DSA — Algorithms

What is an Algorithm?

A finite sequence of well-defined instructions for solving a problem.

Algorithm Properties

Property	Description
Finiteness	Must terminate
Definiteness	Each step is clear
Input	Zero or more inputs
Output	One or more outputs
Effectiveness	Each step is feasible

Algorithm Categories

Brute Force

Try all possibilities:

def find_max(arr):
    max_val = arr[0]
    for num in arr:
        if num > max_val:
            max_val = num
    return max_val

Divide and Conquer

Split into smaller problems:

def merge_sort(arr):
    if len(arr) <= 1:
        return arr
    mid = len(arr) // 2
    left = merge_sort(arr[:mid])
    right = merge_sort(arr[mid:])
    return merge(left, right)

Greedy

Make locally optimal choices:

def coin_change(coins, amount):
    coins.sort(reverse=True)
    count = 0
    for coin in coins:
        while amount >= coin:
            amount -= coin
            count += 1
    return count

Dynamic Programming

Optimize with memoization:

def fibonacci(n, memo={}):
    if n in memo:
        return memo[n]
    if n <= 1:
        return n
    memo[n] = fibonacci(n-1) + fibonacci(n-2)
    return memo[n]

Mini Practice

1. Identify algorithm types
2. Implement brute force solutions
3. Apply divide and conquer
4. Use dynamic programming

Up Next

Continue with Complexity — measuring algorithm efficiency.