update old links (#276)

goswami-rahul · jakobkogler · commit 783512e2a0fb · 2018-10-02T22:58:08.000+02:00
diff --git a/README.md b/README.md
@@ -9,8 +9,8 @@ e-maxx-eng
 
 Translation of http://e-maxx.ru into English
 
-Compiled pages are published at http://e-maxx-eng.appspot.com/
+Compiled pages are published at https://cp-algorithms.com/
 
-Manual for contributors: http://e-maxx-eng.appspot.com/contrib.html
+Manual for contributors: https://cp-algorithms.com/contrib.html
 
-Test-your-page form: http://e-maxx-eng.appspot.com/test.php
+Test-your-page form: https://cp-algorithms.com/test.php
diff --git a/src/combinatorics/generating_combinations.md b/src/combinatorics/generating_combinations.md
@@ -34,7 +34,7 @@ bool next_combination(vector<int>& a, int n) {
 This time we want to generate all $K$-combinations in such
 an order, that adjacent combinations differ exactly by one element.
 
-This can be solved using the [Gray Code](https://e-maxx-eng.appspot.com/algebra/gray-code.html):
+This can be solved using the [Gray Code](./algebra/gray-code.html):
 If we assign a bitmask to each subset, then by generating and iterating over these bitmasks with Gray codes, we can obtain our answer.
 
 The task of generating $K$-combinations can also be solved using Gray Codes in a different way:
diff --git a/src/contrib.md b/src/contrib.md
@@ -6,7 +6,7 @@
 
 We collaborate via means of github.
 
-Generated pages are compiled and published at [http://e-maxx-eng.appspot.com](http://e-maxx-eng.appspot.com).
+Generated pages are compiled and published at [https://cp-algorithms.com](https://cp-algorithms.com).
 
 And sources (to which you may want to contribute) are [here](http://github.com/e-maxx-eng/e-maxx-eng/tree/master/src).
 
diff --git a/src/graph/strongly-connected-components.md b/src/graph/strongly-connected-components.md
@@ -9,7 +9,7 @@ You are given a directed graph $G$ with vertices $V$ and edges $E$. It is possib
 $$
 u \mapsto v, v \mapsto u
 $$
-where $\mapsto$ means reachability, i.e. existance of the path from first vertex to the second.
+where $\mapsto$ means reachability, i.e. existence of the path from first vertex to the second.
 
 It is obvious, that strongly connected components do not intersect each other, i.e. this is a partition of all graph vertices. Thus we can give a definition of condensation graph $G^{SCC}$ as a graph containing every strongly connected component as one vertex. Each vertex of the condensation graph corresponds to the strongly connected component of graph $G$. There is an oriented edge between two vertices $C_i$ and $C_j$ of the condensation graph if and only if there are two vertices $u \in C_i, v \in C_j$ such that there is an edge in initial graph, i.e. $(u, v) \in E$.
 
@@ -18,7 +18,7 @@ The most important property of the condensation graph is that it is **acyclic**.
 The algorithm described in the next section extracts all strongly connected components in a given graph. It is quite easy to build a condensation graph then.
 
 ## Description of the algorithm
-Described algorithm was independently suggested by Kosaraju and Sharir at 1979. This is an easy-to-implement algorithm based on two series of [depth first search](http://e-maxx-eng.appspot.com/graph/depth-first-search.html), and working for $O(n + m)$ time.
+Described algorithm was independently suggested by Kosaraju and Sharir at 1979. This is an easy-to-implement algorithm based on two series of [depth first search](./graph/depth-first-search.html), and working for $O(n + m)$ time.
 
 **On the first step** of the algorithm we are doing sequence of depth first searches, visiting the entire graph. We start at each vertex of the graph and run a depth first search from every non-visited vertex. For each vertex we are keeping track of **exit time** $tout[v]$. These exit times have a key role in an algorithm and this role is expressed in next theorem.
 
@@ -28,7 +28,7 @@ First, let's make notations: let's define exit time $tout[C]$ from the strongly
 
 There are two main different cases at the proof depending on which component will be visited by depth first search first, i.e. depending on difference between $tin[C]$ and $tin[C']$:
 ** The component $C$ was reached first. It means that depth first search comes at some vertex $v$ of component $C$ at some moment, but all other vertices of components $C$ and $C'$ were not visited yet. By condition there is an edge $(C, C')$ in a condensation graph, so not only the entire component $C$ is reachable from $v$ but the whole component $C'$ is reachable as well. It means that depth first search that is running from vertex $v$ will visit all vertices of components $C$ and $C'$, so they will be descendants for $v$ in a depth first search tree, i.e. for each vertex $u \in C \cup C', u \ne v$ we have that $tout[v] > tout[u]$, as we claimed.
-** Assume that component $C'$ was visited first. Similarly, depth first search comes at some vertex $v$ of component $C'$ at some moment, but all other vertices of components $C$ and $C'$ were not visited yet. But by condition there is an edge $(C, C')$ in the condensation graph, so, because of acyclic propery of condensation graph, there is no back path from $C'$ to $C$, i.e. depth first search from vertex $v$ will not reach vertices of $C$. It means that vertices of $C$ will be visited by depth first search later, so $tout[C] > tout[C']$. This completes the proof.
+** Assume that component $C'$ was visited first. Similarly, depth first search comes at some vertex $v$ of component $C'$ at some moment, but all other vertices of components $C$ and $C'$ were not visited yet. But by condition there is an edge $(C, C')$ in the condensation graph, so, because of acyclic property of condensation graph, there is no back path from $C'$ to $C$, i.e. depth first search from vertex $v$ will not reach vertices of $C$. It means that vertices of $C$ will be visited by depth first search later, so $tout[C] > tout[C']$. This completes the proof.
 
 Proved theorem is **the base of algorithm** for finding strongly connected components. It follows that any edge $(C, C')$ in condensation graph comes from a component with a larger value of $tout$ to component with a smaller value.
 
@@ -44,9 +44,9 @@ Thus, we built next **algorithm** for selecting strongly connected components:
 
 2nd step. Build transposed graph $G^T$. Run a series of depth (breadth) first searches in the order determined by list $order$ (to be exact in reverse order, i.e. in decreasing order of exit times). Every set of vertices, reached after the next search, will be the next strongly connected component.
 
-Algorithm asymptotics is $O(n + m)$, because it is just two depth (breadth) first searches.
+Algorithm asymptotic is $O(n + m)$, because it is just two depth (breadth) first searches.
 
-Finally, it is appropriate to mention [topological sort](http://e-maxx-eng.appspot.com/graph/topological-sort.html) here. First of all, step 1 of the algorithm represents topological sort of graph $G$ (actually this is exactly what vertices' sort by exit time means). Secondly, the algorithm's scheme generates strongly connected components by decreasing order of their exit times, thus it generates components - vertices of condensation graph - in topological sort order.
+Finally, it is appropriate to mention [topological sort](./graph/topological-sort.html) here. First of all, step 1 of the algorithm represents topological sort of graph $G$ (actually this is exactly what vertices' sort by exit time means). Secondly, the algorithm's scheme generates strongly connected components by decreasing order of their exit times, thus it generates components - vertices of condensation graph - in topological sort order.
 
 ## Implementation
 ```cpp
