diff --git a/code/Basic/vimrc b/code/Basic/vimrc new file mode 100755 index 0000000..a430ef2 --- /dev/null +++ b/code/Basic/vimrc @@ -0,0 +1,8 @@ +set ts=4 +set sw=4 +set si +set nu +set mouse=a +imap { {}iv :w:!g++ -O2 -std=c++14 -o %.out % && echo "----Test Start----" && ./%.out +imap \ No newline at end of file diff --git a/code/DataStructure/ext_heap.cpp b/code/DataStructure/pb_ds heap.cpp similarity index 59% rename from code/DataStructure/ext_heap.cpp rename to code/DataStructure/pb_ds heap.cpp index 8f4e175..f6e06f8 100755 --- a/code/DataStructure/ext_heap.cpp +++ b/code/DataStructure/pb_ds heap.cpp @@ -1,20 +1,12 @@ #include typedef __gnu_pbds::priority_queue heap_t; heap_t a,b; - int main() { - a.clear(); - b.clear(); - a.push(1); - a.push(3); - b.push(2); - b.push(4); - assert(a.top() == 3); - assert(b.top() == 4); + a.clear();b.clear(); + a.push(1);a.push(3);b.push(2);b.push(4); // merge two heap a.join(b); assert(a.top() == 4); assert(b.empty()); - return 0; } \ No newline at end of file diff --git a/code/DataStructure/pb_ds rbtree.cpp b/code/DataStructure/pb_ds rbtree.cpp new file mode 100755 index 0000000..f9b7245 --- /dev/null +++ b/code/DataStructure/pb_ds rbtree.cpp @@ -0,0 +1,17 @@ +#include +#include +using namespace __gnu_pbds; +#define ordered_set tree, rb_tree_tag,tree_order_statistics_node_update> +int main() { + ordered_set o_set; + o_set.insert(5); + o_set.insert(1); + o_set.insert(2); + cout << *(o_set.find_by_order(1)) << endl; // 2 + cout << o_set.order_of_key(4) << endl; // 2 + cout << o_set.order_of_key(5) << endl; // 2 + if (o_set.find(2) != o_set.end()) + o_set.erase(o_set.find(2)); + cout << *(o_set.find_by_order(1)) << endl; // 5 + cout << o_set.order_of_key(4) << endl; // 1 +} \ No newline at end of file diff --git a/code/Math/FWHT.cpp b/code/Math/FWHT.cpp deleted file mode 100755 index b748742..0000000 --- a/code/Math/FWHT.cpp +++ /dev/null @@ -1,17 +0,0 @@ -// FWHT template - -const int MAXN = 1<<20; - -void FWHT(int a[], int l=0, int r=MAXN-1){ - if (l==r)return; - - int mid = (l+r)>>1+1, n = r-l+1; - FWHT(a,l,mid-1); - FWHT(a,mid,r); - - for (int i=0; i<(n>>1); i++){ - int a1=a[l+i], a2=a[mid+i]; - a[l+i] = a1+a2; - a[mid+i] = a1-a2; - } -} diff --git a/code/Math/Simplex.cpp b/code/Math/Simplex.cpp new file mode 100755 index 0000000..c654b88 --- /dev/null +++ b/code/Math/Simplex.cpp @@ -0,0 +1,124 @@ +// Two-phase simplex algorithm for solving linear programs of the form +// +// maximize c^T x +// subject to Ax <= b +// x >= 0 +// +// INPUT: A -- an m x n matrix +// b -- an m-dimensional vector +// c -- an n-dimensional vector +// x -- a vector where the optimal solution will be stored +// +// OUTPUT: value of the optimal solution (infinity if unbounded +// above, nan if infeasible) +// +// To use this code, create an LPSolver object with A, b, and c as +// arguments. Then, call Solve(x). + +#include +#include +#include +#include +#include + +using namespace std; + +typedef long double DOUBLE; +typedef vector VD; +typedef vector VVD; +typedef vector VI; + +const DOUBLE EPS = 1e-9; + +struct LPSolver { + int m, n; + VI B, N; + VVD D; + + LPSolver(const VVD &A, const VD &b, const VD &c) : + m(b.size()), n(c.size()), N(n + 1), B(m), D(m + 2, VD(n + 2)) { + for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) D[i][j] = A[i][j]; + for (int i = 0; i < m; i++) { B[i] = n + i; D[i][n] = -1; D[i][n + 1] = b[i]; } + for (int j = 0; j < n; j++) { N[j] = j; D[m][j] = -c[j]; } + N[n] = -1; D[m + 1][n] = 1; + } + + void Pivot(int r, int s) { + double inv = 1.0 / D[r][s]; + for (int i = 0; i < m + 2; i++) if (i != r) + for (int j = 0; j < n + 2; j++) if (j != s) + D[i][j] -= D[r][j] * D[i][s] * inv; + for (int j = 0; j < n + 2; j++) if (j != s) D[r][j] *= inv; + for (int i = 0; i < m + 2; i++) if (i != r) D[i][s] *= -inv; + D[r][s] = inv; + swap(B[r], N[s]); + } + + bool Simplex(int phase) { + int x = phase == 1 ? m + 1 : m; + while (true) { + int s = -1; + for (int j = 0; j <= n; j++) { + if (phase == 2 && N[j] == -1) continue; + if (s == -1 || D[x][j] < D[x][s] || D[x][j] == D[x][s] && N[j] < N[s]) s = j; + } + if (D[x][s] > -EPS) return true; + int r = -1; + for (int i = 0; i < m; i++) { + if (D[i][s] < EPS) continue; + if (r == -1 || D[i][n + 1] / D[i][s] < D[r][n + 1] / D[r][s] || + (D[i][n + 1] / D[i][s]) == (D[r][n + 1] / D[r][s]) && B[i] < B[r]) r = i; + } + if (r == -1) return false; + Pivot(r, s); + } + } + + DOUBLE Solve(VD &x) { + int r = 0; + for (int i = 1; i < m; i++) if (D[i][n + 1] < D[r][n + 1]) r = i; + if (D[r][n + 1] < -EPS) { + Pivot(r, n); + if (!Simplex(1) || D[m + 1][n + 1] < -EPS) return -numeric_limits::infinity(); + for (int i = 0; i < m; i++) if (B[i] == -1) { + int s = -1; + for (int j = 0; j <= n; j++) + if (s == -1 || D[i][j] < D[i][s] || D[i][j] == D[i][s] && N[j] < N[s]) s = j; + Pivot(i, s); + } + } + if (!Simplex(2)) return numeric_limits::infinity(); + x = VD(n); + for (int i = 0; i < m; i++) if (B[i] < n) x[B[i]] = D[i][n + 1]; + return D[m][n + 1]; + } +}; + +int main() { + + const int m = 4; + const int n = 3; + DOUBLE _A[m][n] = { + { 6, -1, 0 }, + { -1, -5, 0 }, + { 1, 5, 1 }, + { -1, -5, -1 } + }; + DOUBLE _b[m] = { 10, -4, 5, -5 }; + DOUBLE _c[n] = { 1, -1, 0 }; + + VVD A(m); + VD b(_b, _b + m); + VD c(_c, _c + n); + for (int i = 0; i < m; i++) A[i] = VD(_A[i], _A[i] + n); + + LPSolver solver(A, b, c); + VD x; + DOUBLE value = solver.Solve(x); + + cerr << "VALUE: " << value << endl; // VALUE: 1.29032 + cerr << "SOLUTION:"; // SOLUTION: 1.74194 0.451613 1 + for (size_t i = 0; i < x.size(); i++) cerr << " " << x[i]; + cerr << endl; + return 0; +} \ No newline at end of file diff --git a/code/Math/inverse.cpp b/code/Math/inverse.cpp deleted file mode 100755 index c3e00b0..0000000 --- a/code/Math/inverse.cpp +++ /dev/null @@ -1,13 +0,0 @@ -const int MAXN = 1000006; -int inv[MAXN]; -void invTable(int bound, int p){ - inv[1] = 1; - for (int i=2; i