private void collect(Node x, StringBuilder prefix, int i, string pattern, LinkedQueue <string> queue)
{
if (x == null)
{
return;
}
char c = pattern[i];
if (c == '.' || c < x.c)
{
collect(x.left, prefix, i, pattern, queue);
}
if (c == '.' || c == x.c)
{
if (i == pattern.Length - 1 && x.val != null)
{
queue.Enqueue(prefix.ToString() + x.c);
}
if (i < pattern.Length - 1)
{
collect(x.mid, prefix.Append(x.c), i + 1, pattern, queue);
prefix.Remove(prefix.Length - 1, 1);
}
}
if (c == '.' || c > x.c)
{
collect(x.right, prefix, i, pattern, queue);
}
}
/// <summary>
/// Returns all of the keys in the symbol table that match <c>pattern</c>,
/// where . symbol is treated as a wildcard character.</summary>
/// <param name="pattern">the pattern</param>
/// <returns>all of the keys in the symbol table that match <c>pattern</c>
/// as an iterable, where . is treated as a wildcard character.</returns>
///
public IEnumerable <string> KeysThatMatch(string pattern)
{
LinkedQueue <string> results = new LinkedQueue <string>();
collect(root, new StringBuilder(), pattern, results);
return(results);
}
private void collect(Node x, StringBuilder prefix, string pattern, LinkedQueue <string> results)
{
if (x == null)
{
return;
}
int d = prefix.Length;
if (d == pattern.Length && x.Value != null)
{
results.Enqueue(prefix.ToString());
}
if (d == pattern.Length)
{
return;
}
char c = pattern[d];
if (c == '.')
{
for (int i = 0; i < R; i++)
{
prefix.Append(alphabet.ToChar(i));
collect(x[i], prefix, pattern, results);
prefix.Remove(prefix.Length - 1, 1);
}
}
else
{
prefix.Append(c);
collect(x[alphabet.ToIndex(c)], prefix, pattern, results);
prefix.Remove(prefix.Length - 1, 1);
}
}
/// <summary>
/// Returns all of the keys in the symbol table that match <c>pattern</c>,
/// where . symbol is treated as a wildcard character.</summary>
/// <param name="pattern">the pattern</param>
/// <returns>all of the keys in the symbol table that match <c>pattern</c>
/// as an iterable, where . is treated as a wildcard character.</returns>
///
public IEnumerable <string> KeysThatMatch(string pattern)
{
LinkedQueue <string> queue = new LinkedQueue <string>();
collect(root, new StringBuilder(), 0, pattern, queue);
return(queue);
}
// breadth-first search from multiple sources
private void bfs(Graph G, IEnumerable <int> sources)
{
LinkedQueue <int> q = new LinkedQueue <int>();
foreach (int s in sources)
{
marked[s] = true;
distTo[s] = 0;
q.Enqueue(s);
}
while (!q.IsEmpty)
{
int v = q.Dequeue();
foreach (int w in G.Adj(v))
{
if (!marked[w])
{
edgeTo[w] = v;
distTo[w] = distTo[v] + 1;
marked[w] = true;
q.Enqueue(w);
}
}
}
}
// is there an augmenting path?
// if so, upon termination edgeTo[] will contain a parent-link representation of such a path
// this implementation finds a shortest augmenting path (fewest number of edges),
// which performs well both in theory and in practice
private bool hasAugmentingPath(FlowNetwork G, int s, int t)
{
edgeTo = new FlowEdge[G.V];
marked = new bool[G.V];
// breadth-first search
LinkedQueue <int> queue = new LinkedQueue <int>();
queue.Enqueue(s);
marked[s] = true;
while (!queue.IsEmpty && !marked[t])
{
int v = queue.Dequeue();
foreach (FlowEdge e in G.Adj(v))
{
int w = e.Other(v);
// if residual capacity from v to w
if (e.ResidualCapacityTo(w) > 0)
{
if (!marked[w])
{
edgeTo[w] = e;
marked[w] = true;
queue.Enqueue(w);
}
}
}
}
// is there an augmenting path?
return(marked[t]);
}
// breadth-first search from a single source
private void bfs(Graph G, int s)
{
LinkedQueue <int> q = new LinkedQueue <int>();
for (int v = 0; v < G.V; v++)
{
distTo[v] = INFINITY;
}
distTo[s] = 0;
marked[s] = true;
q.Enqueue(s);
while (!q.IsEmpty)
{
int v = q.Dequeue();
foreach (int w in G.Adj(v))
{
if (!marked[w])
{
edgeTo[w] = v;
distTo[w] = distTo[v] + 1;
marked[w] = true;
q.Enqueue(w);
}
}
}
}
/// <summary>
/// Returns all keys in this symbol table in the given range,
/// as an <c>IEnumerable</c>.</summary>
/// <returns>all keys in this symbol table between <c>lo</c>
/// (inclusive) and <c>hi</c> (exclusive)</returns>
/// <param name="lo">lower bound key</param>
/// <param name="hi">upper bound key</param>
/// <exception cref="ArgumentNullException">if either <c>lo</c> or <c>hi</c>
/// is <c>null</c></exception>
///
public IEnumerable <Key> Keys(Key lo, Key hi)
{
if (lo == null)
{
throw new ArgumentNullException("first argument to Count is null");
}
if (hi == null)
{
throw new ArgumentNullException("second argument to Count is null");
}
LinkedQueue <Key> queue = new LinkedQueue <Key>();
if (lo == null)
{
throw new ArgumentNullException("lo is null in keys()");
}
if (hi == null)
{
throw new ArgumentNullException("hi is null in keys()");
}
if (lo.CompareTo(hi) > 0)
{
return(queue);
}
for (int i = Rank(lo); i < Rank(hi); i++)
{
queue.Enqueue(keys[i]);
}
if (Contains(hi))
{
queue.Enqueue(keys[Rank(hi)]);
}
return(queue);
}
public static void MainTest(string[] args)
{
TextInput input = new TextInput(args[0]);
Graph G = new Graph(input);
CC cc = new CC(G);
// number of connected components
int M = cc.Count;
Console.WriteLine(M + " components");
// compute list of vertices in each connected component
LinkedQueue <int>[] components = new LinkedQueue <int> [M];
for (int i = 0; i < M; i++)
{
components[i] = new LinkedQueue <int>();
}
for (int v = 0; v < G.V; v++)
{
components[cc.Id(v)].Enqueue(v);
}
// print results
for (int i = 0; i < M; i++)
{
foreach (int v in components[i])
{
Console.Write(v + " ");
}
Console.WriteLine();
}
}
/// <summary>
/// Returns all of the keys in the set that start with <c>prefix</c>.</summary>
/// <param name="prefix">the prefix</param>
/// <returns>all of the keys in the set that start with <c>prefix</c>
/// as an iterable</returns>
///
public IEnumerable <string> KeysWithPrefix(string prefix)
{
LinkedQueue <string> results = new LinkedQueue <string>();
Node x = get(root, prefix, 0);
collect(x, new StringBuilder(prefix), results);
return(results);
}
// is there an augmenting path?
// an alternating path is a path whose edges belong alternately to the matching and not to the matchign
// an augmenting path is an alternating path that starts and ends at unmatched vertices
//
// if so, upon termination adj[] contains the level graph;
// if not, upon termination marked[] specifies those vertices reachable via an alternating path
// from one side of the bipartition
private bool hasAugmentingPath(Graph G)
{
// shortest path distances
marked = new bool[V];
distTo = new int[V];
for (int v = 0; v < V; v++)
{
distTo[v] = int.MaxValue;
}
// breadth-first search (starting from all unmatched vertices on one side of bipartition)
LinkedQueue <int> queue = new LinkedQueue <int>();
for (int v = 0; v < V; v++)
{
if (bipartition.Color(v) && !IsMatched(v))
{
queue.Enqueue(v);
marked[v] = true;
distTo[v] = 0;
}
}
// run BFS until an augmenting path is found
// (and keep going until all vertices at that distance are explored)
bool hasAugmentingPath = false;
while (!queue.IsEmpty)
{
int v = queue.Dequeue();
foreach (int w in G.Adj(v))
{
// forward edge not in matching or backwards edge in matching
if (isResidualGraphEdge(v, w))
{
if (!marked[w])
{
distTo[w] = distTo[v] + 1;
marked[w] = true;
if (!IsMatched(w))
{
hasAugmentingPath = true;
}
// stop enqueuing vertices once an alternating path has been discovered
// (no vertex on same side will be marked if its shortest path distance longer)
if (!hasAugmentingPath)
{
queue.Enqueue(w);
}
}
}
}
}
return(hasAugmentingPath);
}
/// <summary>
/// Returns all keys in the symbol table as an <c>Iterable</c>.
/// To iterate over all of the keys in the symbol table named <c>st</c>,
/// use the foreach notation: <c>foreach (Key key in st.Keys())</c>.</summary>
/// <returns>all keys in the sybol table</returns>
///
public IEnumerable <Key> Keys()
{
LinkedQueue <Key> queue = new LinkedQueue <Key>();
for (Node x = first; x != null; x = x.next)
{
queue.Enqueue(x.key);
}
return(queue);
}
public static void MainTest(string[] args)
{
TextInput StdIn = new TextInput();
string filename = args[0];
char[] separator = args[1].ToCharArray();
TextInput input = new TextInput(filename);
ST <string, LinkedQueue <string> > st = new ST <string, LinkedQueue <string> >();
ST <string, LinkedQueue <string> > ts = new ST <string, LinkedQueue <string> >();
while (input.HasNextLine())
{
string line = input.ReadLine();
string[] fields = line.Split(separator);
string key = fields[0];
for (int i = 1; i < fields.Length; i++)
{
string val = fields[i];
if (!st.Contains(key))
{
st[key] = new LinkedQueue <string>();
}
if (!ts.Contains(val))
{
ts[val] = new LinkedQueue <string>();
}
st[key].Enqueue(val);
ts[val].Enqueue(key);
}
}
Console.WriteLine("Done indexing");
// read queries from standard input, one per line
while (!StdIn.IsEmpty)
{
string query = StdIn.ReadLine();
if (st.Contains(query))
{
foreach (string vals in st[query])
{
Console.WriteLine(" " + vals);
}
}
if (ts.Contains(query))
{
foreach (string keys in ts[query])
{
Console.WriteLine(" " + keys);
}
}
}
}
/// <summary>
/// Returns all keys in this symbol table as an <c>Iterable</c>.
/// To iterate over all of the keys in the symbol table named <c>st</c>,
/// use the foreach notation: <c>foreach (Key key in st.Keys())</c>.</summary>
/// <returns>all keys in this sybol table</returns>
///
public IEnumerable <Key> Keys()
{
LinkedQueue <Key> queue = new LinkedQueue <Key>();
for (int i = 0; i < M; i++)
{
if (keys[i] != null)
{
queue.Enqueue((Key)keys[i]);
}
}
return(queue);
}
/// <summary>
/// Returns all keys in the symbol table as an <c>IEnumerable</c>.
/// To iterate over all of the keys in the symbol table named <c>st</c>,
/// use the foreach notation: <c>foreach (Key key in st.Keys())</c>.</summary>
/// <returns>all keys in the sybol table as an <c>IEnumerable</c></returns>
///
public IEnumerable <Key> Keys()
{
LinkedQueue <Key> queue = new LinkedQueue <Key>();
for (int i = 0; i < M; i++)
{
foreach (Key key in st[i].Keys())
{
queue.Enqueue(key);
}
}
return(queue);
}
/// <summary>
/// Returns the edges in a minimum spanning tree (or forest).</summary>
/// <returns>the edges in a minimum spanning tree (or forest) as
/// an iterable of edges</returns>
///
public IEnumerable <Edge> Edges()
{
LinkedQueue <Edge> mst = new LinkedQueue <Edge>();
for (int v = 0; v < edgeTo.Length; v++)
{
Edge e = edgeTo[v];
if (e != null)
{
mst.Enqueue(e);
}
}
return(mst);
}
/// <summary>
/// Determines whether the edge-weighted digraph <c>G</c> has a
/// topological order and, if so, finds such a topological order.</summary>
/// <param name="G">the digraph</param>
///
public TopologicalX(EdgeWeightedDigraph G)
{
// indegrees of remaining vertices
int[] indegree = new int[G.V];
for (int v = 0; v < G.V; v++)
{
indegree[v] = G.Indegree(v);
}
// initialize
rank = new int[G.V];
order = new LinkedQueue <int>();
int count = 0;
// initialize queue to contain all vertices with indegree = 0
LinkedQueue <int> queue = new LinkedQueue <int>();
for (int v = 0; v < G.V; v++)
{
if (indegree[v] == 0)
{
queue.Enqueue(v);
}
}
for (int j = 0; !queue.IsEmpty; j++)
{
int v = queue.Dequeue();
order.Enqueue(v);
rank[v] = count++;
foreach (DirectedEdge e in G.Adj(v))
{
int w = e.To;
indegree[w]--;
if (indegree[w] == 0)
{
queue.Enqueue(w);
}
}
}
// there is a directed cycle in subgraph of vertices with indegree >= 1.
if (count != G.V)
{
order = null;
}
Debug.Assert(check(G));
}
private void bfs(Graph G, int s)
{
LinkedQueue <int> q = new LinkedQueue <int>();
color[s] = WHITE;
marked[s] = true;
q.Enqueue(s);
while (!q.IsEmpty)
{
int v = q.Dequeue();
foreach (int w in G.Adj(v))
{
if (!marked[w])
{
marked[w] = true;
edgeTo[w] = v;
color[w] = !color[v];
q.Enqueue(w);
}
else if (color[w] == color[v])
{
isBipartite = false;
// to form odd cycle, consider s-v path and s-w path
// and let x be closest node to v and w common to two paths
// then (w-x path) + (x-v path) + (edge v-w) is an odd-length cycle
// Note: distTo[v] == distTo[w];
cycle = new LinkedQueue <int>();
LinkedStack <int> stack = new LinkedStack <int>();
int x = v, y = w;
while (x != y)
{
stack.Push(x);
cycle.Enqueue(y);
x = edgeTo[x];
y = edgeTo[y];
}
stack.Push(x);
while (!stack.IsEmpty)
{
cycle.Enqueue(stack.Pop());
}
cycle.Enqueue(w);
return;
}
}
}
}
/// <summary>
/// Determines a depth-first order for the edge-weighted digraph <c>G</c>.</summary>
/// <param name="G">the edge-weighted digraph</param>
///
public DepthFirstOrder(EdgeWeightedDigraph G)
{
pre = new int[G.V];
post = new int[G.V];
postorder = new LinkedQueue <int>();
preorder = new LinkedQueue <int>();
marked = new bool[G.V];
for (int v = 0; v < G.V; v++)
{
if (!marked[v])
{
dfs(G, v);
}
}
}
// all keys in subtrie rooted at x with given prefix
private void collect(Node x, StringBuilder prefix, LinkedQueue <string> queue)
{
if (x == null)
{
return;
}
collect(x.left, prefix, queue);
if (x.val != null)
{
queue.Enqueue(prefix.ToString() + x.c);
}
collect(x.mid, prefix.Append(x.c), queue);
prefix.Remove(prefix.Length - 1, 1);
collect(x.right, prefix, queue);
}
private MinPQ <Edge> pq; // edges with one endpoint in tree
/// <summary>
/// Compute a minimum spanning tree (or forest) of an edge-weighted graph.</summary>
/// <param name="G">the edge-weighted graph</param>
///
public LazyPrimMST(EdgeWeightedGraph G)
{
mst = new LinkedQueue <Edge>();
pq = new MinPQ <Edge>();
marked = new bool[G.V];
for (int v = 0; v < G.V; v++) // run Prim from all vertices to
{
if (!marked[v])
{
prim(G, v); // get a minimum spanning forest
}
}
// check optimality conditions
Debug.Assert(check(G));
}
/// <summary>
/// Returns all keys in the symbol table in the given range,
/// as an <c>IEnumerable</c>.</summary>
/// <param name="lo">lower bound key</param>
/// <param name="hi">upper bound key</param>
/// <returns>all keys in the sybol table between <c>lo</c>
/// (inclusive) and <c>hi</c> (exclusive)</returns>
/// <exception cref="ArgumentNullException" >if either <c>lo</c> or <c>hi</c>
/// is <c>null</c></exception>
///
public IEnumerable <Key> Keys(Key lo, Key hi)
{
if (lo == null)
{
throw new ArgumentNullException("first argument to Keys() is null");
}
if (hi == null)
{
throw new ArgumentNullException("second argument to Keys() is null");
}
LinkedQueue <Key> queue = new LinkedQueue <Key>();
keys(root, queue, lo, hi);
return(queue);
}
/// <summary>
/// Returns all of the keys in the set that start with <c>prefix</c>.</summary>
/// <param name="prefix">the prefix</param>
/// <returns>all of the keys in the set that start with <c>prefix</c>
/// as an iterable</returns>
///
public IEnumerable <string> KeysWithPrefix(string prefix)
{
LinkedQueue <string> queue = new LinkedQueue <string>();
Node x = get(root, prefix, 0);
if (x == null)
{
return(queue);
}
if (x.val != null)
{
queue.Enqueue(prefix);
}
collect(x.mid, new StringBuilder(prefix), queue);
return(queue);
}
// is there an augmenting path?
// an alternating path is a path whose edges belong alternately to the matching and not to the matching
// an augmenting path is an alternating path that starts and ends at unmatched vertices
//
// if so, upon termination edgeTo[] contains a parent-link representation of such a path
// if not, upon terminatation marked[] specifies the subset of vertices reachable via an alternating
// path from one side of the bipartition
//
// this implementation finds a shortest augmenting path (fewest number of edges), though there
// is no particular advantage to do so here
private bool hasAugmentingPath(Graph G)
{
marked = new bool[numVertices];
edgeTo = new int[numVertices];
for (int v = 0; v < numVertices; v++)
{
edgeTo[v] = -1;
}
// breadth-first search (starting from all unmatched vertices on one side of bipartition)
LinkedQueue <int> queue = new LinkedQueue <int>();
for (int v = 0; v < numVertices; v++)
{
if (bipartition.Color(v) && !IsMatched(v))
{
queue.Enqueue(v);
marked[v] = true;
}
}
// run BFS, stopping as soon as an alternating path is found
while (!queue.IsEmpty)
{
int v = queue.Dequeue();
foreach (int w in G.Adj(v))
{
// either (1) forward edge not in matching or (2) backward edge in matching
if (isResidualGraphEdge(v, w))
{
if (!marked[w])
{
edgeTo[w] = v;
marked[w] = true;
if (!IsMatched(w))
{
return(true);
}
queue.Enqueue(w);
}
}
}
}
return(false);
}
/// <summary>
/// Returns all keys in the symbol table in the given range,
/// as an <c>IEnumerable</c>.</summary>
/// <param name="lo">lower bound key</param>
/// <param name="hi">upper bound key</param>
/// <returns>all keys in the sybol table between <c>lo</c></returns>
/// (inclusive) and <c>hi</c> (exclusive) as an <c>IEnumerable</c>
/// <exception cref="ArgumentNullException">if either <c>lo</c> or <c>hi</c>
/// is <c>null</c></exception>
///
public IEnumerable <Key> Keys(Key lo, Key hi)
{
if (lo == null)
{
throw new ArgumentNullException("first argument to keys() is null");
}
if (hi == null)
{
throw new ArgumentNullException("second argument to keys() is null");
}
LinkedQueue <Key> queue = new LinkedQueue <Key>();
// if (IsEmpty || lo.CompareTo(hi) > 0) return queue;
keys(root, queue, lo, hi);
return(queue);
}
private void collect(Node x, StringBuilder prefix, LinkedQueue <string> results)
{
if (x == null)
{
return;
}
if (x.Value != null)
{
results.Enqueue(prefix.ToString());
}
for (int i = 0; i < R; i++)
{
prefix.Append(alphabet.ToChar(i));
collect(x[i], prefix, results);
prefix.Remove(prefix.Length - 1, 1);
}
}
/// <summary>
/// Returns the keys in the BST in level order (for debugging).</summary>
/// <returns>the keys in the BST in level order traversal</returns>
///
public IEnumerable <Key> LevelOrder()
{
LinkedQueue <Key> keys = new LinkedQueue <Key>();
LinkedQueue <Node> queue = new LinkedQueue <Node>();
queue.Enqueue(root);
while (!queue.IsEmpty)
{
Node x = queue.Dequeue();
if (x == null)
{
continue;
}
keys.Enqueue(x.key);
queue.Enqueue(x.left);
queue.Enqueue(x.right);
}
return(keys);
}
public static void MainTest(string[] args)
{
LinkedQueue <string> q = new LinkedQueue <string>();
TextInput StdIn = new TextInput();
while (!StdIn.IsEmpty)
{
string item = StdIn.ReadString();
if (!item.Equals("-"))
{
q.Enqueue(item);
}
else if (!q.IsEmpty)
{
Console.Write(q.Dequeue() + " ");
}
}
Console.WriteLine("(" + q.Count + " left on queue)");
}
// add the keys between lo and hi in the subtree rooted at x
// to the queue
private void keys(Node x, LinkedQueue <Key> queue, Key lo, Key hi)
{
if (x == null)
{
return;
}
int cmplo = lo.CompareTo(x.key);
int cmphi = hi.CompareTo(x.key);
if (cmplo < 0)
{
keys(x.left, queue, lo, hi);
}
if (cmplo <= 0 && cmphi >= 0)
{
queue.Enqueue(x.key);
}
if (cmphi > 0)
{
keys(x.right, queue, lo, hi);
}
}
private IEnumerable <DirectedEdge> cycle; // negative cycle (or null if no such cycle)
/// <summary>Computes a shortest paths tree from <c>s</c> to every other vertex in
/// the edge-weighted digraph <c>G</c>.</summary>
/// <param name="G">the acyclic digraph</param>
/// <param name="s">the source vertex</param>
/// <exception cref="ArgumentException">unless 0 <= <c>s</c> <= <c>V</c> - 1</exception>
///
public BellmanFordSP(EdgeWeightedDigraph G, int s)
{
distTo = new double[G.V];
edgeTo = new DirectedEdge[G.V];
onQueue = new bool[G.V];
for (int v = 0; v < G.V; v++)
{
distTo[v] = double.PositiveInfinity;
}
distTo[s] = 0.0;
// Bellman-Ford algorithm
queue = new LinkedQueue <int>();
queue.Enqueue(s);
onQueue[s] = true;
while (!queue.IsEmpty && !HasNegativeCycle)
{
int v = queue.Dequeue();
onQueue[v] = false;
relax(G, v);
}
Debug.Assert(check(G, s));
}
