Check whether a number has consecutive 0's in the given base or not using Python

When working with different number bases, we sometimes need to check if a number contains consecutive zeros in its representation. Python provides an efficient way to convert numbers between bases and detect patterns like consecutive zeros.

Understanding the Problem

For example, the number 8 in base 2 (binary) is represented as "1000", which contains consecutive zeros. We need to convert the number to the specified base and then check for consecutive zero digits.

Complete Solution

def check_consecutive_zero(N, K):
    my_result = convert_to_base(N, K)
    if (check_consecutive_zeros(my_result)):
        print("Yes")
    else:
        print("No")

def convert_to_base(N, K):
    weight = 1
    s = 0
    while (N != 0):
        r = N % K
        N = N // K
        s = r * weight + s
        weight *= 10
    return s

def check_consecutive_zeros(N):
    prev_zero = False
    while (N != 0):
        r = N % 10
        N = N // 10
        
        if (prev_zero == True and r == 0):
            return True
        if (r > 0):
            prev_zero = False
            continue
        prev_zero = True
    return False

# Test the function
N, K = 8, 2
print("Does the number have consecutive zeroes in the base?")
check_consecutive_zero(N, K)

# Additional test cases
print("\nTesting with different numbers:")
test_cases = [(12, 2), (15, 3), (20, 4)]
for num, base in test_cases:
    print(f"Number {num} in base {base}:", end=" ")
    check_consecutive_zero(num, base)

Does the number have consecutive zeroes in the base?
Yes

Testing with different numbers:
Number 12 in base 2: Yes
Number 15 in base 3: No
Number 20 in base 4: Yes

How It Works

The solution works in three steps:

1. Base Conversion: The convert_to_base() function converts a decimal number to the specified base representation
2. Zero Detection: The check_consecutive_zeros() function examines each digit to find consecutive zeros
3. Result Display: The main function coordinates the process and displays the result

Example Breakdown

Let's trace through the example where N=8 and K=2:

# Converting 8 to base 2
# 8 ÷ 2 = 4 remainder 0
# 4 ÷ 2 = 2 remainder 0  
# 2 ÷ 2 = 1 remainder 0
# 1 ÷ 2 = 0 remainder 1
# Result: 1000 (reading remainders bottom to top)

number = 8
base = 2
converted = convert_to_base(number, base)
print(f"Number {number} in base {base} is: {converted}")

# Check for consecutive zeros in 1000
# We find three consecutive zeros

Number 8 in base 2 is: 1000

Conclusion

This approach efficiently converts numbers to any base and detects consecutive zeros by tracking the previous digit state. The algorithm works for any base greater than 1 and handles edge cases properly.