Algorithm Design Patterns

Algorithm PalindromeCheck

Function IsPalindrome(arr, size)
    var left = 0
    var right = size - 1
    
    While left < right Do
        If arr[left] != arr[right] Then
            Return false
        Endif
        
        left = left + 1
        right = right - 1
    Endwhile
    
    Return true
Endfunction

var test1 = [1, 2, 3, 2, 1]
var test2 = [1, 2, 3, 4, 5]

Print "[1,2,3,2,1] is palindrome:", IsPalindrome(test1, 5)
Print "[1,2,3,4,5] is palindrome:", IsPalindrome(test2, 5)

Endalgorithm

Algorithm MaxSumWindow

var arr = [2, 1, 5, 1, 3, 2]
var windowSize = 3
var n = 6

# Calculate first window sum
var windowSum = 0
For i = 0 To windowSize - 1
    windowSum = windowSum + arr[i]
Endfor

var maxSum = windowSum

# Slide window through array
For i = windowSize To n - 1
    # Remove leftmost element, add new element
    windowSum = windowSum - arr[i - windowSize] + arr[i]
    
    If windowSum > maxSum Then
        maxSum = windowSum
    Endif
Endfor

Print "Maximum sum of 3 consecutive elements:", maxSum

Endalgorithm

Algorithm CoinChange

var amount = Input "Enter amount (cents):"

var coins = [25, 10, 5, 1]  # Quarters, dimes, nickels, pennies
var coinNames = ["quarters", "dimes", "nickels", "pennies"]
var coinCount[4]

Print ""
Print "=== MAKING CHANGE ==="
Print ""

For i = 0 To 3
    coinCount[i] = amount / coins[i]  # Integer division
    amount = amount mod coins[i]  # Remaining amount
    
    If coinCount[i] > 0 Then
        Print coinCount[i], coinNames[i]
    Endif
Endfor

Endalgorithm

Algorithm DivideConquerMax

Function FindMax(arr, left, right)
    # BASE CASE: single element
    If left == right Then
        Return arr[left]
    Endif
    
    # DIVIDE: split into two halves
    var mid = (left + right) / 2
    
    # CONQUER: find max in each half
    var leftMax = FindMax(arr, left, mid)
    var rightMax = FindMax(arr, mid + 1, right)
    
    # COMBINE: return the greater of two maxes
    If leftMax > rightMax Then
        Return leftMax
    Else
        Return rightMax
    Endif
Endfunction

var numbers = [3, 41, 52, 26, 38, 57, 9, 49]
var max = FindMax(numbers, 0, 7)

Print "Maximum value:", max

Endalgorithm

Algorithm FibonacciDP

var memo[100]  # Store calculated values

# Initialize memo array
For i = 0 To 99
    memo[i] = -1  # -1 means not calculated yet
Endfor

Function Fib(n)
    # BASE CASES
    If n == 0 Then
        Return 0
    Else If n == 1 Then
        Return 1
    Endif
    
    # Check if already calculated
    If memo[n] != -1 Then
        Return memo[n]  # Return stored value
    Endif
    
    # Calculate and store
    memo[n] = Fib(n - 1) + Fib(n - 2)
    Return memo[n]
Endfunction

Print "Fibonacci numbers:"
For i = 0 To 10
    Print "F(", i, ") =", Fib(i)
Endfor

Endalgorithm

Algorithm FrequencyCounter

var arr = [1, 2, 2, 3, 1, 4, 2, 5, 3, 1]
var frequency[6]  # For numbers 0-5

# Initialize frequency array
For i = 0 To 5
    frequency[i] = 0
Endfor

# Count occurrences
For i = 0 To Size(arr) - 1
    var value = arr[i]
    frequency[value] = frequency[value] + 1
Endfor

# Display frequencies
Print "=== FREQUENCY TABLE ==="
For i = 1 To 5
    If frequency[i] > 0 Then
        Print "Number", i, "appears", frequency[i], "times"
    Endif
Endfor

Endalgorithm

Algorithm PatternSearch

var data = [1, 2, 3, 4, 2, 3, 5, 6, 2, 3]
var pattern = [2, 3]

var dataSize = 10
var patternSize = 2

Print "Searching for pattern [2,3]..."
Print ""

var foundCount = 0

For i = 0 To dataSize - patternSize
    var match = true
    
    # Check if pattern matches at position i
    For j = 0 To patternSize - 1
        If data[i + j] != pattern[j] Then
            match = false
        Endif
    Endfor
    
    If match == true Then
        Print "✅ Pattern found at index", i
        foundCount = foundCount + 1
    Endif
Endfor

Print ""
Print "Total matches:", foundCount

Endalgorithm