t; | ||
| } | ||
| } | ||
| } | ||
| char buf[705 * 705]; | ||
| int mcnt[705][705]; | ||
| bool match[705][705], color[705][705]; | ||
| Complex S[size], T[size]; | ||
| int n, m, w, h; | ||
| void DFS(int x, int y) { | ||
| match[x][y] = false; | ||
| S[x * m + y] = 1.0; | ||
| if(x + 1 + h - 1 <= n && match[x + 1][y]) | ||
| DFS(x + 1, y); | ||
| if(x > 1 && match[x - 1][y]) | ||
| DFS(x - 1, y); | ||
| if(y + 1 + w - 1 <= m && match[x][y + 1]) | ||
| DFS(x, y + 1); | ||
| if(y > 1 && match[x][y - 1]) | ||
| DFS(x, y - 1); | ||
| } | ||
| int main() { | ||
| scanf("%d%d", &n, &m); | ||
| int ml = m + 1, mr = 0, mt = n + 1, mb = 0; | ||
| for(int i = 1; i <= n; ++i) { | ||
| scanf("%s", buf + i * m + 1); | ||
| for(int j = 1; j <= m; ++j) | ||
| if(buf[i * m + j] == 'o') { | ||
| ml = std::min(ml, j); | ||
| mr = std::max(mr, j); | ||
| mt = std::min(mt, i); | ||
| mb = std::max(mb, i); | ||
| } | ||
| } | ||
| int begS = 1 * m + 1, endS = n * m + m; | ||
| int lenS = endS - begS + 1; | ||
| int begT = mt * m + ml, endT = mb * m + mr; | ||
| int lenT = endT - begT + 1; | ||
| int end = lenS + lenT + 1; | ||
| w = mr - ml + 1, h = mb - mt + 1; | ||
| int p = 1; | ||
| while(p < end) | ||
| p <<= 1; | ||
| init(p); | ||
| //# | ||
| { | ||
| memset(S, 0, sizeof(Complex) * p); | ||
| memset(T, 0, sizeof(Complex) * p); | ||
| for(int i = begS; i <= endS; ++i) | ||
| S[i - begS + 1] = (buf[i] == '#'); | ||
| for(int i = begT; i <= endT; ++i) | ||
| T[i - begT + 1] = (buf[i] != 'o'); | ||
| std::reverse(T + 1, T + lenT + 1); | ||
| FFT(p, S, root); | ||
| FFT(p, T, root); | ||
| for(int i = 0; i < p; ++i) | ||
| S[i] *= T[i]; | ||
| FFT(p, S, invR); | ||
| for(int i = 1; i + h - 1 <= n; ++i) | ||
| for(int j = 1; j + w - 1 <= m; ++j) | ||
| mcnt[i][j] += round( | ||
| S[lenT + (i * m + j - begS + 1)] | ||
| .real() / | ||
| p); | ||
| } | ||
| // o | ||
| { | ||
| memset(S, 0, sizeof(Complex) * p); | ||
| memset(T, 0, sizeof(Complex) * p); | ||
| for(int i = begS; i <= endS; ++i) | ||
| S[i - begS + 1] = (buf[i] != '#'); | ||
| for(int i = begT; i <= endT; ++i) | ||
| T[i - begT + 1] = 1.0; | ||
| std::reverse(T + 1, T + lenT + 1); | ||
| FFT(p, S, root); | ||
| FFT(p, T, root); | ||
| for(int i = 0; i < p; ++i) | ||
| S[i] *= T[i]; | ||
| FFT(p, S, invR); | ||
| for(int i = 1; i + h - 1 <= n; ++i) | ||
| for(int j = 1; j + w - 1 <= m; ++j) | ||
| mcnt[i][j] += round( | ||
| S[lenT + (i * m + j - begS + 1)] | ||
| .real() / | ||
| p); | ||
| } | ||
| for(int i = 1; i + h - 1 <= n; ++i) | ||
| for(int j = 1; j + w - 1 <= m; ++j) | ||
| match[i][j] = (mcnt[i][j] >= lenT); | ||
| memset(S, 0, sizeof(Complex) * p); | ||
| memset(T, 0, sizeof(Complex) * p); | ||
| DFS(mt, ml); | ||
| for(int i = 1; i <= n; ++i) | ||
| for(int j = 1; j <= m; ++j) | ||
| if(buf[i * m + j] == 'o') | ||
| T[i * m + j - begT] = 1.0; | ||
| FFT(p, S, root); | ||
| FFT(p, T, root); | ||
| for(int i = 0; i < p; ++i) | ||
| S[i] *= T[i]; | ||
| FFT(p, S, invR); | ||
| int res = 0; | ||
| for(int i = 1; i <= n; ++i) | ||
| for(int j = 1; j <= m; ++j) | ||
| res += (S[i * m + j].real() / p >= 0.5); | ||
| printf("%d\n", res); | ||
| return 0; | ||
| } |
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