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Author: alexnaiman

Lab11/BacktrackingIterative.py

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+l = [0, "-", "+"]
+
+
+def backIter():
+    x = [0]  # candidate solution
+    while len(x) > 0:
+        choosed = False
+        while (not choosed) and l.index(x[-1]) < len(l) - 1:
+            x[-1] = l[l.index(x[-1]) + 1]  # increase the last component
+            choosed = consistent(x)
+        if choosed:
+            if solution(x):
+                solutionFound(x)
+            x.append(0)  # expand candidate solution
+        else:
+            x.pop()  # go back one component
+
+
+def consistent(s):
+    return len(s) < n
+
+
+def solution(s):
+    summ = list2[0]
+    if not len(s) == n - 1:
+        return False
+    for i in range(n - 1):
+        if s[i] == "-":
+            summ -= list2[i + 1]
+        else:
+            summ += list2[i + 1]
+    return summ > 0
+
+
+def solutionFound(s):
+    print(s)
+
+
+n = int(input("Give number"))
+list2 = []
+for i in range(n):
+    list2.append(int(input(str(i) + ":")))
+
+backIter()
+print("test")

Lab11/BacktrackingRecursive.py

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+l = ["+", "-"]
+
+
+def backRec(x):
+    for j in l:
+        x.append(j)
+        if consistent(x):
+            if solution(x):
+                solutionFound(x)
+            backRec(x)
+        x.pop()
+
+
+def consistent(s):
+    return len(s) < n
+
+
+def solution(s):
+    summ = list2[0]
+    if not len(s) == n - 1:
+        return False
+    for i in range(n - 1):
+        if s[i] == "-":
+            summ -= list2[i + 1]
+        else:
+            summ += list2[i + 1]
+    return summ > 0
+
+
+def solutionFound(s):
+    print(s)
+
+
+n = int(input("Give number"))
+list2 = []
+for i in range(n):
+    list2.append(int(input(str(i) + ":")))
+
+backRec([])

Lab11/README.md

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+# Requirements (the exact problem statement)
+You will be assigned with a problem from the list below and you are required to solve the problem
+using the BACKTRACKING programming method, using both an ITERATIVE and a RECURSIVE
+backtracking implementation
+
+##### The problem statement I chose
+Consider the natural number n (n<=10) and the natural numbers a1, ... , an. Determine all the
+possibilities to insert between all numbers a1, ..., an the operators + and – such that by evaluating the
+expression the result is positive

Laborator1/README.md

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+# About this assignment
+There were three sets of problems and we have to solve one from each one
+
+### Requirements (the exact problem statement)
+Select one problem statement from each set and solve it.
+* Each solution must have a console-based interface
+* Use procedural programming, make sure that each function only does one thing
+* Expected inputs as well as output must be clearly stated to the user

Laborator1/SetA/Problem1/problema1.py

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+# Generate the first prime number larger than a given natural number n.
+
+
+import math
+
+
+def isPrime(number):
+    '''
+    in: number - integer
+    out: True if number is prime
+    '''
+    if number == 1:
+        return False
+    elif number == 2:
+        return True
+    if number % 2 == 0:
+        return False
+    else:
+        for i in range(3, int(math.sqrt(number)) + 1, 2):
+            if number % i == 0:
+                return False
+    return True
+
+
+def readNaturalNotNullNumber():
+    '''
+    in: read a number and checks if it is an integer
+    out: it returns the writen number
+    '''
+    while True:
+        try:
+            auxNumber = int(input("Enter a natural number: "))
+            if auxNumber < 0:
+                print("The number is not bigger than 0")
+                continue
+            return auxNumber
+        except ValueError:
+            print("Oops! That was no valid number. Try again...")
+            continue
+
+
+def searchForNumber(myNumber):
+    '''
+    in: myNumber integer
+    out: returns the first prime number large than myNumber
+    '''
+
+    auxNumber = myNumber + 1
+    while not isPrime(auxNumber):
+        auxNumber += 1
+    return auxNumber
+
+
+number = readNaturalNotNullNumber()
+print(searchForNumber(number))

Laborator1/SetA/Problem2/Main.py

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+'''
+Given the natural number n, determine the prime numbers p1 and p2 such that n = p1 + p2
+(check the Goldbach hypothesis)
+'''
+
+import math
+
+
+def checkConditions(conditions, number):
+    for condition in conditions:
+        if not condition(number):
+            return False
+    return True
+
+
+def naturalNumber(number):
+    if number < 0:
+        print("The number is not bigger than 0")
+        return False
+    return True
+
+
+def evenNumber(number):
+    if number % 2 != 0:
+        print("The number is not even!")
+        return False
+    return True
+
+
+def readIntegerWithGivenConditions(conditionsToCheck):
+    '''
+    in:
+        read number and checks if it is a natural number
+    out:
+        returns the written number
+    '''
+    while True:
+        try:
+            auxNumber = int(input("Enter a natural (even) number: "))
+            if not checkConditions(conditionsToCheck, auxNumber):
+                continue
+            return auxNumber
+        except ValueError:
+            print("Ooops.... tht wast not a valid number. Try again...")
+            continue
+
+
+def isPrime(number):
+    '''
+    in:
+        number - integer
+    out:
+        boolean if number is prime or not
+    '''
+    if number == 1:
+        return False
+    elif number == 2:
+        return True
+    if number % 2 == 0:
+        return False
+    else:
+        for i in range(3, int(math.sqrt(number)) + 1, 2):
+            if number % i == 0:
+                return False
+    return True
+
+
+def searchForNumbersGoldbachNumbers(naturalNumber):
+    '''
+    in:
+       naturalNumber -  a natural even number
+    out:
+        returns the Goldbach numbers for the given number - natural numbers
+    '''
+    auxList = []
+    for i in range(2, naturalNumber // 2 + 1):
+        if isPrime(i) and isPrime(naturalNumber - i):
+            auxList.append([i, naturalNumber - i])
+    return auxList
+
+
+def run():
+    '''
+        main function of our program
+        it "runs" and "controls" the functions we need
+    '''
+    print("Goldbach's conjecture: \n Every even integer greater than 2 can be expressed as "
+          "the sum of two primes (there are some odd numbers that respect this conjecture too)")
+    n = readIntegerWithGivenConditions([naturalNumber, evenNumber])
+    listOfGoldBachNumbers = searchForNumbersGoldbachNumbers(n)
+    print("The Goldbach numbers are:\n " + str(listOfGoldBachNumbers))
+
+
+run()

Laborator1/SetA/Problem3/Main.py

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+'''
+For a given natural number n find the minimal natural number m formed with the same digits.
+E.g. n=3658, m=3568
+'''
+
+
+from functools import reduce
+
+
+def readNaturalNumber(message):
+    '''
+    in:
+        message - string -> the message shown before reading the number
+    out:
+        it returns a natural number read from the keyboard
+    '''
+
+    while True:
+        try:
+            auxNumber = int(input(message))
+            if auxNumber < 0:
+                print("The number should be positive!")
+                continue
+            return auxNumber
+        except ValueError:
+            print("Ooops... something went wrong... please try again!")
+            continue
+
+def getDigits(naturalNumber):
+    auxList = []
+    copy = naturalNumber
+    while copy:
+        auxList.append(copy%10)
+        copy//=10
+    return auxList
+
+
+def makeNumberFromDigits(list):
+    return reduce(lambda x,y: x*10+y,list)
+
+
+def makeMinimalNumberFromDigits(list):
+    list.sort()
+    return makeNumberFromDigits(list)
+
+
+def run():
+    n = readNaturalNumber("The given number is?\n")
+    print("The minimal number is: " + str(makeMinimalNumberFromDigits(getDigits((n)))))
+
+run()

Laborator1/SetB/Problem10/Main.py

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+'''
+Consider a given natural number n. Determine the product p of all the proper factors of n
+'''
+
+import math
+from functools import reduce
+
+
+def readNaturalNumber(message):
+    '''
+    in:
+        message - string -> the message shown before reading the number
+    out:
+        it returns a natural number read from the keyboard
+    '''
+
+    while True:
+        try:
+            auxNumber = int(input(message))
+            if auxNumber < 0:
+                print("The number should be positive!")
+                continue
+            if isPrime(auxNumber):
+                print("The number is prime!")
+                continue
+            return auxNumber
+        except ValueError:
+            print("Ooops... something went wrong... please try again!")
+            continue
+
+
+def getProperFactors(naturalNumber):
+    auxList = []
+    for i in range(2, naturalNumber // 2 + 1):
+        if naturalNumber % i == 0:
+            auxList.append(i)
+    return auxList
+
+
+def isPrime(number):
+    '''
+    in:
+        number - integer
+    out:
+        boolean if number is prime or not
+    '''
+    if number == 1:
+        return False
+    elif number == 2:
+        return True
+    if number % 2 == 0:
+        return False
+    else:
+        for i in range(3, int(math.sqrt(number)) + 1, 2):
+            if number % i == 0:
+                return False
+    return True
+
+
+def listToProduct(list):
+    return reduce(lambda x, y: x * y, list)
+
+
+def run():
+    '''
+        main function of our program
+        it "runs" and "controls" the functions we need
+    '''
+    n = readNaturalNumber("The number is?\n")
+
+    print("The product of the number's factors is: " + str(listToProduct(getProperFactors(n))))
+
+
+run()