Solving Project Euler Problem 8: Largest Product in a Series

Problem

"The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

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Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?"

Solution

A consecutive digit product is the result of multiplying a sequence of consecutive digits within a larger number. For example, in the 1000-digit number provided in the problem statement, the product of the four consecutive digits "9, 9, 8, 9" is 5832.

To find the largest product of consecutive digits, we need to slide a window of a specified size (in this case, thirteen) through the number and calculate the product of the digits within that window. We then compare the products obtained as we slide the window and keep track of the largest product encountered.

 

1.      We define a helper function, calculate_product, which takes a string of digits and calculates the product of those digits.

2.      The find_largest_product function takes two arguments: number, the large number as a string, and consecutive_digits, the number of consecutive digits to consider.

3.      We initialize max_product to 0, which will store the maximum product encountered.

4.      Using a for loop that iterates through the string representation of the number, we extract a window of consecutive digits of length consecutive_digits.

5.      We calculate the product of the digits within the window using the calculate_product function.

6.      We compare the calculated product with the current max_product and update max_product if the new product is greater.

7.      We continue sliding the window through the string until we reach the end.

8.      After the loop finishes, max_product will contain the largest product of consecutive_digits consecutive digits.

Solving Project Euler Problems provides a great opportunity to practice coding and algorithmic thinking.