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Prime Numbers: Divisibility: The prime number law stated above means that, in order for a number x to divide a number y (written x/y, or mod(y, x) = 0), all primes in x's prime factorization must be in y's prime factorization. Or, more specifically, Let x = Let y = if x/y, then for all I, ji

You are a product manager and currently leading a team to develop a new product. Unfortunately, the latest version of your product fails the quality check. Since each version is developed based on the previous version, all the versions after a bad version are also bad. Suppose you have n versions [1, 2, ..., n] and you want to find out the first bad one, which causes all the following ones to be..

Bit Manipulation by Hand: ^ means XOR, ~ is a Not (Negation) - XOR: If it's a different bit, it will be 1. EX) 1101 ^ (~1101) = 1111 - If you XOR a bit with its own negated value, you will always get 1. Therefore, the solution to a^(~a) will be a sequence of 1s. EX) 1011 & (~0

Example: Print all positive integer solutions to the equation a^3 + b^3 = c^3 + d^3 and a, b, c, d are integers between 1 and 1000. 1. A brute force solutions n = 1000 n = 1000 for a from 1 to n for b from 1 to n for c from 1 to n for d from 1 to n if a^3 + b^3 = c^3 + d^3 print a, b, c, d This returns O(n^4) To optimize it we can make a break when we find it n = 1000 for a from 1 to n for b fro..

A problem Solving Flow Chart Listen Pay very close attention to any information in the problem description. You probably need it all for an optimal algorithm. Example Most examples are too small or are special cases. Debug your example. Is there any way it's a special case? Is it big enough? Brute Force get a brute-force solution as soon as possible. Don't worry about developing an efficient alg..

From Cracking the Coding Interview: Question 10: int sumDigits(int n) { int sum = 0; while (n < 0) { num += n % 10; n /= 10; } return sum; } The runtime will be the number of digits in the number. A number with d digits can have a value up to 10^d. if n = 10^d, then d = log n. Therefore, the runtime is 0(log n). Question 11: The following code prints all strings of length k where the characters ..

From Craking the Coding Interview Example 10: boolean isPrime(int n) { for (int x = 2; x * x

Efficient Procedures for solving large scale problems Scalability Classical Data Structures Sorting & Matching Real Implementation of Algorithms in Python Order of this classes Algorithmic Thinking: Peak Finding Sorting & Trees: Event simulation Hashing: Genome comparison Numerics: RSA Encryption (SSL | Backend) Graphs: Rubik's Cube Shortest Paths: Caltech -> MIT Dynamic Programming: Image Compr..