Daily Lessons

Day 1:

Math: Geometric Sequences
Python: List (enumarate), Dict (keys(), values(),items())
LeetCode: 50. Pow(x, n): using Recursive with Pow(x,n) = Pow(x,n//2), rmb for n = odd and even cases

Day 2:

Math: Modular Arithmetic
- Congruence a ≡ b (mod n) For a positive integer n, the integers a and b are congruent mod n if their remainders when divided by n are the same.
  - For example: 52≡24(mod7): 52 and 24 are congruent (mod 7) because (52 mod 7) = 3 and (24 mod 7) = 3.
- Properties of multiplication in Modular Arithmetic:
- (a mod n) mod n = a mod n: This is obvious because a mod n ∈ [0,𝑛−1] and so the second modmod cannot have an effect.
- (A^2) mod C = (A * A) mod C = ((A mod C) * (A mod C)) mod C
LeetCode: Fast Exponentiation

Day 3:

Python:
- Nested List Comprehension [[item if not item.isspace() else -1 for item in row] for row in board] to build 2D matrix
- String Formatting with Padding 0: For example, convert integer 2 to "02" f"{month:02d}"
- Math's Ceil & Floor: math.ceil(), math.floor()
Math:
- Modular Multiplicative Inverse (MMI): MMI(a, b) = x s.t a*x ≡ 1 (mod n)
  - For example: a = 3, m = 11 => x = 4 as (3*4) mod 11 = 1
- Euclidean Algorithm to find GCD of A & B & Extended Euclidean Algorithm to find MMI(A, B)

Day 4:

LeetCode: Best Time to Buy and Sell Stock (Keep track on the buying price, compare to the next days), Climbing Stairs (At T(n): first step = 1, remaining steps = T(n-1) or first step = 2, remaing steps = T(n-2). This recurrence relationship is similar to Fibonacci number)

Day 5:

LeetCode: 3 Sum, Longest Palindromic Substring and Container With Most Water

Day 6:

LeetCode: Number of Islands, Design Circular Queue