Made pr03 ready for handing it in

activateEnv.srcme

@@ -0,0 +1,24 @@
+#!/bin/bash -u
+
+# 
+# Source python venv (installed via curl https://pyenv.run | bash) to use specific python-version for this project without affecting system
+# For Algorithms and Datastructures Class
+#
+# For WSLg support for matplotlib export="DISPLAY:0" and 
+# echo "backend: TkAgg" > ~/.config/matplotlib/matplotlibrc
+
+export PYENV_ROOT="$HOME/.pyenv"
+export PATH="$PYENV_ROOT/bin:$PATH"
+export PYTHONPATH=".:$PYTHONPATH"
+eval "$(pyenv init --path)"
+eval "$(pyenv init -)"
+eval "$(pyenv virtualenv-init -)"
+
+# Create virtualenv if it doesn't exist
+if ! pyenv versions | grep -q AUD; then
+    echo "Creating Python environment..."
+    pyenv install -s 3.12.0
+    pyenv virtualenv 3.12.0 AUD
+fi
+
+pyenv activate AUD

myreqs.txt

@@ -0,0 +1,13 @@
+contourpy==1.3.1
+cycler==0.12.1
+fonttools==4.56.0
+kiwisolver==1.4.8
+matplotlib==3.10.1
+numpy==2.2.4
+packaging==24.2
+pillow==11.1.0
+pygame==2.6.1
+pyparsing==3.2.3
+python-dateutil==2.9.0.post0
+six==1.17.0
+tk==0.1.0

schoeffelbe/pr01.py

@@ -0,0 +1,165 @@
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.literal import Literal
+from utils.constants import MIN_VALUE
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+
+def max_sequence_1(z: MemoryArray):
+    n = z.length()
+    m = MemoryCell(MIN_VALUE)
+    s = MemoryCell()
+    l = MemoryCell()
+    r = MemoryCell()
+    for i in mrange(n):
+        for j in mrange(i, n):
+            s.set(0)
+            for k in mrange(i, j):
+                s += z[k]
+            if s > m:
+                m.set(s)
+                l.set(i)
+                r.set(j)
+    return m, l, r
+
+def max_sequence_2(z: MemoryArray):
+    n = z.length()
+    m = MemoryCell(MIN_VALUE)
+    s = MemoryCell()
+    l = MemoryCell()
+    r = MemoryCell()
+    for i in mrange(n):
+        s.set(0)
+        for j in mrange(i, n):
+            s += z[j]
+            if s > m:
+                m.set(s)
+                l.set(i)
+                r.set(j)
+    return m, l, r
+
+def _max_sequence_3_sub(z: MemoryArray, l: Literal, m: Literal, r: Literal):
+    # find max-sum from Middle to left
+    linksMax = MemoryCell(MIN_VALUE)
+    sum = MemoryCell(0)
+    links = MemoryCell(l)
+    rechts = MemoryCell(l)
+    for i in mrange(m, MemoryCell(l)-Literal(1), -1):
+        sum += z[i]
+        if sum > linksMax :
+            linksMax.set(sum)
+            links.set(i)
+        
+    # find max-sum from Middle to right 
+    rechtsMax = MemoryCell(MIN_VALUE)
+    sum.set(0);
+    # MRange is exclusive
+    startRight = MemoryCell(1) + m
+    for i in mrange(startRight, MemoryCell(1) + r):
+        sum += z[i]
+        if sum > rechtsMax:
+            rechtsMax.set(sum)
+            rechts.set(i)
+    return (linksMax + rechtsMax), links, rechts
+
+def _max_sequence_3(z: MemoryArray, l: Literal, r: Literal):
+    # Calc-Vars -> illegal to use Literal(0) here? Probably
+    # CAN ALLLL BE LITERALS
+    linksMax = MemoryCell()
+    linksL = MemoryCell()
+    linksR = MemoryCell()
+    rechtsMax = MemoryCell()
+    rechtsL = MemoryCell()
+    rechtsR = MemoryCell()
+    zwiMax = MemoryCell()
+    zwiL = MemoryCell()
+    zwiR = MemoryCell()
+    # Middle
+    m = MemoryCell() 
+    # Rec-Term - Reached subarray of size 1
+    if l == r:
+        return (z[l], l, r)
+    # calc middle
+    m.set(MemoryCell(l) + r)
+    # Use cutoff/floor here, did not check
+    m //= Literal(2);
+    # get maxLeft, then maxRight and then cross them (rec)
+    (linksMax, linksL, linksR) = _max_sequence_3(z, l, m)
+    startRight = MemoryCell(1) + m
+    (rechtsMax, rechtsL, rechtsR) = _max_sequence_3(z, startRight, r)
+    (zwiMax, zwiL, zwiR) = _max_sequence_3_sub(z, l, m, r)
+
+    if linksMax >= rechtsMax and linksMax >= zwiMax:
+        return (linksMax, linksL, linksR)
+
+    if rechtsMax >= linksMax and rechtsMax >= zwiMax:
+        return (rechtsMax, rechtsL, rechtsR)
+
+    return (zwiMax, zwiL, zwiR)
+
+# Wrapper for Seq DivAndConquer to keep call/teststructure possible
+def max_sequence_3(z: MemoryArray):
+    # Start with full range
+    lstart = Literal(0)
+    rend = Literal(len(z) - 1)
+    return _max_sequence_3(z, lstart, rend)
+
+def max_sequence_4(z: MemoryArray):
+    n = z.length()
+    max = MemoryCell(MIN_VALUE)
+    aktLinks = MemoryCell()
+    links = MemoryCell()
+    rechts = MemoryCell()
+    aktSum = MemoryCell()
+    for i in mrange(n):
+        aktSum += z[i]
+        if aktSum > max:
+            max.set(aktSum)
+            links.set(aktLinks)
+            rechts.set(i)
+        # if negative we start new Sum -> Restart must be better than continue
+        if aktSum < Literal(0):
+            aktSum.set(0)
+            aktLinks.set(MemoryCell(1) + i)
+    return (max, links, rechts)
+
+def example(max_sequence_func):
+    l = [-59, 52, 46, 14, -50, 58, -87, -77, 34, 15]
+    print(l)
+    z = MemoryArray(l)
+    m, l, r = max_sequence_func(z)
+    print(m, l, r)
+    assert(m == Literal(120))
+
+
+def seq(filename, max_sequence_func):
+    z = MemoryArray.create_array_from_file(filename)
+    m, l, r = max_sequence_func(z)
+    print(m, l, r)
+
+
+def analyze_complexity(max_sequence_func, sizes):
+    """
+    Analysiert die Komplexität einer maximalen Teilfolgenfunktion.
+
+    :param max_sequence_func: Die Funktion, die analysiert wird.
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        random_array = MemoryArray.create_random_array(size, -100, 100)
+        max_sequence_func(random_array)
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "adds"])
+
+
+if __name__ == '__main__':
+    # fn = max_sequence_4
+    for fn in [max_sequence_1, max_sequence_2, max_sequence_3, max_sequence_4]:
+        example(fn)
+        # for filename in ["data/seq0.txt", "data/seq1.txt", "data/seq2.txt", "data/seq3.txt"]:
+        for filename in ["data/seq0.txt", "data/seq1.txt"]:
+            print(filename)
+            seq(filename, fn)
+        analyze_complexity(fn, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100])

schoeffelbe/pr02.py

@@ -0,0 +1,125 @@
+import logging
+logger = logging.getLogger(__name__)
+# logging.basicConfig(level=logging.DEBUG)
+
+import time
+
+def timeMS(func, *args, **kwargs):
+    startTime = time.perf_counter()
+    result = func(*args, **kwargs)
+    endTime = time.perf_counter()
+    elapsedMS = (endTime - startTime) * 1000  # Convert to milliseconds
+    print(f"{func.__name__} took {elapsedMS:.2f} ms")
+    return result
+
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.literal import Literal
+from utils.constants import MIN_VALUE
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+
+def example():
+    initial = [6, 5, 3, 8, 1, 7, 2, 4]
+    # initial = [-6, -5, -3, -8, 1, 7, 2, 4]
+    toSort = MemoryArray(initial)
+    # init_from_size not accessible?
+    sorted = MemoryArray([-1] * len(initial))
+    mergeSort(toSort, sorted)
+    logger.debug(f"sorted {sorted} vs initial {initial}")
+    assert all(sorted[Literal(i)] == Literal(i+1) for i in range(len(initial))), "Array not sorted correctly"
+
+    analyze_complexity(mergeSort, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+
+def merge(left: MemoryArray, right: MemoryArray, sort: MemoryArray):
+    pointerLeft = MemoryCell(0)
+    pointerRight = MemoryCell(0)
+    pointerSort = MemoryCell(0)
+
+    compare = lambda x, y: x <= y
+
+    logger.debug(f"Merging left {left} with right {right} in sort {sort}")
+
+    while pointerLeft < left.length() and pointerRight < right.length():
+        if compare(left[pointerLeft], right[pointerRight]):
+            sort[pointerSort] = left[pointerLeft]
+            pointerLeft += Literal(1)
+        else:
+            sort[pointerSort] = right[pointerRight]
+            pointerRight += Literal(1)
+
+        logger.debug(f"Now are at sort {sort} with {pointerLeft} (l) and {pointerRight} (r)")
+        pointerSort += Literal(1)
+
+    # Consume remaining elements
+    while pointerLeft < left.length():
+        logger.debug(f"Consuming left {left} from {pointerSort} at {pointerLeft}")
+        sort[pointerSort] = left[pointerLeft]
+        pointerLeft += Literal(1)
+        pointerSort += Literal(1)
+
+    while pointerRight < right.length():
+        logger.debug(f"Consuming right {right} from {pointerSort} at {pointerRight}")
+        sort[pointerSort] = right[pointerRight]
+        pointerRight += Literal(1)
+        pointerSort += Literal(1)
+
+# Sort the array passed as "toSort" and place the result in array "sort"
+# Does not change the original Array
+def mergeSort(toSort: MemoryArray, sort: MemoryArray):
+    logger.debug(toSort)
+    toSortLength = MemoryCell(toSort.length())
+
+    # Splitting
+    # Rec-Term -> Reached single Element. Single Element is already sorted so we place it! 
+    if toSortLength <= Literal(1):
+        # still working for empty array
+        if toSortLength == Literal(1):
+            sort[Literal(0)] = toSort[Literal(0)]
+        return
+
+    # TODO - Use a global var or a reference to an array passed as argument for this
+    # TODO - Tried non-temp-array approach with alternating Work-Arrays passed to the function, but made code really unreadable. Decided not worth it for now
+    # Temporary Arrays to hold the split arrays
+    mid : Literal = toSortLength // Literal(2)
+    left : MemoryArray = MemoryArray([toSort[i] for i in mrange(mid)])
+    right : MemoryArray = MemoryArray([toSort[i] for i in mrange(mid, toSortLength)])
+
+    # Temporary arrays for sorted halves
+    leftSort = MemoryArray([-1] * mid.get())
+    rightSort = MemoryArray([-1] * (toSortLength - mid).get())
+
+    # Split further
+    mergeSort(left, leftSort)
+    mergeSort(right, rightSort)
+
+    # Recreate the array from the seperated parts 
+    merge(leftSort, rightSort, sort)
+
+def analyze_complexity(fn, sizes):
+    """
+    Analysiert die Komplexität einer maximalen Teilfolgenfunktion.
+
+    :param max_sequence_func: Die Funktion, die analysiert wird.
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        random_array = MemoryArray.create_random_array(size, -100, 100)
+        other_array = MemoryArray([-1] * size)
+        fn(random_array, other_array)
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "adds", "compares"])
+
+
+if __name__ == '__main__':
+    # For debug, assert if working and complexity-analysis
+    # example()
+
+    for filename in ["data/seq0.txt", "data/seq1.txt", "data/seq2.txt", "data/seq3.txt"]:
+        print(filename)
+        toSort = MemoryArray.create_array_from_file(filename)
+        sorted = MemoryArray([-1] * toSort.length().get())
+        timeMS(mergeSort, toSort, sorted)
+        # print(sorted)

schoeffelbe/pr03.py

@@ -0,0 +1,190 @@
+import logging
+logger = logging.getLogger(__name__)
+# logging.basicConfig(level=logging.DEBUG)
+
+import time
+
+def timeMS(func, *args, **kwargs):
+    startTime = time.perf_counter()
+    result = func(*args, **kwargs)
+    endTime = time.perf_counter()
+    elapsedMS = (endTime - startTime) * 1000  # Convert to milliseconds
+    print(f"{func.__name__} took {elapsedMS:.2f} ms")
+    return result
+
+
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.literal import Literal
+from utils.constants import MIN_VALUE
+from utils.memory_manager import MemoryManager
+from utils.memory_range import mrange
+
+def example():
+    initial = [6, 5, 3, 8, 1, 7, 2, 4]
+    # initial = [-6, -5, -3, -8, 1, 7, 2, 4]
+    toSort = MemoryArray(initial)
+    quickSortIterative(toSort, Literal(0), toSort.length().pred())
+    logger.debug(f"sorted {toSort} vs initial {initial}")
+    assert all(toSort[Literal(i)] == Literal(i+1) for i in range(len(initial))), "Array not sorted correctly"
+
+    # analyze_complexity(quickSort, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+
+def getPivot(z: MemoryArray, l: Literal, r: Literal, mode) -> Literal:
+    if mode == 0:
+        return r
+    else:
+        mid_offset = r.value - l.value
+        mid_offset = mid_offset // 2
+        mid = Literal(l.value + mid_offset)
+    
+        # Return median of left, middle, and right elements
+        if ((z[l] <= z[mid] and z[mid] <= z[r]) or 
+            (z[r] <= z[mid] and z[mid] <= z[l])):
+            return mid
+        elif ((z[mid] <= z[l] and z[l] <= z[r]) or 
+              (z[r] <= z[l] and z[l] <= z[mid])):
+            return l
+        else:
+            return r
+
+
+def swap(z: MemoryArray, i: int, j: int):
+    tmp = z[Literal(i)].value
+    z[Literal(i)] = z[Literal(j)]
+    z[Literal(j)].set(tmp)
+
+# toSort[] --> Array to be sorted,
+# left     --> Starting index,
+# right    --> Ending index
+# adapted from https://stackoverflow.com/questions/68524038/is-there-a-python-implementation-of-quicksort-without-recursion
+def quickSortIterative(toSort : MemoryArray, left : Literal, right : Literal, mode=0):
+    # Create a manually managed stack and avoid pythons recursion-limit
+    size = right.value - left.value + 1
+    stack : MemoryArray = MemoryArray([0] * size)
+    top : MemoryCell = MemoryCell(-1)
+
+    # push initial values of l and h to stack
+    top += Literal(1)
+    stack[top] = left
+    top += Literal(1)
+    stack[top] = right
+  
+    # Keep popping from stack until its empty
+    while top >= Literal(0):
+        logger.debug(f"size {size}, stack {stack}, right {right} and left {left}, top {top}") 
+
+        # Pop h and l - Ensure we are not getting them by Ref, this will produce weird "JUST A LITTLE OF" Results
+        right = Literal(stack[top].get())
+        top -= Literal(1)
+        left = Literal(stack[top].get())
+        top -= Literal(1)
+  
+        # Set pivot element at its correct position in sorted array
+        p = partitionIterative(toSort, left, right, mode)
+  
+        # If there are elements on left side of pivot, then push left side to stack
+        if p.pred() > left:
+            top += Literal(1)
+            stack[top] = left
+            top += Literal(1)
+            stack[top] = p.pred()
+  
+        # If there are elements on right side of pivot, then push right side to stack
+        if p.succ() < right:
+            top += Literal(1)
+            stack[top] = p.succ()
+            top += Literal(1)
+            stack[top] = right
+
+def partitionIterative(arr : MemoryArray, l : Literal, h : Literal, mode=0):
+    logger.debug(f"Partitioning {arr}, {l} and {h}")
+    pivot_idx : Literal = getPivot(arr, l, h, mode)
+
+    # If pivot isn't at the high end, swap it there
+    if pivot_idx != h:
+        swap(arr, int(pivot_idx), int(h))
+
+    # Carefull that we do not use a reference. I suppose python would return one here if we just assign without value>Literal cast.
+    # At least this helped fix weird issue
+    pivotValue : Literal = Literal(arr[h].value)
+    i : MemoryCell = MemoryCell(l.pred())
+  
+    for j in mrange(l, h):
+        if arr[j] <= pivotValue:
+            i += Literal(1)                 # increment index of smaller element
+            swap(arr, int(i), int(j))
+  
+    swap(arr, int(i.succ()), int(h))
+    return i.succ()
+
+def LEGACY_quickSort(z: MemoryArray, l: Literal = Literal(0), r: Literal = Literal(-1), mode=0):
+    if r == Literal(-1):
+        r = z.length().pred();
+    if l < r:
+        q = LEGACY_partition(z, l, r, mode)
+        LEGACY_quickSort(z, l, q.pred())
+        LEGACY_quickSort(z, q.succ(), r)
+
+def LEGACY_partition(z: MemoryArray, l: Literal, r: Literal, mode):
+    # Get pivot
+    pivot_idx = getPivot(z, l, r, mode)
+    
+    # If pivot is not already at the right end, swap it there
+    if pivot_idx != r:
+        swap(z, int(pivot_idx), int(r))
+
+    with MemoryCell(z[r]) as pivot, MemoryCell(l) as i, MemoryCell(r.pred()) as j:
+        while i < j:
+            while z[i] < pivot:
+                i.set(i.succ())
+            while j > l and z[j] >= pivot:
+                j.set(j.pred())
+            if i < j:
+                swap(z, int(i), int(j))
+                i.set(i.succ())
+                j.set(j.pred())
+        if i == j and z[i] < pivot:
+            i.set(i.succ())
+        if z[i] != pivot:
+            swap(z, int(i), int(r))
+        return Literal(i)
+
+
+def analyze_complexity(fn, sizes):
+    """
+    Analysiert die Komplexität einer maximalen Teilfolgenfunktion.
+
+    :param max_sequence_func: Die Funktion, die analysiert wird.
+    :param sizes: Eine Liste von Eingabegrößen für die Analyse.
+    """
+    for size in sizes:
+        MemoryManager.purge()  # Speicher zurücksetzen
+        random_array = MemoryArray.create_random_array(size, -100, 100)
+        fn(random_array, Literal(0), random_array.length().pred())
+        MemoryManager.save_stats(size)
+
+    MemoryManager.plot_stats(["cells", "adds", "compares", "reads", "writes"])
+
+
+if __name__ == '__main__':
+    # For debug, assert if working and complexity-analysis
+    example()
+
+    print("I ran into a MaxRecursionDepth Error. From what I read on the Internet python does not do Tailcall Optimizations")
+    print("Increasing recursion-limit seems like a poor Idea, therefore tried an iterative approach with manual stack-keeping")
+
+    toSort = MemoryArray.create_array_from_file("data/seq0.txt")
+    print(toSort)
+    quickSortIterative(toSort, Literal(0), toSort.length().pred())
+    print(toSort)
+
+    # analyze_complexity(quickSortIterative, [10, 20, 30, 40, 50, 60, 70, 80, 90, 100])
+    for filename in ["data/seq0.txt", "data/seq1.txt", "data/seq2.txt" ,"data/seq3.txt"]:
+    # for filename in [ "data/seq1.txt"]:
+        print(filename)
+        toSort = MemoryArray.create_array_from_file(filename)
+        timeMS(quickSortIterative, toSort, Literal(0), toSort.length().pred(), mode=1)
+        # print(toSort)
+
+    print("Kann durch die Modifikation eine besser Laufzeit als nlog(n) erreicht werden? Nein! nlog(n) ist das Minimum. Durch die Änderung kann aber der Worst-Case fall von n^2 für z.B. bereits vorsortierte Arrays oder Arrays mit vielen Duplikaten vermieden werden.")

schoeffelbe/priorityQueue.py

@@ -0,0 +1,158 @@
+from utils.memory_array import MemoryArray
+from utils.memory_cell import MemoryCell
+from utils.literal import Literal
+from utils.constants import MAX_VALUE
+from utils.memory_range import mrange
+
+# Impl of MemoryArray says we cant add our own Datatypes beside Literal and List
+# BUUUUT we can just wrap our Datatype in a List :-)
+# We store them in a MemoryArray internaly tho anyhow so we increment our Counters for the RAM
+class HeapEntry:
+    def __init__(self, item, priority=1):
+        self.data = MemoryArray(Literal(2))
+        # 0: Content, 1: Prio
+        self.data[Literal(0)] = Literal(item)
+        self.data[Literal(1)] = Literal(priority)
+    
+    def getItem(self):
+        return self.data[Literal(0)]
+    
+    def getPriority(self):
+        return self.data[Literal(1)]
+    
+    def setPriority(self, priority):
+        self.data[Literal(1)] = Literal(priority)
+    
+    def __lt__(self, other):
+        if other is None:
+            return True 
+        if isinstance(other, (int, float)):
+            return self.getPriority().value > other
+        return self.getPriority() > other.getPriority()
+    
+    def __gt__(self, other):
+        if other is None:
+            return False 
+        if isinstance(other, (int, float)):
+            return self.getPriority().value < other
+        return self.getPriority() < other.getPriority()
+    
+    def __eq__(self, other):
+        return self.getPriority() == other.getPriority()
+    
+    def __str__(self):
+        return f"({self.getItem()}, prio={self.getPriority()})"
+
+class PriorityQueue:
+    def __init__(self, max_size : Literal = Literal(100)):
+        self.heap = MemoryArray(max_size) 
+        # Add uninitialized HeapEntry Values so the Adds/Compares do not fail on emtpy stack. 
+        # Would have to switch to MIN_VALUE if we switch what is a "Higher" Prio
+        for i in mrange(max_size.value):
+            self.heap[i].set([HeapEntry(MAX_VALUE, MAX_VALUE)])
+        self.size = MemoryCell(0)
+    
+    def parent(self, i: Literal) -> Literal:
+        return MemoryCell(i.pred()) // Literal(2)
+    
+    def leftChild(self, i: Literal) -> Literal:
+        return MemoryCell(MemoryCell(2) * i) + Literal(1)
+    
+    def rightChild(self, i: Literal) -> Literal:
+        return MemoryCell(MemoryCell(2) * i) + Literal(2)
+    
+    # Swap the Lists -> Therefore get the value which is the List and then Set it again
+    def swap(self, i: Literal, j: Literal):
+        tmp_i = self.heap[i].value
+        tmp_j = self.heap[j].value
+        self.heap[i].set(tmp_j)
+        self.heap[j].set(tmp_i)
+    
+    def maxHeapify(self, i: Literal):
+        left = self.leftChild(i)
+        right = self.rightChild(i)
+        largest = i
+        
+        if left < Literal(self.size.value) and self.heap[left].value[0] > self.heap[largest].value[0]:
+            largest = left
+        
+        if right < Literal(self.size.value) and self.heap[right].value[0] > self.heap[largest].value[0]:
+            largest = right
+        
+        if largest != i:
+            self.swap(i, largest)
+            self.maxHeapify(largest)
+    
+    def insert(self, entry : HeapEntry):
+        if self.size >= self.heap.length():
+            raise IndexError("Heap full")
+        
+        i = self.size
+        self.heap[i].set([entry])
+        self.size += Literal(1)
+        
+        while i > Literal(0) and self.heap[self.parent(i)].value[0] < self.heap[i].value[0]:
+            self.swap(i, self.parent(i))
+            i = self.parent(i)
+    
+    def pop(self):
+        if self.isEmpty():
+            raise IndexError("Queue is empty!")
+        
+        max_item = self.heap[Literal(0)].value[0]
+        
+        self.heap[Literal(0)] = self.heap[self.size - Literal(1)]
+        self.size -= Literal(1)
+        
+        self.maxHeapify(Literal(0))
+        
+        return max_item
+    
+    def peek(self):
+        if self.isEmpty():
+            raise IndexError("Queue is empty")
+        return self.heap[Literal(0)].value[0]
+    
+    def isEmpty(self):
+        return self.size == Literal(0)
+    
+    def __len__(self):
+        return self.size
+
+
+if __name__ == '__main__':
+    # Proof of Concept
+    testEntry = HeapEntry("A", 2)
+    print(testEntry)
+    testArray = MemoryArray([testEntry])
+    print(testArray)
+    print(testArray[Literal(0)])
+
+    # Queue Testing
+    pq = PriorityQueue()
+    try:
+        pq.pop()
+        assert False, "Queue should be empty"
+    except IndexError:
+        pass  
+    assert(pq.isEmpty() and pq.size == Literal(0))
+    entry = HeapEntry("A", 1)
+    pq.insert(entry)
+    assert(not pq.isEmpty() and pq.size == Literal(1))
+    pq.peek()
+    assert(not pq.isEmpty())
+    assert(pq.pop() == HeapEntry("A", 1))
+    assert(pq.isEmpty())
+    pq.insert(HeapEntry("A", 1))
+    pq.insert(HeapEntry("C", 3))
+    pq.insert(HeapEntry("B", 2))
+    assert(pq.size == Literal(3))
+    assert(pq.pop() == HeapEntry("A", 1))
+    assert(pq.pop() == HeapEntry("B", 2))
+    assert(pq.pop() == HeapEntry("C", 3))
+    pq.insert(HeapEntry("A", 1))
+    pq.insert(HeapEntry("C", 3))
+    pq.insert(HeapEntry("B", 2))
+    print(pq.pop())
+    print(pq.pop())
+    print(pq.pop())