Python Program to find out the number of matches in an array containing pairs of (base, number)

We need to find pairs in the format (base, number) that represent the same decimal value. For example, (10, 15) means 15 in base 10, and (8, 17) means 17 in base 8. Both equal 15 in decimal, so they match.

So, if the input is like num_inputs = 2, input_arr = [(10, 15), (8, 17)], then the output will be 1.

The variable num_inputs specifies the number of inputs, and the array input_arr lists the number pairs. Here if we look at the two pairs: 15 in base 10 (decimal) is the same as 17 in base 8 (octal). Both equal 15 in decimal, so there is one match.

Algorithm Steps

To solve this, we will follow these steps ?

• Create a dictionary to count occurrences of each decimal value

• For each pair (base, number), convert the number from given base to decimal

• Count how many times each decimal value appears

• For each decimal value appearing n times, the number of matches is n*(n-1)/2

Example

Let us see the following implementation to get better understanding ?

from collections import defaultdict

def solve(num_inputs, input_arr):
    temp_dict = defaultdict(int)
    
    for i in range(num_inputs):
        base, number = input_arr[i][0], input_arr[i][1]
        # Convert number from given base to decimal
        decimal_value = int(str(number), base)
        temp_dict[decimal_value] += 1
    
    cnt = 0
    for value in temp_dict.values():
        # Calculate combinations: n*(n-1)/2
        cnt += value * (value - 1) // 2
    
    return cnt

# Test the function
print(solve(2, [(10, 15), (8, 17)]))

The output of the above code is ?

1

How It Works

The algorithm converts each (base, number) pair to its decimal equivalent:

• (10, 15) ? 15 in decimal

• (8, 17) ? 1×8¹ + 7×8? = 8 + 7 = 15 in decimal

Both pairs represent the same decimal value (15), so we have 2 occurrences. The number of matches for n occurrences is n×(n-1)/2 = 2×1/2 = 1.

Another Example

from collections import defaultdict

def solve(num_inputs, input_arr):
    temp_dict = defaultdict(int)
    
    for i in range(num_inputs):
        base, number = input_arr[i][0], input_arr[i][1]
        decimal_value = int(str(number), base)
        temp_dict[decimal_value] += 1
    
    cnt = 0
    for value in temp_dict.values():
        cnt += value * (value - 1) // 2
    
    return cnt

# Test with multiple matches
print(solve(4, [(10, 15), (8, 17), (16, 15), (2, 1111)]))

The output of the above code is ?

6

Here we have:

• (10, 15) ? 15 decimal

• (8, 17) ? 15 decimal

• (16, 15) ? 21 decimal

• (2, 1111) ? 15 decimal

Three pairs equal 15 in decimal, giving us 3×2/2 = 3 matches for value 15. One pair equals 21, giving 0 matches. Total = 3 matches.

Conclusion

This solution efficiently finds matching number pairs by converting all values to decimal and counting combinations. The time complexity is O(n) where n is the number of input pairs.