From e06d662de2a01673ce6151ef66d2aa00b271a44c Mon Sep 17 00:00:00 2001 From: Santo Cariotti Date: Mon, 20 Jul 2020 12:26:37 +0200 Subject: feat: add exercises of 20/07/2020 exam --- .../exercises/exam_20_07_20/ex1.cpp | 39 +++ .../exercises/exam_20_07_20/ex2.cpp | 63 +++++ .../exercises/exam_20_07_20/ex3.cpp | 284 ++++++++++++++++++++ .../exercises/exam_20_07_20/ex4.cpp | 293 +++++++++++++++++++++ .../exercises/exam_20_07_20/ex5.cpp | 285 ++++++++++++++++++++ 5 files changed, 964 insertions(+) create mode 100644 I_anno/Programmazione_2/exercises/exam_20_07_20/ex1.cpp create mode 100644 I_anno/Programmazione_2/exercises/exam_20_07_20/ex2.cpp create mode 100644 I_anno/Programmazione_2/exercises/exam_20_07_20/ex3.cpp create mode 100644 I_anno/Programmazione_2/exercises/exam_20_07_20/ex4.cpp create mode 100644 I_anno/Programmazione_2/exercises/exam_20_07_20/ex5.cpp diff --git a/I_anno/Programmazione_2/exercises/exam_20_07_20/ex1.cpp b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex1.cpp new file mode 100644 index 0000000..4f08a74 --- /dev/null +++ b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex1.cpp @@ -0,0 +1,39 @@ +#include +#include +#include +#include + +using namespace std; +int insertionsort(vector& a, int n) { + int c = 0; + for(int i = 1; i < n; ++i) { + int j = i-1; + int key = a[i]; + while(j > -1 && a[j] > key) { + swap(a[j+1], a[j]); + --j; + c++; + } + a[j+1] = key; + } + return c; +} +int main() { + ifstream in("input.txt"); + ofstream out("output.txt"); + + for(int ts = 0; ts < 100; ++ts) { + int N; + in >> N; + int a, b; + vector v; + for(int i = 0; i < N; ++i) { + in >> a >> b; + v.push_back(a+b); + } + out << insertionsort(v, v.size()) << endl; + } + in.close(); + out.close(); + return 0; +} diff --git a/I_anno/Programmazione_2/exercises/exam_20_07_20/ex2.cpp b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex2.cpp new file mode 100644 index 0000000..aed25e4 --- /dev/null +++ b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex2.cpp @@ -0,0 +1,63 @@ +#include +#include +#include +#include + +using namespace std; +using pi = tuple>; + +class comp { +public: + bool operator()(const pi& lhs, const pi& rhs) const { + auto xl = get<0>(lhs); + auto yl = get<0>(rhs); + + auto il = get<1>(lhs); + auto jl = get<1>(rhs); + if(xl == yl) + return il > jl; + return xl > yl; + } +}; + +int main() { + ifstream in("input.txt"); + ofstream out("output.txt"); + + for(int ts = 0; ts < 100; ++ts) { + int R, C; + in >> R >> C; + vector> v; + priority_queue, comp> pq; + int k; + for(int i = 0; i < R; ++i) { + v.push_back(vector{}); + for(int j = 0; j < C; ++j) { + in >> k; + v[i].push_back(k); + } + } + + int index = 0; + for(auto const& i : v) { + int s = 0; + pi qq; + for(auto const& j : i) + s += j; + get<0>(qq) = s; + get<1>(qq) = index++; + get<2>(qq) = i; + pq.push(qq); + } + while(!pq.empty()) { + auto q = pq.top(); + pq.pop(); + for(auto const& i : get<2>(q)) + out << i << ' '; + } + out << endl; + } + in.close(); + out.close(); + return 0; +} diff --git a/I_anno/Programmazione_2/exercises/exam_20_07_20/ex3.cpp b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex3.cpp new file mode 100644 index 0000000..71f9c65 --- /dev/null +++ b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex3.cpp @@ -0,0 +1,284 @@ +#include +#include +#include + +using namespace std; + +template +struct node { + T key; + node* prev; + node* right; + node* left; +}; + +template +class bst { +public: + bst() : root{nullptr} , _val{0}{} + + ~bst() { + // TODO + } + + bst* insert(initializer_list&& list) { + for(auto const& i : list) + insert(i); + + return this; + } + + bst* insert(T k) { + node* nodus = new node{k, nullptr, nullptr, nullptr}; + node* iter = root; + node* prev = nullptr; + + while(iter) { + prev = iter; + iter = (k < iter->key) ? iter->left : iter->right; + } + + nodus->prev = prev; + if(!prev) + root = nodus; + else if(k < prev->key) + prev->left = nodus; + else + prev->right = nodus; + + return this; + } + + bst* remove(initializer_list&& list) { + for(auto const& i : list) + remove(i); + + return this; + } + + bst* remove(T k) { + node* nodus = search(k); + if(!nodus) return this; + + if(!nodus->left) { + _transplant(nodus, nodus->right); + } else if(!nodus->right) { + _transplant(nodus, nodus->left); + } else { + node* iter = _min(nodus->right); + if(iter->prev != nodus) { + _transplant(iter, iter->right); + iter->right = nodus->right; + iter->right->prev = iter; + } + _transplant(nodus, iter); + iter->left = nodus->left; + iter->left->prev = iter; + } + + delete nodus; + return this; + } + + node* min() { + return _min(root); + } + + node* min(node* nodus) { + return _min(nodus); + } + + node* max() { + return _max(root); + } + + node* max(node* nodus) { + return _max(nodus); + } + + node* search(T k) { + node* iter = root; + while(iter && iter->key != k) + iter = (iter->key > k) ? iter->left : iter->right; + + return iter; + } + + node* successor(T k) { + node* nodus = search(k); + if(!nodus) return nullptr; + + if(nodus->right) + return min(nodus->right); + + node* prev = nodus->prev; + while(prev && nodus == prev->right) { + nodus = prev; + prev = prev->prev; + } + + return prev; + + } + node* predecessor(T k) { + node* nodus = search(k); + if(!nodus) return nullptr; + + if(nodus->left) + return max(nodus->left); + + node* prev = nodus->prev; + while(prev && nodus == prev->left) { + nodus = prev; + prev = prev->prev; + } + + return prev; + } + + friend ostream& operator<<(ostream& os, bst* tree) { + tree->_inorder(os, tree->root); + return os; + } + T sol(T k) { + return _max(search(k))->key; + } +private: + int _val; + void _transplant(node* u, node* v) { + if(!u->prev) { + root = v; + } else if(u == u->prev->left) { + u->prev->left = v; + } else { + u->prev->right = v; + } + + if(v) + v->prev = u->prev; + } + + node* _min(node* root) { + node* iter = root; + while(iter && iter->left) + iter = iter->left; + + return iter; + } + + node* _max(node* root) { + node* iter = root; + while(iter && iter->right) + iter = iter->right; + + return iter; + } + + void _inorder(ostream& os, node* root) { + if(root) { + if(root->right && root->left) { + _val++; + } + _inorder(os, root->left); + os << root->key << ' '; + _inorder(os, root->right); + } + } + + void _preorder(ostream& os, node* root) { + if(root) { + os << root->key << ' '; + _inorder(os, root->left); + _inorder(os, root->right); + } + } + + void _postorder(ostream& os, node* root) { + if(root) { + _inorder(os, root->left); + _inorder(os, root->right); + os << root->key << ' '; + } + } + node* root; +}; + +int main() { + ifstream in("input.txt"); + ofstream out("output.txt"); + + for(int ts = 0; ts < 100; ++ts) { + string t, comm; + in >> t; + int n; + switch(t.at(0)) { + case 'd': + { + bst* b = new bst{}; + in >> n; + double k; + for(int i = 0; i < n; ++i) { + in >> comm; + stringstream tcomm(comm); + int ex= 0; + while(getline(tcomm, comm, ':')) { + if(ex == 0) { + if(comm == "ins") + ex = 1; + else + ex = 2; + } else { + if(ex == 1) + b->insert(stod(comm)); + else + b->remove(stod(comm)); + ex = 0; + } + } + } + in >> k; + cout << b << endl; + out << b->sol(k) << endl; + + delete b; + break; + } + case 'i': + { + bst* b = new bst{}; + in >> n; + int k; + for(int i = 0; i < n; ++i) { + in >> comm; + stringstream tcomm(comm); + int ex= 0; + while(getline(tcomm, comm, ':')) { + if(ex == 0) { + if(comm == "ins") + ex = 1; + else + ex = 2; + } else { + if(ex == 1) + b->insert(stoi(comm)); + else + b->remove(stoi(comm)); + ex = 0; + } + } + } + in >> k; + cout << b << endl; + out << b->sol(k) << endl; + + delete b; + break; + } + } + } + + in.close(); + out.close(); + return 0; +} + diff --git a/I_anno/Programmazione_2/exercises/exam_20_07_20/ex4.cpp b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex4.cpp new file mode 100644 index 0000000..e234363 --- /dev/null +++ b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex4.cpp @@ -0,0 +1,293 @@ +#include +#include +#include + +using namespace std; + +template +struct node { + T key; + node* prev; + node* right; + node* left; +}; + +template +class bst { +public: + bst() : root{nullptr} , _val{0}{} + + ~bst() { + // TODO + } + + bst* insert(initializer_list&& list) { + for(auto const& i : list) + insert(i); + + return this; + } + + bst* insert(T k) { + node* nodus = new node{k, nullptr, nullptr, nullptr}; + node* iter = root; + node* prev = nullptr; + + while(iter) { + prev = iter; + iter = (k < iter->key) ? iter->left : iter->right; + } + + nodus->prev = prev; + if(!prev) + root = nodus; + else if(k < prev->key) + prev->left = nodus; + else + prev->right = nodus; + + return this; + } + + bst* remove(initializer_list&& list) { + for(auto const& i : list) + remove(i); + + return this; + } + + bst* remove(T k) { + node* nodus = search(k); + if(!nodus) return this; + + if(!nodus->left) { + _transplant(nodus, nodus->right); + } else if(!nodus->right) { + _transplant(nodus, nodus->left); + } else { + node* iter = _min(nodus->right); + if(iter->prev != nodus) { + _transplant(iter, iter->right); + iter->right = nodus->right; + iter->right->prev = iter; + } + _transplant(nodus, iter); + iter->left = nodus->left; + iter->left->prev = iter; + } + + delete nodus; + return this; + } + + node* min() { + return _min(root); + } + + node* min(node* nodus) { + return _min(nodus); + } + + node* max() { + return _max(root); + } + + node* max(node* nodus) { + return _max(nodus); + } + + node* search(T k) { + node* iter = root; + while(iter && iter->key != k) + iter = (iter->key > k) ? iter->left : iter->right; + + return iter; + } + + node* successor(T k) { + node* nodus = search(k); + if(!nodus) return nullptr; + + if(nodus->right) + return min(nodus->right); + + node* prev = nodus->prev; + while(prev && nodus == prev->right) { + nodus = prev; + prev = prev->prev; + } + + return prev; + + } + node* predecessor(T k) { + node* nodus = search(k); + if(!nodus) return nullptr; + + if(nodus->left) + return max(nodus->left); + + node* prev = nodus->prev; + while(prev && nodus == prev->left) { + nodus = prev; + prev = prev->prev; + } + + return prev; + } + + friend ostream& operator<<(ostream& os, bst* tree) { + tree->_inorder(os, tree->root); + return os; + } + T sol(T k) { + auto x = search(k); + auto m = _max(x)->key; + auto mnn = _min(x); + T mn; + if(mnn->right) + mn = _min(mnn->right)->key; + else + mn = mnn->key; + cout << m << ' ' << mn << endl; + return m - mn; + } +private: + int _val; + void _transplant(node* u, node* v) { + if(!u->prev) { + root = v; + } else if(u == u->prev->left) { + u->prev->left = v; + } else { + u->prev->right = v; + } + + if(v) + v->prev = u->prev; + } + + node* _min(node* root) { + node* iter = root; + while(iter && iter->left) + iter = iter->left; + + return iter; + } + + node* _max(node* root) { + node* iter = root; + while(iter && iter->right) + iter = iter->right; + + return iter; + } + + void _inorder(ostream& os, node* root) { + if(root) { + if(root->right && root->left) { + _val++; + } + _inorder(os, root->left); + os << root->key << ' '; + _inorder(os, root->right); + } + } + + void _preorder(ostream& os, node* root) { + if(root) { + os << root->key << ' '; + _inorder(os, root->left); + _inorder(os, root->right); + } + } + + void _postorder(ostream& os, node* root) { + if(root) { + _inorder(os, root->left); + _inorder(os, root->right); + os << root->key << ' '; + } + } + node* root; +}; + +int main() { + ifstream in("input.txt"); + ofstream out("output.txt"); + + for(int ts = 0; ts < 100; ++ts) { + string t, comm; + in >> t; + int n; + switch(t.at(0)) { + case 'd': + { + bst* b = new bst{}; + in >> n; + double k; + for(int i = 0; i < n; ++i) { + in >> comm; + stringstream tcomm(comm); + int ex= 0; + while(getline(tcomm, comm, ':')) { + if(ex == 0) { + if(comm == "ins") + ex = 1; + else + ex = 2; + } else { + if(ex == 1) + b->insert(stod(comm)); + else + b->remove(stod(comm)); + ex = 0; + } + } + } + in >> k; + cout << b << endl; + out << b->sol(k) << endl; + + delete b; + break; + } + case 'i': + { + bst* b = new bst{}; + in >> n; + int k; + for(int i = 0; i < n; ++i) { + in >> comm; + stringstream tcomm(comm); + int ex= 0; + while(getline(tcomm, comm, ':')) { + if(ex == 0) { + if(comm == "ins") + ex = 1; + else + ex = 2; + } else { + if(ex == 1) + b->insert(stoi(comm)); + else + b->remove(stoi(comm)); + ex = 0; + } + } + } + in >> k; + cout << b << endl; + out << b->sol(k) << endl; + + delete b; + break; + } + } + } + + in.close(); + out.close(); + return 0; +} + diff --git a/I_anno/Programmazione_2/exercises/exam_20_07_20/ex5.cpp b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex5.cpp new file mode 100644 index 0000000..dd8fc98 --- /dev/null +++ b/I_anno/Programmazione_2/exercises/exam_20_07_20/ex5.cpp @@ -0,0 +1,285 @@ +#include +#include +#include +#include +#include +#include +#define INF 99999999 +#define W -1 +#define G 0 +#define B 1 + +using namespace std; + +template +class graph { +public: + graph(int len) : _len{len}, _nodes{0}, _edges{0} { + _k = new H*[len]; + _adj = new vector[len]; + _colors = new int[len]; + _d = new int[len]; + _f = new int[len]; + _p = new int[len]; + + for(int i = 0; i < len; ++i) { + _k[i] = nullptr; + } + } + ~graph() { + delete[] _k; + delete[] _adj; + } + + graph* add_node(H x) { + if(_index(x) > -1) return this; + if(_nodes == _len) return this; + _k[_nodes++] = new H(x); + + return this; + } + graph* add_edge(H u, H v) { + int i = _index(u); + int j = _index(v); + if(i < 0 || j < 0) return this; + + if(find(_adj[i].begin(), _adj[i].end(), j) == _adj[i].end()) { + _adj[i].push_back(j); + } + return this; + } + void print() { + for(int i = 0; i < _nodes; ++i) { + cout << "(" << *_k[i] << ", " << i << "): "; + for(auto const& j : _adj[i]) { + cout << "(" << *_k[j] << ", " << j << ") "; + } + cout << endl; + } + } + void dfsvisit(int u, bool visited[]) { + visited[u] = true; + cout << "(" << *_k[u] << ", " << u << ") "; + for(auto const& i : _adj[u]) { + if(!visited[i]) + dfsvisit(i, visited); + } + } + int dfsvisit(int u) { + int cycle = 0; + _colors[u] = G; + _d[u] = _time++; + + for(auto const& j : _adj[u]) { + if(_colors[j] == W) + cycle |= dfsvisit(j); + } + + _colors[u] = B; + _stack.push(u); + _f[u] = _time++; + return cycle; + } + int dfs() { + int cycle = 0; + for(int i = 0; i < _nodes; ++i) { + _colors[i] = W; + } + _time = 0; + for(int i = 0; i < _nodes; ++i) { + if(_colors[i] == W) + cycle |= dfsvisit(i); + else if(_colors[i] == G) + cycle = 1; + } + for(int i = 0; i < _nodes; ++i) { + cout << "(" << *_k[i] << ", " << i << "): [" << _d[i] << "," << _f[i] << "]" << endl; + } + return cycle; + } + + void top_sort() { + int cycle = dfs(); + if(cycle) { + cout << "cyclic graph!" << endl; + return; + } + int* s = new int[_nodes]; + for(int i = 0; i < _nodes; ++i) s[i] = i; + _sort(s, _nodes, _f); + for(int i = 0; i < _nodes; ++i) { + cout << "(" << s[i] << ", " << _f[s[i]] << ") "; + } + + } + + void bfs(H v) { + int s = _index(v); + if(s < 0) return; + + for(int i = 0; i < _nodes; ++i) { + _colors[i] = W; + _d[i] = INF; + _p[i] = -1; + } + _colors[s] = G; + _d[s] = 0; + queue q; + q.push(s); + while(!q.empty()) { + int u = q.front(); + q.pop(); + for(auto const& j : _adj[u]) { + if(_colors[j] == W) { + _colors[j] = G; + _d[j] = _d[u]+1; + _p[j] = u; + q.push(j); + } + } + _colors[u] = B; + } + for(int i = 0; i < _nodes; ++i) { + cout << "(" << *_k[i] << ", " << i << "): [" << _d[i] << "]" << endl; + } + } + int ssc() { + dfs(); + cout << endl << endl; + bool* visited = new bool[_nodes]; + for(int i = 0; i < _nodes; ++i) + visited[i] = false; + int count = 0; + while(!_stack.empty()) { + int v = _stack.top(); + _stack.pop(); + if(!visited[v]) { + dfsvisit(v, visited); + count++; + cout << endl; + } + } + delete[] visited; + return count; + } +private: + graph* _transpose() { + graph* g = new graph{_len}; + for(int i = 0; i < _nodes; ++i) { + g->add_node(*_k[i]); + } + + for(int i = 0; i < _nodes; ++i) { + for(auto const& j : _adj[i]) { + g->add_edge(j, i); + } + } + + return g; + } + void _sort(int* d, int n, int* s) { + for(int i = -1; i < n; ++i) { + int j = i-1; + while(j > -1 && s[d[j+1]]>s[d[j]]) { + swap(d[s[j+1]], d[s[j]]); + --j; + } + } + } + int _index(H x) { + for(int i = 0; i < _nodes; ++i) + if(*_k[i] == x) return i; + + return -1; + } + stack _stack; + H** _k; + vector* _adj; + int _len, _nodes, _edges; + int* _colors; + int _time; + int* _d; + int* _f; + int* _p; +}; + +int main() { + ifstream in("input.txt"); + ofstream out("output.txt"); + + for(int ts = 0; ts < 100; ++ts) { + int n, e; + in >> n>>e; + string t; + in >> t; + char _t; + switch(t.at(0)){ + case 'd':{ + graph* g = new graph{n}; + double x, y; + for(int i = 0; i < n; ++i) { + in >> x; + g->add_node(x); + } + for(int i = 0; i < e; ++i) { + in >>_t; + in >> x >> y; + in >> _t; + g->add_edge(x, y); + g->add_edge(y, x); + } + g->print(); + cout << endl << endl; + out << g->ssc()<* g = new graph{n}; + int x, y; + for(int i = 0; i < n; ++i) { + in >> x; + g->add_node(x); + } + for(int i = 0; i < e; ++i) { + in >>_t; + in >> x >> y; + in >> _t; + g->add_edge(x, y); + g->add_edge(y, x); + } + g->print(); + cout << endl << endl; + out << g->ssc()<* g = new graph{n}; + char x, y; + for(int i = 0; i < n; ++i) { + in >> x; + g->add_node(x); + } + for(int i = 0; i < e; ++i) { + in >>_t; + in >> x >> y; + in >> _t; + g->add_edge(x, y); + g->add_edge(y, x); + } + g->print(); + cout << endl << endl; + out << g->ssc()<