Merge remote-tracking branch 'upstream/master'

geometry/jarvis_algorithm.cpp

+/**
+ * @file
+ * @brief Implementation of [Jarvis’s](https://en.wikipedia.org/wiki/Gift_wrapping_algorithm) algorithm.
+ *
+ * @details
+ * Given a set of points in the plane. the convex hull of the set
+ * is the smallest convex polygon that contains all the points of it.
+ *
+ * ### Algorithm
+ * The idea of Jarvis’s Algorithm is simple, we start from the leftmost point
+ * (or point with minimum x coordinate value) and we
+ * keep wrapping points in counterclockwise direction.
+ *
+ * The idea is to use orientation() here. Next point is selected as the
+ * point that beats all other points at counterclockwise orientation, i.e.,
+ * next point is q if for any other point r,
+ * we have “orientation(p, q, r) = counterclockwise”.
+ *
+ * For Example,
+ * If points = {{0, 3}, {2, 2}, {1, 1}, {2, 1},
+                      {3, 0}, {0, 0}, {3, 3}};
+ *
+ * then the convex hull is
+ * (0, 3), (0, 0), (3, 0), (3, 3)
+ *
+ * @author [Rishabh Agarwal](https://github.com/rishabh-997)
+ */
+
+#include <vector>
+#include <cassert>
+#include <iostream>
+
+/**
+ *  @namespace geometry
+ *  @brief Geometry algorithms
+ */
+namespace geometry {
+    /**
+     * @namespace jarvis
+     * @brief Functions for [Jarvis’s](https://en.wikipedia.org/wiki/Gift_wrapping_algorithm) algorithm
+     */
+    namespace jarvis {
+        /**
+         * Structure defining the x and y co-ordinates of the given
+         * point in space
+         */
+        struct Point {
+            int x, y;
+        };
+
+        /**
+         * Class which can be called from main and is globally available
+         * throughout the code
+         */
+        class Convexhull {
+            std::vector<Point> points;
+            int size;
+
+        public:
+            /**
+             * Constructor of given class
+             *
+             * @param pointList list of all points in the space
+             * @param n number of points in space
+             */
+            explicit Convexhull(const std::vector<Point> &pointList) {
+                points = pointList;
+                size = points.size();
+            }
+
+            /**
+             * Creates convex hull of a set of n points.
+             * There must be 3 points at least for the convex hull to exist
+             *
+             * @returns an vector array containing points in space
+             * which enclose all given points thus forming a hull
+             */
+            std::vector<Point> getConvexHull() const {
+                // Initialize Result
+                std::vector<Point> hull;
+
+                // Find the leftmost point
+                int leftmost_point = 0;
+                for (int i = 1; i < size; i++) {
+                    if (points[i].x < points[leftmost_point].x) {
+                        leftmost_point = i;
+                    }
+                }
+                // Start from leftmost point, keep moving counterclockwise
+                // until reach the start point again.  This loop runs O(h)
+                // times where h is number of points in result or output.
+                int p = leftmost_point, q = 0;
+                do {
+                    // Add current point to result
+                    hull.push_back(points[p]);
+
+                    // Search for a point 'q' such that orientation(p, x, q)
+                    // is counterclockwise for all points 'x'. The idea
+                    // is to keep track of last visited most counter clock-
+                    // wise point in q. If any point 'i' is more counter clock-
+                    // wise than q, then update q.
+                    q = (p + 1) % size;
+                    for (int i = 0; i < size; i++) {
+                        // If i is more counterclockwise than current q, then
+                        // update q
+                        if (orientation(points[p], points[i], points[q]) == 2) {
+                            q = i;
+                        }
+                    }
+
+                    // Now q is the most counterclockwise with respect to p
+                    // Set p as q for next iteration, so that q is added to
+                    // result 'hull'
+                    p = q;
+
+                } while (p != leftmost_point);        // While we don't come to first point
+
+                return hull;
+            }
+
+            /**
+             * This function returns the geometric orientation for the three points
+             * in a space, ie, whether they are linear ir clockwise or
+             * anti-clockwise
+             * @param p first point selected
+             * @param q adjacent point for q
+             * @param r adjacent point for q
+             *
+             * @returns 0 -> Linear
+             * @returns 1 -> Clock Wise
+             * @returns 2 -> Anti Clock Wise
+             */
+            static int orientation(const Point &p, const Point &q, const Point &r) {
+                int val = (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);
+
+                if (val == 0) {
+                    return 0;
+                }
+                return (val > 0) ? 1 : 2;
+            }
+
+        };
+
+    } // namespace jarvis
+} // namespace geometry
+
+/**
+ * Test function
+ * @returns void
+ */
+static void test() {
+    std::vector<geometry::jarvis::Point> points = {{0, 3},
+                                                   {2, 2},
+                                                   {1, 1},
+                                                   {2, 1},
+                                                   {3, 0},
+                                                   {0, 0},
+                                                   {3, 3}
+    };
+    geometry::jarvis::Convexhull hull(points);
+    std::vector<geometry::jarvis::Point> actualPoint;
+    actualPoint = hull.getConvexHull();
+
+    std::vector<geometry::jarvis::Point> expectedPoint = {{0, 3},
+                                                          {0, 0},
+                                                          {3, 0},
+                                                          {3, 3}};
+    for (int i = 0; i < expectedPoint.size(); i++) {
+        assert(actualPoint[i].x == expectedPoint[i].x);
+        assert(actualPoint[i].y == expectedPoint[i].y);
+    }
+    std::cout << "Test implementations passed!\n";
+}
+
+/** Driver Code */
+int main() {
+    test();
+    return 0;
+}

graph/kosaraju.cpp

@@ -4,77 +4,84 @@
 
 #include <iostream>
 #include <vector>
+#include <stack>
 
-using namespace std;
 
 /**
  * Iterative function/method to print graph:
- * @param a[] : array of vectors (2D)
- * @param V : vertices
+ * @param a adjacency list representation of the graph
+ * @param V number of vertices
  * @return void
  **/
-void print(vector<int> a[], int V) {
+void print(const std::vector< std::vector<int> > &a, int V) {
     for (int i = 0; i < V; i++) {
-        if (!a[i].empty())
-            cout << "i=" << i << "-->";
-        for (int j = 0; j < a[i].size(); j++) cout << a[i][j] << " ";
-        if (!a[i].empty())
-            cout << endl;
+        if (!a[i].empty()) {
+            std::cout << "i=" << i << "-->";
+        }
+        for (int j : a[i]) {
+            std::cout << j << " ";
+        }
+        if (!a[i].empty()) {
+            std::cout << std::endl;
+        }
     }
 }
 
 /**
  * //Recursive function/method to push vertices into stack passed as parameter:
- * @param v : vertices
- * @param &st : stack passed by reference
- * @param vis[] : array to keep track of visited nodes (boolean type)
- * @param adj[] : array of vectors to represent graph
+ * @param v vertices
+ * @param st stack passed by reference
+ * @param vis array to keep track of visited nodes (boolean type)
+ * @param adj adjacency list representation of the graph
  * @return void
  **/
-void push_vertex(int v, stack<int> &st, bool vis[], vector<int> adj[]) {
-    vis[v] = true;
+void push_vertex(int v, std::stack<int> *st, std::vector<bool> *vis, const std::vector< std::vector<int> > &adj) {
+    (*vis)[v] = true;
     for (auto i = adj[v].begin(); i != adj[v].end(); i++) {
-        if (vis[*i] == false)
+        if ((*vis)[*i] == false) {
             push_vertex(*i, st, vis, adj);
+        }
     }
-    st.push(v);
+    st->push(v);
 }
 
 /**
  * //Recursive function/method to implement depth first traversal(dfs):
- * @param v : vertices
- * @param vis[] : array to keep track of visited nodes (boolean type)
- * @param grev[] : graph with reversed edges
+ * @param v vertices
+ * @param vis array to keep track of visited nodes (boolean type)
+ * @param grev graph with reversed edges
  * @return void
  **/
-void dfs(int v, bool vis[], vector<int> grev[]) {
-    vis[v] = true;
+void dfs(int v, std::vector<bool> *vis, const std::vector< std::vector<int> > &grev) {
+    (*vis)[v] = true;
     // cout<<v<<" ";
     for (auto i = grev[v].begin(); i != grev[v].end(); i++) {
-        if (vis[*i] == false)
+        if ((*vis)[*i] == false) {
             dfs(*i, vis, grev);
+        }
     }
 }
 
 // function/method to implement Kosaraju's Algorithm:
 /**
 * Info about the method
-* @param V : vertices in graph
-* @param adj[] : array of vectors that represent a graph (adjacency list/array)
+* @param V vertices in graph
+* @param adj array of vectors that represent a graph (adjacency list/array)
 * @return int ( 0, 1, 2..and so on, only unsigned values as either there can be
 no SCCs i.e. none(0) or there will be x no. of SCCs (x>0)) i.e. it returns the
 count of (number of) strongly connected components (SCCs) in the graph.
 (variable 'count_scc' within function)
 **/
-int kosaraju(int V, vector<int> adj[]) {
-    bool vis[V] = {};
-    stack<int> st;
+int kosaraju(int V, const std::vector< std::vector<int> > &adj) {
+    std::vector<bool> vis(V, false);
+    std::stack<int> st;
     for (int v = 0; v < V; v++) {
-        if (vis[v] == false)
-            push_vertex(v, st, vis, adj);
+        if (vis[v] == false) {
+            push_vertex(v, &st, &vis, adj);
+        }
     }
     // making new graph (grev) with reverse edges as in adj[]:
-    vector<int> grev[V];
+    std::vector< std::vector<int> > grev(V);
     for (int i = 0; i < V + 1; i++) {
         for (auto j = adj[i].begin(); j != adj[i].end(); j++) {
             grev[*j].push_back(i);
@@ -89,7 +96,7 @@ int kosaraju(int V, vector<int> adj[]) {
         int t = st.top();
         st.pop();
         if (vis[t] == false) {
-            dfs(t, vis, grev);
+            dfs(t, &vis, grev);
             count_scc++;
         }
     }
@@ -101,21 +108,21 @@ int kosaraju(int V, vector<int> adj[]) {
 // All critical/corner cases have been taken care of.
 // Input your required values: (not hardcoded)
 int main() {
-    int t;
-    cin >> t;
+    int t = 0;
+    std::cin >> t;
     while (t--) {
-        int a, b;  // a->number of nodes, b->directed edges.
-        cin >> a >> b;
-        int m, n;
-        vector<int> adj[a + 1];
+        int a = 0, b = 0;  // a->number of nodes, b->directed edges.
+        std::cin >> a >> b;
+        int m = 0, n = 0;
+        std::vector< std::vector<int> > adj(a + 1);
         for (int i = 0; i < b; i++)  // take total b inputs of 2 vertices each
                                      // required to form an edge.
         {
-            cin >> m >> n;  // take input m,n denoting edge from m->n.
+            std::cin >> m >> n;  // take input m,n denoting edge from m->n.
             adj[m].push_back(n);
         }
         // pass number of nodes and adjacency array as parameters to function:
-        cout << kosaraju(a, adj) << endl;
+        std::cout << kosaraju(a, adj) << std::endl;
     }
     return 0;
 }

graph/kruskal.cpp

 #include <iostream>
+#include <vector>
+#include <algorithm>
+#include <array>
 //#include <boost/multiprecision/cpp_int.hpp>
 // using namespace boost::multiprecision;
 const int mx = 1e6 + 5;
-const long int inf = 2e9;
-typedef long long ll;
-#define rep(i, n) for (i = 0; i < n; i++)
-#define repp(i, a, b) for (i = a; i <= b; i++)
-#define pii pair<int, int>
-#define vpii vector<pii>
-#define vi vector<int>
-#define vll vector<ll>
-#define r(x) scanf("%d", &x)
-#define rs(s) scanf("%s", s)
-#define gc getchar_unlocked
-#define pc putchar_unlocked
-#define mp make_pair
-#define pb push_back
-#define lb lower_bound
-#define ub upper_bound
-#define endl "\n"
-#define fast                          \
-    ios_base::sync_with_stdio(false); \
-    cin.tie(NULL);                    \
-    cout.tie(NULL);
-using namespace std;
-void in(int &x) {
-    register int c = gc();
-    x = 0;
-    int neg = 0;
-    for (; ((c < 48 || c > 57) && c != '-'); c = gc())
-        ;
-    if (c == '-') {
-        neg = 1;
-        c = gc();
-    }
-    for (; c > 47 && c < 58; c = gc()) {
-        x = (x << 1) + (x << 3) + c - 48;
-    }
-    if (neg)
-        x = -x;
-}
-void out(int n) {
-    int N = n, rev, count = 0;
-    rev = N;
-    if (N == 0) {
-        pc('0');
-        return;
-    }
-    while ((rev % 10) == 0) {
-        count++;
-        rev /= 10;
-    }
-    rev = 0;
-    while (N != 0) {
-        rev = (rev << 3) + (rev << 1) + N % 10;
-        N /= 10;
-    }
-    while (rev != 0) {
-        pc(rev % 10 + '0');
-        rev /= 10;
-    }
-    while (count--) pc('0');
-}
-ll parent[mx], arr[mx], node, edge;
-vector<pair<ll, pair<ll, ll>>> v;
+using ll = int64_t;
+
+std::array<ll, mx> parent;
+ll node, edge;
+std::vector<std::pair<ll, std::pair<ll, ll>>> edges;
 void initial() {
-    int i;
-    rep(i, node + edge) parent[i] = i;
+    for (int i = 0; i < node + edge; ++i) {
+      parent[i] = i;
+    }
 }
+
 int root(int i) {
     while (parent[i] != i) {
         parent[i] = parent[parent[i]];
@@ -75,41 +23,42 @@ int root(int i) {
     }
     return i;
 }
+
 void join(int x, int y) {
     int root_x = root(x);  // Disjoint set union by rank
     int root_y = root(y);
     parent[root_x] = root_y;
 }
+
 ll kruskal() {
-    ll mincost = 0, i, x, y;
-    rep(i, edge) {
-        x = v[i].second.first;
-        y = v[i].second.second;
+    ll mincost = 0;
+    for (int i = 0; i < edge; ++i) {
+        ll x = edges[i].second.first;
+        ll y = edges[i].second.second;
         if (root(x) != root(y)) {
-            mincost += v[i].first;
+            mincost += edges[i].first;
             join(x, y);
         }
     }
     return mincost;
 }
+
 int main() {
-    fast;
-    while (1) {
-        int i, j, from, to, cost, totalcost = 0;
-        cin >> node >> edge;  // Enter the nodes and edges
-        if (node == 0 && edge == 0)
+    while (true) {
+        int from = 0, to = 0, cost = 0, totalcost = 0;
+        std::cin >> node >> edge;  // Enter the nodes and edges
+        if (node == 0 && edge == 0) {
             break;  // Enter 0 0 to break out
+        }
         initial();  // Initialise the parent array
-        rep(i, edge) {
-            cin >> from >> to >> cost;
-            v.pb(mp(cost, mp(from, to)));
+        for (int i = 0; i < edge; ++i) {
+            std::cin >> from >> to >> cost;
+            edges.emplace_back(make_pair(cost, std::make_pair(from, to)));
             totalcost += cost;
         }
-        sort(v.begin(), v.end());
-        // rep(i,v.size())
-        // 	cout<<v[i].first<<"  ";
-        cout << kruskal() << endl;
-        v.clear();
+        sort(edges.begin(), edges.end());
+        std::cout << kruskal() << std::endl;
+        edges.clear();
     }
     return 0;
 }