Aho corasick Algorithm Added

Aho-Corasick/Aho_Corasick.cpp

@@ -0,0 +1,195 @@
+// C++ program for implementation of Aho Corasick algorithm
+// for string matching
+using namespace std;
+#include <bits/stdc++.h>
+
+// Max number of states in the matching machine.
+// Should be equal to the sum of the length of all keywords.
+const int MAXS = 500;
+
+// Maximum number of characters in input alphabet
+const int MAXC = 26;
+
+// OUTPUT FUNCTION IS IMPLEMENTED USING out[]
+// Bit i in this mask is one if the word with index i
+// appears when the machine enters this state.
+int out[MAXS];
+
+// FAILURE FUNCTION IS IMPLEMENTED USING f[]
+int f[MAXS];
+
+// GOTO FUNCTION (OR TRIE) IS IMPLEMENTED USING g[][]
+int g[MAXS][MAXC];
+
+// Builds the string matching machine.
+// arr -   array of words. The index of each keyword is important:
+//         "out[state] & (1 << i)" is > 0 if we just found word[i]
+//         in the text.
+// Returns the number of states that the built machine has.
+// States are numbered 0 up to the return value - 1, inclusive.
+int buildMatchingMachine(string arr[], int k)
+{
+    // Initialize all values in output function as 0.
+    memset(out, 0, sizeof out);
+
+    // Initialize all values in goto function as -1.
+    memset(g, -1, sizeof g);
+
+    // Initially, we just have the 0 state
+    int states = 1;
+
+    // Construct values for goto function, i.e., fill g[][]
+    // This is same as building a Trie for arr[]
+    for (int i = 0; i < k; ++i)
+    {
+        const string &word = arr[i];
+        int currentState = 0;
+
+        // Insert all characters of current word in arr[]
+        for (int j = 0; j < word.size(); ++j)
+        {
+            int ch = word[j] - 'a';
+
+            // Allocate a new node (create a new state) if a
+            // node for ch doesn't exist.
+            if (g[currentState][ch] == -1)
+                g[currentState][ch] = states++;
+
+            currentState = g[currentState][ch];
+        }
+
+        // Add current word in output function
+        out[currentState] |= (1 << i);
+    }
+
+    // For all characters which don't have an edge from
+    // root (or state 0) in Trie, add a goto edge to state
+    // 0 itself
+    for (int ch = 0; ch < MAXC; ++ch)
+        if (g[0][ch] == -1)
+            g[0][ch] = 0;
+
+    // Now, let's build the failure function
+
+    // Initialize values in fail function
+    memset(f, -1, sizeof f);
+
+    // Failure function is computed in breadth first order
+    // using a queue
+    queue<int> q;
+
+    // Iterate over every possible input
+    for (int ch = 0; ch < MAXC; ++ch)
+    {
+        // All nodes of depth 1 have failure function value
+        // as 0. For example, in above diagram we move to 0
+        // from states 1 and 3.
+        if (g[0][ch] != 0)
+        {
+            f[g[0][ch]] = 0;
+            q.push(g[0][ch]);
+        }
+    }
+
+    // Now queue has states 1 and 3
+    while (q.size())
+    {
+        // Remove the front state from queue
+        int state = q.front();
+        q.pop();
+
+        // For the removed state, find failure function for
+        // all those characters for which goto function is
+        // not defined.
+        for (int ch = 0; ch <= MAXC; ++ch)
+        {
+            // If goto function is defined for character 'ch'
+            // and 'state'
+            if (g[state][ch] != -1)
+            {
+                // Find failure state of removed state
+                int failure = f[state];
+
+                // Find the deepest node labeled by proper
+                // suffix of string from root to current
+                // state.
+                while (g[failure][ch] == -1)
+                    failure = f[failure];
+
+                failure = g[failure][ch];
+                f[g[state][ch]] = failure;
+
+                // Merge output values
+                out[g[state][ch]] |= out[failure];
+
+                // Insert the next level node (of Trie) in Queue
+                q.push(g[state][ch]);
+            }
+        }
+    }
+
+    return states;
+}
+
+// Returns the next state the machine will transition to using goto
+// and failure functions.
+// currentState - The current state of the machine. Must be between
+//                0 and the number of states - 1, inclusive.
+// nextInput - The next character that enters into the machine.
+int findNextState(int currentState, char nextInput)
+{
+    int answer = currentState;
+    int ch = nextInput - 'a';
+
+    // If goto is not defined, use failure function
+    while (g[answer][ch] == -1)
+        answer = f[answer];
+
+    return g[answer][ch];
+}
+
+// This function finds all occurrences of all array words
+// in text.
+void searchWords(string arr[], int k, string text)
+{
+    // Preprocess patterns.
+    // Build machine with goto, failure and output functions
+    buildMatchingMachine(arr, k);
+
+    // Initialize current state
+    int currentState = 0;
+
+    // Traverse the text through the nuilt machine to find
+    // all occurrences of words in arr[]
+    for (int i = 0; i < text.size(); ++i)
+    {
+        currentState = findNextState(currentState, text[i]);
+
+        // If match not found, move to next state
+        if (out[currentState] == 0)
+            continue;
+
+        // Match found, print all matching words of arr[]
+        // using output function.
+        for (int j = 0; j < k; ++j)
+        {
+            if (out[currentState] & (1 << j))
+            {
+                cout << "Word " << arr[j] << " appears from "
+                     << i - arr[j].size() + 1 << " to " << i << endl;
+            }
+        }
+    }
+}
+
+// Driver program to test above
+int main()
+{
+    string arr[] = {"he", "she", "hers", "his"};
+    string text = "ahishers";
+    int k = sizeof(arr) / sizeof(arr[0]);
+
+    searchWords(arr, k, text);
+
+    return 0;
+}

Dijkstra’s shortest path algorithm/Dijkstra.cpp

@@ -0,0 +1,92 @@
+// A C++ program for Dijkstra's single source shortest path algorithm. 
+// The program is for adjacency matrix representation of the graph 
+
+#include <stdio.h> 
+#include <limits.h> 
+
+// Number of vertices in the graph 
+#define V 9 
+
+// A utility function to find the vertex with minimum distance value, from 
+// the set of vertices not yet included in shortest path tree 
+int minDistance(int dist[], bool sptSet[]) 
+{ 
+   // Initialize min value 
+   int min = INT_MAX, min_index; 
+
+   for (int v = 0; v < V; v++) 
+     if (sptSet[v] == false && dist[v] <= min) 
+         min = dist[v], min_index = v; 
+
+   return min_index; 
+} 
+
+// A utility function to print the constructed distance array 
+int printSolution(int dist[], int n) 
+{ 
+   printf("Vertex   Distance from Source\n"); 
+   for (int i = 0; i < V; i++) 
+      printf("%d tt %d\n", i, dist[i]); 
+} 
+
+// Function that implements Dijkstra's single source shortest path algorithm 
+// for a graph represented using adjacency matrix representation 
+void dijkstra(int graph[V][V], int src) 
+{ 
+     int dist[V];     // The output array.  dist[i] will hold the shortest 
+                      // distance from src to i 
+
+     bool sptSet[V]; // sptSet[i] will true if vertex i is included in shortest 
+                     // path tree or shortest distance from src to i is finalized 
+
+     // Initialize all distances as INFINITE and stpSet[] as false 
+     for (int i = 0; i < V; i++) 
+        dist[i] = INT_MAX, sptSet[i] = false; 
+
+     // Distance of source vertex from itself is always 0 
+     dist[src] = 0; 
+
+     // Find shortest path for all vertices 
+     for (int count = 0; count < V-1; count++) 
+     { 
+       // Pick the minimum distance vertex from the set of vertices not 
+       // yet processed. u is always equal to src in the first iteration. 
+       int u = minDistance(dist, sptSet); 
+
+       // Mark the picked vertex as processed 
+       sptSet[u] = true; 
+
+       // Update dist value of the adjacent vertices of the picked vertex. 
+       for (int v = 0; v < V; v++) 
+
+         // Update dist[v] only if is not in sptSet, there is an edge from  
+         // u to v, and total weight of path from src to  v through u is  
+         // smaller than current value of dist[v] 
+         if (!sptSet[v] && graph[u][v] && dist[u] != INT_MAX  
+                                       && dist[u]+graph[u][v] < dist[v]) 
+            dist[v] = dist[u] + graph[u][v]; 
+     } 
+
+     // print the constructed distance array 
+     printSolution(dist, V); 
+} 
+
+// driver program to test above function 
+int main() 
+{ 
+   /* Let us create the example graph discussed above */
+   int graph[V][V] = {{0, 4, 0, 0, 0, 0, 0, 8, 0}, 
+                      {4, 0, 8, 0, 0, 0, 0, 11, 0}, 
+                      {0, 8, 0, 7, 0, 4, 0, 0, 2}, 
+                      {0, 0, 7, 0, 9, 14, 0, 0, 0}, 
+                      {0, 0, 0, 9, 0, 10, 0, 0, 0}, 
+                      {0, 0, 4, 14, 10, 0, 2, 0, 0}, 
+                      {0, 0, 0, 0, 0, 2, 0, 1, 6}, 
+                      {8, 11, 0, 0, 0, 0, 1, 0, 7}, 
+                      {0, 0, 2, 0, 0, 0, 6, 7, 0} 
+                     }; 
+
+    dijkstra(graph, 0); 
+
+    return 0; 
+} 

KMP/kmp.cpp

@@ -0,0 +1,95 @@
+// C++ program for implementation of KMP pattern searching
+// algorithm
+#include <bits/stdc++.h>
+
+void computeLPSArray(char *pat, int M, int *lps);
+
+// Prints occurrences of txt[] in pat[]
+void KMPSearch(char *pat, char *txt)
+{
+    int M = strlen(pat);
+    int N = strlen(txt);
+
+    // create lps[] that will hold the longest prefix suffix
+    // values for pattern
+    int lps[M];
+
+    // Preprocess the pattern (calculate lps[] array)
+    computeLPSArray(pat, M, lps);
+
+    int i = 0; // index for txt[]
+    int j = 0; // index for pat[]
+    while (i < N)
+    {
+        if (pat[j] == txt[i])
+        {
+            j++;
+            i++;
+        }
+
+        if (j == M)
+        {
+            printf("Found pattern at index %d ", i - j);
+            j = lps[j - 1];
+        }
+
+        // mismatch after j matches
+        else if (i < N && pat[j] != txt[i])
+        {
+            // Do not match lps[0..lps[j-1]] characters,
+            // they will match anyway
+            if (j != 0)
+                j = lps[j - 1];
+            else
+                i = i + 1;
+        }
+    }
+}
+
+// Fills lps[] for given patttern pat[0..M-1]
+void computeLPSArray(char *pat, int M, int *lps)
+{
+    // length of the previous longest prefix suffix
+    int len = 0;
+
+    lps[0] = 0; // lps[0] is always 0
+
+    // the loop calculates lps[i] for i = 1 to M-1
+    int i = 1;
+    while (i < M)
+    {
+        if (pat[i] == pat[len])
+        {
+            len++;
+            lps[i] = len;
+            i++;
+        }
+        else // (pat[i] != pat[len])
+        {
+            // This is tricky. Consider the example.
+            // AAACAAAA and i = 7. The idea is similar
+            // to search step.
+            if (len != 0)
+            {
+                len = lps[len - 1];
+
+                // Also, note that we do not increment
+                // i here
+            }
+            else // if (len == 0)
+            {
+                lps[i] = 0;
+                i++;
+            }
+        }
+    }
+}
+
+// Driver program to test above function
+int main()
+{
+    char txt[] = "ABABDABACDABABCABAB";
+    char pat[] = "ABABCABAB";
+    KMPSearch(pat, txt);
+    return 0;
+}