#1308 Added Colussi Algorithm in String Algorithms

String Algorithms/Colussi Algorithm/Program.c

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+#include <stdio.h>
+#include <string.h>
+
+#define MAX_PATTERN_LENGTH 100
+
+// Function to compute the prefix function for the pattern
+void computePrefixFunction(char* pattern, int m, int* pi) {
+    int i = 1, j = 0;
+    pi[0] = 0;
+
+    while (i < m) {
+        if (pattern[i] == pattern[j]) {
+            pi[i] = j + 1;
+            i++;
+            j++;
+        }
+        else if (j > 0) {
+            j = pi[j - 1];
+        }
+        else {
+            pi[i] = 0;
+            i++;
+        }
+    }
+}
+
+// Function to perform string matching using Colussi algorithm
+void colussi(char* text, char* pattern) {
+    int n = strlen(text);
+    int m = strlen(pattern);
+    int pi[MAX_PATTERN_LENGTH];
+
+    // Compute the prefix function for the pattern
+    computePrefixFunction(pattern, m, pi);
+
+    int i = 0, j = 0;
+    while (i < n) {
+        if (text[i] == pattern[j]) {
+            i++;
+            j++;
+            if (j == m) {
+                printf("Pattern found at index %d\n", i - j);
+                j = pi[j - 1];
+            }
+        }
+        else {
+            if (j > 0) {
+                j = pi[j - 1];
+            }
+            else {
+                i++;
+            }
+        }
+    }
+}
+
+int main() {
+    char text[] = "ABABDABACDABABCABAB";
+    char pattern[] = "ABABCABAB";
+
+    printf("Text: %s\n", text);
+    printf("Pattern: %s\n\n", pattern);
+
+    printf("Matches:\n");
+    colussi(text, pattern);
+
+    return 0;
+}

String Algorithms/Colussi Algorithm/README.md

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+# Colussi Algorithm
+
+## Description
+
+The Colussi algorithm, also known as the KMP-Colussi algorithm, is a string matching algorithm that combines ideas from the Knuth-Morris-Pratt (KMP) algorithm and the Boyer-Moore algorithm. It was introduced by Livio Colussi in 1991. The algorithm achieves linear time complexity for string matching by utilizing the prefix function and a shifting heuristic.
+
+### Problem Definition
+
+Given:
+- A text string T of length n
+- A pattern string P of length m
+
+Objective:
+- Find all occurrences of pattern P in text T
+
+### Algorithm Overview
+
+1. **Preprocessing**:
+   - Compute the prefix function for the pattern string
+   - The prefix function helps in determining the proper shift when a mismatch occurs
+
+2. **Searching**:
+   - Scan the text from left to right
+   - Compare characters of the text and pattern
+   - If a match is found, continue comparing until either the end of the pattern is reached (indicating a complete match) or a mismatch occurs
+   - In case of a mismatch, use the prefix function to determine the appropriate shift
+
+### Time Complexity
+
+- Preprocessing: O(m), where m is the length of the pattern
+- Searching: O(n), where n is the length of the text
+- Overall time complexity: O(n + m)
+
+### Space Complexity
+
+O(m), where m is the length of the pattern (for storing the prefix function)
+
+## Implementation
+
+The implementation in C demonstrates the Colussi algorithm for string matching. It includes:
+
+1. Function to compute the prefix function for the pattern
+2. The main string matching function implementing the Colussi algorithm
+3. A demonstration of the algorithm's usage
+
+## Usage
+
+Compile the program and run it. The example in the main function demonstrates how to use the Colussi algorithm to find occurrences of a pattern string in a given text.
+
+## Note
+
+The Colussi algorithm combines the ideas of the KMP algorithm and the Boyer-Moore algorithm to achieve efficient string matching. It utilizes the prefix function for determining proper shifts and provides linear time complexity for searching patterns in a text.