Mastering Practical Algorithms: Project Euler Challenges

Break down problem six by computing the sum of squares and the square of sums, then take their difference, demonstrated with 1-10 and a Python loop for 1-100.

Compute the difference between the square of the sum and the sum of the squares for numbers 1 to 100 using Python.

Demonstrate a node.js approach to project euler problem 6 by computing the sum of squares and the square of the sum with a for loop, then log the difference.

Explore brute-force and optimized approaches to find the 10,001st prime, using a known primes list, modulus checks, and the sieve of Eratosthenes concept to prune non-primes.

Learn how to solve Project Euler problem 7 in Python by building a prime finder with known primes, comparing brute force checks to a sieve-based approach, and timing the run.

Solve project euler problem 7 by iterating primes with a known primes list in node/javascript, testing divisibility, and optimizing with a prime-of-known-primes approach for faster results.

Find largest product of thirteen consecutive digits in a 1000-digit number from Project Euler, using strings or lists and a subset of 13 digits with zero checks and divide‑and‑multiply optimization.

Apply a Python solution to Project Euler 8 by extracting thirteen adjacent digits from a large number, computing their product via a sliding window, and optimizing with zero checks.

We break down finding a pythagorean triplet with a+b+c=1000 using a and b loops. Compute c=1000-a-b, check a^2+b^2=c^2, and multiply a, b, and c.

Explore a Python brute-force solution to Project Euler problem 9, finding a, b, c with a^2 + b^2 = c^2 and c = 1000 - a - b.

Apply the sieve of Eratosthenes to sum all primes below two million, starting at the square of each prime to improve efficiency and relate it to the earlier problem.

Implement a Python sieve of Eratosthenes to sum primes below two million. Compare naive and optimized approaches and demonstrate dramatic speedups in Project Euler problem 10.

Learn to compute the largest product of four adjacent numbers in a 20x20 grid using Python with nested loops across horizontal, vertical, normal diagonal, and reverse diagonal directions.

Master the problem 11 solution in Python by parsing a 20x20 grid into a list of lists, then compute the largest product of four adjacent numbers horizontally, vertically, and diagonally.

Explore triangular numbers and their divisors to find the first with over 500 divisors in Project Euler problem 12, using the square-root optimization to count factors efficiently.

Apply Python to solve Project Euler problem 12 by finding the first triangular number with at least 500 divisors, using factorization, square-root optimization, and efficient looping.

Solve a large-sum challenge by looping through 100 fifty-digit numbers, casting data types, and grabbing the first ten digits of the 52-digit sum via a substring.

This lecture walks through solving Project Euler problem 13 in Python by parsing a 150-digit string, converting to integers, summing 100 numbers, and printing the first ten digits.

Solve Project Euler problem 14 by finding the starting number under 1 million that yields the longest Collatz sequence, using memoization and efficient data types to speed up calculation.

Solve project euler problem 14 in Python by finding the starting number under 1 million that yields the longest collatz chain, using a dictionary to store computed chain lengths.

Solve Project Euler problem 15 by counting lattice paths on a 2x2 and 20x20 grid with a simple pattern; implement a Python dynamic programming grid.

This lecture solves Project Euler problem 15 in Python by building a dynamic programming grid and updating each cell as the sum of top and left neighbors to count routes.

Solve problem 16 by summing digits of 2 to the 1000th power, using Python's arbitrary-precision integers and converting the number to a string to sum its digits.

Compute 2 to the 1000th power in Python, convert the result to a string, and sum its digits to obtain 1366. Shows 302 digits and Python's big integers.

Explore problem 17 by looping through numbers up to 1000 and counting letters in their English names using string manipulation, ignoring hyphens and spaces.

Demonstrates solving Project Euler problem 17 in Python by building a number list from digits, tens, and hundreds with and, then counting letters without spaces or hyphens to yield 21124.

we break down problem 18 from Project Euler by solving the triangle maximum path sum with a bottom-up dynamic approach that uses triangular subproblems instead of brute force.

Parse the Project Euler triangle in Python, convert rows to integers, and compute maximum path sum from bottom to top by choosing the larger between down left and down right.

Solve Project Euler problem 19 by counting how often the first day of each month falls on Sunday from 1901 to 2000, using the Gregorian calendar and a 28-year cycle.

Compute the number of Sundays on the first of the month from 1901 to 2000 using a Python script, handling leap years and month lengths.

Demonstrate calculating the sum of digits of a 100 factorial using Python's math.factorial. Convert the result to a string, iterate digits, and accumulate the total to obtain the digit sum.

Explore solving problem 20 in Python by computing 100 factorial, converting it to a string, and summing its digits with loops or map and sum to yield 648.

Explore amicable numbers and their pairs, define proper divisors, and apply a two-part approach under 10,000 using divisor sums and a sieve optimization.

Explore Python solutions to Project Euler problem 21, deriving amicable numbers through divisor analysis, sqrt-based optimization, and a fast sieve approach for massive scale.

Explore Project Euler problem 22: compute names scores by summing letter values and multiplying by sorted position, comparing radix sort with built-in sorted, using ord in Python.

Explore solving Project Euler problem 22 with a Python radix sort approach, reading and cleaning a names file, sorting uppercase names, and computing name scores by letter values times positions.

Explore problem 23 from Project Euler by using a sieve to compute proper divisors and identify abundant numbers, then sum numbers not expressible as a sum of two abundant numbers.

Python solution to Project Euler problem 23 using a sieve to generate abundant numbers and proper divisors, identifying numbers not expressible as the sum of two abundant numbers.

Find the first Fibonacci number with 1000 digits by tracking only the two previous values in a Python loop using big integers; the solution yields Fibonacci number 4782.

Explore project Euler problem 26: determine the longest repeating decimal cycle for 1/n up to 1000 using long division and remainder tracking, with optimizations that skip factors 2 and 5.