EvilZone

Well tell you what you should really read about the numbers before coding it out. Bruteforcing isn't a good practice. You should carefully observe the stuff.

I will give you a simple hint with which you can improve your code.

Lets examine the Fibo series :-

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, .....


Do you observe something ?

What we observe is that every third number is even.

Well that's your hint for now.

Ah, I get it.
For loop incrementing the fib sequence by 3 at a time, adding to the tally/total avoiding the need to verify whether it is even or not.
I posted this before receiving your feedback in the first project euler question. I'll look back into it all for a while before doing any more as I clearly have more to learn before I can benefit fully from the exercises.

Looks good, yes. Did it work?

Yep, thanks for the pointer.

Think Logically and a bit mathematically as well.

How many multiple of 3 are present within 1000 --> int(999 / 3) = 333 i.e {3, 6, ... 15, ... 30, ... 999) 
How many multiple of 5 are present within 1000 --> int(995 / 5) = 199 i.e. {5, 10, ... 15... 25, 30, ... 995}

Now subtract the number of common multiples that is 15. So, how many multiples of 15 are present ? ---> 66.

Now all of these are in A.P series. So what you can do is calculate the sum of these AP series and get the result.

The Formula for Sum of A.P. Series (3 variations are there but I will use a only one)

Sum_N_Terms = N * (A + L) / 2

where N = No of terms, A = First Term, L = Last term

Therefore the complete workout would be :-

{333 * (3 + 999) / 2} + {199 * (5 + 995) / 2} - {66  * (15 + 990) / 2} = 233168

Pretty Easy

Now how is it an improvisation ?

The Bruteforce way would be to loop from 1 - 999 and check for multiplicity of 3 and 5 and then add. So the loop run for 999 times. But in the second case its just -> 333 + 199 + 66 = 598

So 401 loop cycles are saved.

Before solving any Project Euler problem always try to keep a mathematical mind and it will help a lot


EDIT:-

Python Code. (Here we use python builtin sum function)

Code: [Select]

sum(i for i in range(3, 1000, 3)) + sum(i for i in range(5, 996, 5)) - sum(i for i in range(15, 991, 15))


Will keep that in mind for future, thank you very much.

Just calculate all multiples below 1000 instead of checking all numbers if they are multiples.

Thank you very much for the feedback, do you mean like this?



def ProblemOne():

i = 0
tally = 0
increments = 0

for i in range(0,1000,3):
if i % 5 != 0:
tally += i

for i in range(0,1000,5):
tally += i;

print "My first answer is: %d" % tally




def main():
ProblemOne()


if __name__ == '__main__':
main()


I used the two loops to ensure it doesn't add some numbers twice (such as 15) without needing to use any more memory.

I have changed my Tic Tac Toe to include the computer playing against you:



#String for X wins
xWin = "\t _______\n\t/       \\\n\t|VICTORY|\n\t|  FOR  |\n\t|PLAYER |\n\t|   O   |\n\t\\_______/"


#String for Y wins
yWin = "\t _______\n\t/       \\\n\t|VICTORY|\n\t|  FOR  |\n\t|PLAYER |\n\t|   Y   |\n\t\\_______/"


#String for draw
draw = "\t _______\n\t/       \\\n\t|  DRAW |\n\t\\_______/"


#Create Empty Board
matrice = [[ '-' for i in range(3) ] for j in range(3)]


#Check if bot can win from a row
def BotWinRow():
    for i in range(3):
        if matrice[0][i] == matrice[1][i]:
            if matrice[0][i] == 'X' and matrice[2][i] == '-':
                matrice[2][i] = 'X'
                return False
        if matrice[0][i] == matrice[2][i]:
            if matrice[0][i] == 'X' and matrice[1][i] == '-':
                matrice[1][i] = 'X'
                return False
        if matrice[1][i] == matrice[2][i]:
            if matrice[1][i] == 'X' and matrice[o][i] == '-':
                matrice[0][i] = 'X'
                return False
    return True
           
#Check if bot can win from a collumn
def BotWinColumn():
    for i in range(3):
        if matrice[i][0] == matrice[i][1]:
            if matrice[i][0] == 'X' and matrice[i][2] == '-':
                matrice[i][2] = 'X'
                return False
        if matrice[i][0] == matrice[i][2]:
            if matrice[i][0] == 'X' and matrice[i][1] == '-':
                matrice[i][1] = 'X'
                return False
        if matrice[i][1] == matrice[i][2]:
            if matrice[i][1] == 'X' and matrice[i][0] == '-':
                matrice[i][0] = 'X'
                return False
    return True


#Check if bot can win from a diagonal
def BotWinDiagonal():


    #Top Left to Bottom Right
    if matrice[0][0] == matrice[1][1]:
        if matrice[0][0] == 'X' and matrice[2][2] == '-':
            matrice[2][2] = 'X'
            return False
    if matrice[0][0] == matrice[2][2]:
        if matrice[0][0] == 'X' and matrice[1][1] == '-':
            matrice[1][1] = 'X'
            return False
    if matrice[1][1] == matrice[2][2]:
        if matrice[1][1] == 'X' and matrice[0][0] == '-':
            matrice[0][0] = 'X'
            return False


    #Top Right to Bottom Left
    if matrice[2][0] == matrice[1][1]:
        if matrice[2][0] == 'X' and matrice[0][2] == '-':
            matrice[0][2] = 'X'
            return False
    if matrice[2][0] == matrice[0][2]:
        if matrice[2][0] == 'X' and matrice[1][1] == '-':
            matrice[1][1] = 'X'
            return False
    if matrice[1][1] == matrice[0][2]:
        if matrice[1][1] == 'X' and matrice[2][0] == '-':
            matrice[2][0] = 'X'
            return False


    return True




#Check if opponent can win from a row
def OpponentWinRow():
    for i in range(3):
        if matrice[0][i] == matrice[1][i]:
            if matrice[0][i] == 'O' and matrice[2][i] == '-':
                matrice[2][i] = 'X'
                return False
        if matrice[0][i] == matrice[2][i]:
            if matrice[0][i] == 'O' and matrice[1][i] == '-':
                matrice[1][i] = 'X'
                return False
        if matrice[1][i] == matrice[2][i]:
            if matrice[1][i] == 'O' and matrice[0][i] == '-':
                matrice[0][i] = 'X'
                return False
    return True




#Check if opponents can win from a collumn
def OpponentWinColumn():
    for i in range(3):
        if matrice[i][0] == matrice[i][1]:
            if matrice[i][0] == 'O' and matrice[i][2] == '-':
                matrice[i][2] = 'X'
                return False
        if matrice[i][0] == matrice[i][2]:
            if matrice[i][0] == 'O' and matrice[i][1] == '-':
                matrice[i][1] = 'X'
                return False
        if matrice[i][1] == matrice[i][2]:
            if matrice[i][1] == 'O' and matrice[i][0] == '-':
                matrice[i][0] = 'X'
                return False
    return True




#Check if opponents can win from a Diagonal
def OpponentWinDiagonal():


    #Top Left to Bottom Right
    if matrice[0][0] == matrice[1][1]:
        if matrice[0][0] == 'O' and matrice[2][2] == 'O':
            matrice[2][2] = 'X'
            return False
    if matrice[0][0] == matrice[2][2]:
        if matrice[0][0] == 'O' and matrice[1][1] == 'O':
            matrice[1][1] = 'X'
            return False
    if matrice[1][1] == matrice[2][2]:
        if matrice[1][1] == 'O' and matrice[0][0] == 'O':
            matrice[0][0] = 'X'
            return False


    #Top Right to Bottom Left
    if matrice[2][0] == matrice[1][1]:
        if matrice[2][0] == 'O' and matrice[0][2] == 'O':
            matrice[0][2] = 'X'
            return False
    if matrice[2][0] == matrice[0][2]:
        if matrice[2][0] == 'O' and matrice[1][1] == 'O':
            matrice[1][1] = 'X'
            return False
    if matrice[1][1] == matrice[0][2]:
        if matrice[1][1] == 'O' and matrice[2][0] == 'O':
            matrice[2][0] = 'X'
            return False
       
    return True


#Defence against human tactic
def TacticalDefense():
    #Top Left
    if matrice[0][0] == 'O' and matrice[2][2] == '-':
        matrice[2][2] = 'X'
        return False


    #Top Right
    if matrice[2][0] == 'O' and matrice[0][2] == '-':
        matrice[0][2] = 'X'
        return False


    #Bottom Right
    if matrice[2][2] == 'O' and matrice[0][0] == '-':
        matrice[0][0] = 'X'
        return False


    #Bottom Left
    if matrice[0][2] == 'O' and matrice[2][0] == '-':
        matrice[2][0] = 'X'
        return False


    return True




#Select next move
def OtherNextMove():


    #Middle
    if matrice[1][1] == '-':
        matrice[1][1] = 'X'
        return False


    #Top Left
    if matrice[0][0] == '-':
        matrice[0][0] = 'X'
        return False


    #Top Right
    if matrice[2][0] == '-':
        matrice[2][0] = 'X'
        return False


    #Bottom Right
    if matrice[2][2] == '-':
        matrice[2][2] = 'X'
        return False


    #Bottom Left
    if matrice[0][2] == '-':
        matrice[0][2] = 'X'
        return False
   
    #Up
    if matrice[1][0] == '-':
        matrice[1][0] = 'X'
        return False
   
    #Right
    if matrice[2][1] == '-':
        matrice[2][1] = 'X'
        return False


    #Down
    if matrice[1][2] == '-':
        matrice[1][2] = 'X'
        return False


    #Left
    if matrice[0][1] == '-':
        matrice[0][1] = 'X'
        return False


    return True


   
#Bot takes a turn
def BotShot():
    MyTurn = True
    if MyTurn:
        MyTurn = BotWinRow()
    if MyTurn:
        MyTurn = BotWinColumn()
    if MyTurn:
        MyTurn = BotWinDiagonal()
    if MyTurn:
        MyTurn = OpponentWinRow()
    if MyTurn:
        MyTurn = OpponentWinColumn()
    if MyTurn:
        MyTurn = OpponentWinDiagonal()
    if MyTurn:
        MyTurn = TacticalDefense()
    if MyTurn:
        MyTurn = OtherNextMove()
    if MyTurn:
        print "I dont know"
    print "Your turn."


#Print Matrice
def printMatrix():
    print "\n\n"
    for i in range(3):
        print " | ",
        for j in range(3):
            print matrice[i][j],
            print " | ",
        print "\n",
    print"\n\n"
   
#Take player one's turn
def TakeTurn():
    printMatrix()
    x = int(input("Enter X co-ordinate: ")) - 1
    y = int(input("Enter Y co-ordinate: ")) - 1
    if matrice[y][x] == '-':
        matrice[y][x] = 'O'
    else:
        print "Please choose another square\n\n"
        playerOneTurn()


#Test if Game Has Come to End
def gameStatus():
    over = '='
    for i in range(3):
        for j in range(3):
            if matrice[i][j] == '-':
                over = '-'
                break
    for i in range(3):
        if matrice[0][i] == matrice[1][i] == matrice[2][i]:
            victory(matrice[1][i])
        if matrice[i][0] == matrice[i][1] == matrice[i][2]:
            victory(matrice[i][1])
    if matrice[0][0] == matrice[1][1] == matrice[2][2]:
        victory(matrice[1][1])
    if matrice[2][0] == matrice[1][1] == matrice[0][2]:
        victory(matrice[1][1])
    if over == '=':
        victory(over)


#Victory Print
def victory(c):
    if c == 'O':
        print yWin
        printMatrix()
        raise SystemExit
    if c == 'X':
        print xWin
        printMatrix()
        raise SystemExit
    if c == '=':
        print draw
        printMatrix()
        raise SystemExit
   


#main logic
def main():
    while True:
        TakeTurn()
        gameStatus()
        BotShot()
        gameStatus()


#Set to run main
if __name__ == "__main__":
    main()




I have updated it to protect against the wrong number being entered and changed the two player turn methods into takeTurn. I haven't done anything about the victory method yet. 


#Create Empty Board
matrice = [[ '-' for i in range(3) ] for j in range(3)]


#Print Matrice
def printMatrix():
    print "\n\n"
    for i in range(3):
        print " | ",
        for j in range(3):
            print matrice[i][j],
            print " | ",
        print "\n",
    print"\n\n"
   
#Take player one's turn
def takeTurn(c):
    printMatrix()
    print "Player " ,c
    x = int(input("Enter X co-ordinate: "))
    y = int(input("Enter Y co-ordinate: "))
    if y > 3 or y < 1 or x > 3 or x < 1:
        print "Please choose another square\n\n"
        takeTurn(c)
    x -= 1
    y -= 1
    if matrice[y][x] == '-':
        matrice[y][x] = c
    else:
        print "Please choose another square\n\n"
        takeTurn(c)


#Test if Game Has Come to End
def gameStatus():
    over = '='
    for i in range(3):
        for j in range(3):
            if matrice[i][j] == '-':
                over = '-'
                break
    for i in range(3):
        if matrice[0][i] == matrice[1][i] == matrice[2][i]:
            victory(matrice[1][i])
        if matrice[i][0] == matrice[i][1] == matrice[i][2]:
            victory(matrice[i][1])
    if matrice[0][0] == matrice[1][1] == matrice[2][2]:
        victory(matrice[1][1])
    if matrice[2][0] == matrice[1][1] == matrice[0][2]:
        victory(matrice[1][1])
    if over == '=':
        victory(over)


#Victory Print
def victory(c):
    if c == 'X':
        print "\t _______"
        print "\t/       \\"
        print "\t|VICTORY|"
        print "\t|  FOR  |"
        print "\t|PLAYER |"
        print "\t|  ONE  |"
        print "\t\\_______/"
        printMatrix()
        raise SystemExit
    if c == 'Y':
        print "\t _______"
        print "\t/       \\"
        print "\t|VICTORY|"
        print "\t|  FOR  |"
        print "\t|PLAYER |"
        print "\t|  TWO  |"
        print "\t\\_______/"
        printMatrix()
        raise SystemExit
    if c == '=':
        print "\t _______"
        print "\t/       \\"
        print "\t|  DRAW |"
        print "\t\\_______/"
        printMatrix()
        raise SystemExit
   
#main logic
def main():
    while True:
        takeTurn('X')
        gameStatus()
        takeTurn('O')
        gameStatus()


#Set to run main
if __name__ == "__main__":
    main()


Thank you very much for the feedback.