Find All 0(1+)0 Patterns in a String | C Program & Explanation

Identifying patterns in binary strings is a common problem in competitive programming and technical interviews. In this article, we will discuss how to find all occurrences of the pattern 0(1+)0 in a given binary string, where:

• The pattern must start and end with ‘0’.
• There must be at least one ‘1’ between the two ‘0’s.

This problem can be solved efficiently by scanning the string and counting the occurrences of this pattern.

Example & Explanation

Example 1

Input:

01101111010

Output:

3

Explanation:
The given binary string: 01101111010

• First occurrence: 01101111010 → count = 1
• Second occurrence: 01101111010 → count = 2
• Third occurrence: 01101111010 → count = 3

So, the total number of patterns 0(1+)0 in this string is 3.

Example 2

Input:

binary_str = "01101111010"

Step-by-Step Process:

1. Start scanning the string from left to right.
2. Identify every ‘0’ and check if it’s followed by at least one ‘1’ and another ‘0’.
3. Keep a count of the valid patterns.

Stepwise Matching:

Final Count:

Total 0(1+)0 patterns found = 3

Output:

3

Example 3

Input:

binary_str = "01010"

Stepwise Matching:

Final Count:

Total 0(1+)0 patterns found = 2

Output:

2

Edge Case Examples

Example 4 (No Valid Pattern)

Input:

binary_str = "0000"

Explanation:

• There is no ‘1’ between any two ‘0’s.
• So, there are 0 valid patterns.

Output:

0

Example 5 (All ‘1’s in Between)

Input:

binary_str = "011110"

Explanation:

• Found one valid pattern: 0(1111)0

Output:

1

Efficient Algorithm to Find 0(1+)0 Patterns

To find and count the required patterns in the given binary string, follow these steps:

1. Take input – Accept the binary string from the user.
2. Scan the string – Traverse each character one by one.
3. Detect pattern – If a ‘0’ is encountered, check if there are ‘1’s followed by another ‘0’.
4. Count occurrences – Increase the count whenever the pattern is found.
5. Print the result – Display the final count.

Python Program to Find All 0(1+)0 Patterns in a String

def count_patterns(binary_str):
    count = 0
    i = 0
    while i < len(binary_str) - 1:
        if binary_str[i] == '0':  
            j = i + 1  
            while j < len(binary_str) and binary_str[j] == '1':  
                j += 1  
            if j < len(binary_str) and binary_str[j] == '0':  
                count += 1  
                i = j  
        i += 1  
    return count  

# Example usage
binary_str = input("Enter the binary string: ")
print("Total 0(1+)0 patterns:", count_patterns(binary_str))

Time Complexity Analysis

• Best Case: O(n) (Single scan when no ‘1’s are present).
• Worst Case: O(n) (Traversing each character once).
• Overall Complexity: O(n) (Efficient for large inputs).

Visual Representation

To better understand how the program works, consider the following flow diagram:

Input: 01101111010  
Index: 01234567890  
------------------
0 → 1 → 1 → 0  → Found (1st pattern)  
0 → 1 → 1 → 1 → 1 → 0 → Found (2nd pattern)  
0 → 1 → 0 → Found (3rd pattern)  
Total patterns found: 3

Applications & Use Cases

• Pattern matching in binary data
• Network packet analysis
• DNA sequence analysis (for patterns in genetic sequences)
• Competitive programming & coding interviews

Conclusion

Finding patterns in binary strings is a crucial skill for technical interviews and problem-solving challenges. The 0(1+)0 pattern can be efficiently identified using a linear scan approach with an O(n) complexity. By implementing the given algorithm, you can quickly determine the number of occurrences in any binary string.