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Given the following problem:
You are given an integer array nums. You are initially positioned at the array's first index, and each element in the array represents your maximum jump length at that position.
Return true if you can reach the last index, or false otherwise.
Example 1:
Input: nums = [2,3,1,1,4]
Output: True
Explanation: Jump 1 step from index 0 to 1, then 3 steps to the last index.
Example 2:
Input: nums = [3,2,1,0,4]
Output: False
Explanation: You will always arrive at index 3 no matter what. Its maximum jump length is 0, which makes it impossible to reach the last index.
I am trying to come up with a recursive solution. This is what I have so far. I am not looking for the optimal solution. I am just trying to solve using recursion for now. If n[i] is 0 I want the loop to go back to the previous loop and continue recursing, but I can't figure out how to do it.
def jumpGame(self, n: []) -> bool:
if len(n) < 2:
return True
for i in range(len(n)):
for j in range(1, n[i]+1):
next = i + j
return self.jumpGame(n[next:])
return False
If you want to do recursively and you said no need to be optimal ( so not memoized ), you could go with the below method. You don't need nested loops.
Also no need to explore all paths, you could optimize by looking at the step that you are going by checking i + (jump) < n
def jumpGame(a, i):
if i > len(a) - 1:
return False
if i == len(a) - 1:
return True
reached = False
for j in range(1, a[i] + 1):
if i + j < len(a):
reached = jumpGame(a, i + j)
if reached:
return True
return reached
print(jumpGame([2, 3, 1, 1, 4], 0))
print(jumpGame([3,2,1,0,4], 0))
True
False
When considering recursive solutions, the first thing you should consider is the 'base case', followed by the 'recursive case'. The base case is just 'what is the smallest form of this problem for which I can determine an answer', and the recursive is 'can I get from some form n of this problem to some form n - 1'.
That's a bit pedantic, but lets apply it to your situation. What is the base case? That case is if you have a list of length 1. If you have a list of length 0, there is no last index and you can return false. That would simply be:
if len(ls) == 0:
return False
if len(ls) == 1:
return True
Since we don't care what is in the last index, only at arriving at the last index, we know these if statements handle our base case.
Now for the recursive step. Assuming you have a list of length n, we must consider how to reduce the size of the problem. This is by making a 'jump', and we know that we can make a jump equal to a length up to the value of the current index. Then we just need to test each of these lengths. If any of them return True, we succeed.
any(jump_game(n[jump:] for jump in range(1, n[0] + 1)))
There are two mechanisms we are using here to make this easy. any takes in a sequence and quits as soon as one value is True, returning True. If none of them are true, it will return False. The second is a list slice, n[jump:] which takes a slice of a list from the index jump to the end. This might result in an empty list.
Putting this together we get:
def jump_game(n: list) -> bool:
# Base cases
if len(n) == 0:
return False
if len(n) == 1:
return True
# Recursive case
return any(jump_game(n[jump:]) for jump in range(1, n[0] + 1))
The results:
>>> jump_game([2,3,1,1,4])
True
>>> jump_game([3,2,1,0,1])
False
>>> jump_game([])
False
>>> jump_game([1])
True
I'm trying to lay out the rigorous approach here, because I think it helps to clarify where recursion goes wrong. In your recursive case you do need to iterate through your options - but that is only one loop, not the two you have. In your solution, in each recursion, you're iterating (for i in range(len(n))) through the entire list. So, you're really hiding an iterative solution inside a recursive one. Further, your base case is wrong, because a list of length 0 is considered a valid solution - but in fact, only a list of length 1 should return a True result.
What you should focus on for recursion is, again, solving the smallest possible form(s) of the problem. Here, it is if the list is one or zero length long. Then, you need to step each other possible size of the problem (length of the list) to a base case. We know we can do that by examining the first element, and choosing to jump anywhere up to that value. This gives us our options. We try each in turn until a solution is found - or until the space is exhausted and we can confidently say there is no solution.
I am trying to build a function that will take a number and return a list. If the number is even, the second integer of the list will be the number divided by two. If it is odd, then following number will be number multiplied by 3 plus one and so on until it reaches 1.
For example:
Function(5) will give
[5, 16, 8, 4, 2, 1]
My code is:
def Collatz(n):
out=[]
while n>1:
if n%2==0:
out.append(n/2)
elif n%2!=0:
out.append((n*3)+1)
print(out)
Collatz(20)
It doesn't produce anything. Any suggestion? I want to do this with while loop.
This code is close to be working, a few insights and improvements:
Change n inside the while loop (otherwise n remains larger than 1 and you get infinity loop)
Use lower case in function names and use underscore to separate between words
def collatz(n):
out = [n]
while n > 1:
if n % 2 == 0:
n = int(n / 2)
elif n % 2 != 0:
n = (n * 3) + 1
out.append(n)
print(out)
# [5, 16, 8, 4, 2, 1]
collatz(5)
It is because the while loop never terminates, this is because you aren't actually changing the value of n each time. So before you append to the array say something like n=n/2 (or whatever the calculation is) then append n. This means that n will eventually reach one and you get a print out
The problem with your code is you are not decrementing the value of n which is leading to an infinite loop.
Every time when you are appending a new value in the list you also need to update the value for n.
Try this:
def Collatz(n):
out=[]
while n>1:
if n%2==0:
out.append(n//2)
#updating n
n= n//2
elif n%2!=0:
out.append((n*3)+1)
#updating n
n= (n*3)+1
print(out)
Collatz(20)
Output:
[10, 5, 16, 8, 4, 2, 1]
Try this:
def Collatz(n):
l=[n]
while l[-1]!=1:
x=l[-1]/2 if l[-1]%2==0 else l[-1]*3+1
l.append(int(x))
return l
Here's a version that works.
def Collatz(n):
out=[n]
while n>1:
if n%2==0:
n = n/2
else:
n = (n*3)+1
out.append(int(n))
return out
print(Collatz(5))
Some notes on your version:
Your loop never updates "n" so n stays at its initial value forever, leaving you in an infinite loop.
The "elif" can be simply "else" - if the value is not even, then it's odd (assuming we're working with integers)
If you want the initial value to be in the list, we should probably initialize the list that way.
In your problem statement, you say you need the function to "return a list". Printing from inside the function is fine if that's really all you need, but if we actually return the list with a return statement, then the list it generates can be used by other code.
If you're using Python 3, the operation n/2 will return a float, even if n was an integer to start. If we only want integers in our list, we need to do one of two things:
Make it explicitly integer division with n//2
Or re-cast n to an integer with int(n) before we insert it into the list. (Which is how I did it here.)
Notice that your code doesn't change n.Therefore your loop never terminates. Check this out:
def collatz(n):
my_list = [n]
while n > 1:
if n % 2:
n = n * 3 + 1
else:
n = n / 2
my_list.append(n)
return(my_list)
Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.
My solution:
def findDuplicate(nums):
slow = fast = finder = 0
while fast is not None:
slow = nums[slow]
fast = nums[nums[fast]]
if fast is slow:
return slow
return False
nums = [1,2,2,3,4]
print findDuplicate(nums)
My above solution works and gives me o/p 2 but it doesn't work for every input for example it doesn't work for [11,15,17,17,14] or [3,1,2,6,2,3] and gives me error IndexError: list index out of range. I am not able to find patterns and am not able to track down the exact problem. Also tried to change my while condition:
while fast is not None and nums[nums[fast]] is not None:
your help will be greatly appreciated! Thank you.
Since the numbers are between 1 and n and you have been told there is only one duplicate, you can use difference between the sum of the numbers in the array and the sum of numbers from 1 to n to get the duplicate.
def findDuplicate(l):
n = len(l) - 1 # Get n as length of list - 1
return sum(l) - (n * (n + 1) / 2) # n*(n+1)/2 is the sum of integers from 1 to n
So the duplicate is the sum of the list - n*(n+1)/2
Of course, this doesn't generalize to finding duplicates for any list. For that case, you need to use #Jalepeno112 's answer.
The fact that the first one works is a fluke. Let's look at what it does on the first pass.
nums = [1,2,2,3,4]
# slow starts as index 0. So now, you've reassigned slow to be nums[0] which is 1.
# so slow equals 1
slow = nums[slow]
# now you are saying that fast equals nums[nums[0]].
# nums[0] is 1. nums[1] is 2
# so fast = 2
fast = nums[nums[fast]]
On the next pass, slow will be nums[1] which is 2. fast will be nums[nums[2]] which is nums[2] which is 2. At this point slow and fast are equal.
In your second example, you are getting an IndexError because of fast = nums[nums[fast]] If the value at nums[fast] is not a valid index, then this code will fail. Specifically in the second example, nums[0] is 11. nums doesn't have an element at index 11, so you get an error.
What you really want to be doing is performing a nested for loop on the array:
# range(0,len(nums)-1) will give a list of numbers from [0, to the length of nums-1)
# range(1, len(nums)) does the same,
# except it will start at 1 more than i is currently at (the next element in the array).
# So it's range is recomputed on each outer loop to be [i+1, length of nums)
for i in range(0,len(nums)-1):
for j in range(i+1,len(nums)):
# if we find a matching element, return it
if nums[i] == nums[j]:
return nums[i]
# if we don't find anything return False
return False
There are likely other more Pythonic ways to achieve this, but that wasn't your original question.
first you must ensure all numbers in list satisfy your constrains.
to find duplicated numbers in a list Use Counter in collections it will return each number and number of occurrence example :
>>> from collections import Counter
>>> l=Counter([11,15,17,17,14])
>>> l
Counter({17: 2, 11: 1, 14: 1, 15: 1})
to get the most common one use :
>>> l.most_common(n=1)
[(17, 2)]
where n is the number most common numbers you want to get
def duplicates(num_list):
if type(num_list) is not list:
print('No list provided')
return
if len(num_list) is 0 or len(num_list) is 1:
print('No duplicates')
return
for index,numA in enumerate(num_list):
num_len = len(num_list)
for indexB in range(index+1, num_len):
if numA == num_list[indexB]:
print('Duplicate Number:'+str(numA))
return
duplicates([11,15,17,17,14])
duplicates([3,1,2,6,2,3])
duplicates([])
duplicates([5])
l=[]
n= int(input("the number of digit is :"))
l=[0 for k in range(n)]
for j in range(0,n):
l[j]=int(input("the component is"))
print(l)
b=0; c=0
for i in range(n):
if l[i]== l[n-1-i]:
b=1;c=i
if b==1:
print("duplicate found! it is",l[c])
elif b==0:
print("no duplicate")
The answer is unfinished. It tries to convert the array to a linked list. So far it found where the slow pointer and fast pointer met, but this is the halfway solution. To get the solution, we need to initialize another pointer from the beginning of the linked list and walk towards each other. When they meet, that point is the where cycle is detected, in our question it is where the single point is:
class Solution:
def findDuplicate(self, nums: List[int]) -> int:
slow,fast=0,0
while True:
slow=nums[slow]
fast=nums[nums[fast]]
if slow==fast:
break
slow2=0
while True:
slow2=nums[slow2]
slow=nums[slow]
if slow==slow2:
return slow2
I'm having a very odd problem. I wrote a method that determines the degree of a formula describing a set of numbers, when given the said set. The method is fairly simple, I've added in a couple of lines for debugging purposes:
def getdeg(numlist, cnt): #get the degree of the equation describing numlist
count = cnt #initial run should be with cnt as 0
templist = []
for i in range(len(numlist) - 1): #exclude the last item (which doesn't have an item after it)
templist.append(numlist[i+1] - numlist[i]) #append the val of index i+1 minus index i
count += 1
print(templist)
if not allEqual(templist):
print("Not all equal, iterating again")
getdeg(templist, count)
else:
print(count)
return count
def allEqual(numlist):
if len(numlist) == 1:
return True
for i in range(len(numlist) -1):
if not (numlist[i] == numlist[i+1]):
return False
return True
Now, I'm running this on a set of numbers I KNOW to be described by a 3rd-degree equation, like so:
x = getdeg([2, 8, 9, 11, 20], 0)
print(x)
Fairly simple, yes? Except when you run this, it prints out the following:
[6, 1, 2, 9]
Not all equal, iterating again
[-5, 1, 7]
Not all equal, iterating again
[6, 6]
3
None
Everything is looking good, right up until that "None." What is it doing there? I would assume that the else conditional isn't being executed, but it's printing out 3 just fine, so it obviously is. That also means that the program "knows" what the value of count is, but it's not returning it right. Could someone enlighten me as to what on earth is going on?
if not allEqual(templist):
print("Not all equal, iterating again")
getdeg(templist, count)
Remember, when a method recursively calls itself, you still need to explicitly return the value if you want a value to be returned.
if not allEqual(templist):
print("Not all equal, iterating again")
return getdeg(templist, count)
You need to return a value in the if clause as well.
return getdeg(templist, count)
I'm trying to do a lab work from the textbook Zelle Python Programming
The question asked me to "write and test a recursive function max() to find the largest number in a list. The max is the larger of the first item and the max of all the other items." I don't quite understand the question from the textbook.
def Max(list):
if len(list) <= 1:
else:
return list[0]
else:
m = Max(list[1:])
return m if m > list[0] else list[0]
def main():
list = eval(raw_input(" please enter a list of numbers: "))
print("the largest number is: ", Max(list))
main()
Or maybe I'm suppose to open a txt file with numbers in it and then use recursive?
I believe recursive works like this
def function()
> if something:
>>return 0
>else:
>>return function()
Your understanding of how recursion works seems fine.
Your if-block is messed up, you have two elses to one if and the alignment is out. You need to remove your first else and un-indent everything below the if one level. eg:
def Max(list):
if len(list) == 1:
return list[0]
else:
m = Max(list[1:])
return m if m > list[0] else list[0]
def main():
list = eval(raw_input(" please enter a list of numbers: "))
print("the largest number is: ", Max(list))
main()
I post a different solution approach of the problem. Most of the answers manipulate the list using the slice operator in each recursive call. By the time the exercise does not provide a strict function prototype to be used, I also pass as function parameter the length of the list.
Suppose that we try to find and return the maximum element from a sequence S, of n elements.
Function prototype: Max(S, n)
Base case: If S contains only one item, return it. (Obviously the only item in the sequence is the max one.)
Recur: If not the base case, call Max each time for one less item, that is call Max(S, n-1). We then store the returning value to a variable called previous that indicate the previous element from the sequence and check that value with the next element in the sequence, which is the right most element in the current recursive call, and return the max of these values.
A recursion trace of the above procedure is given in the following figure. Suppose we try to find the max from a list that contains [5, 10, 20, 11, 3].
Note: To help you further, keep in mind that we recursively iterate the list from the right most element to the left most one.
Finally here is the working code:
def find_max_recursively(S, n):
"""Find the maximum element in a sequence S, of n elements."""
if n == 1: # reached the left most item
return S[n-1]
else:
previous = find_max_recursively(S, n-1)
current = S[n-1]
if previous > current:
return previous
else:
return current
if __name__ == '__main__':
print(find_max_recursively([5, 10, 20, 11, 3], 5))
Note: The recursive implementation will work by default only with sequences of 1000 most elements.
To combat against infinite recursions, the designers of Python made an
intentional decision to limit the overall number of function
activations that can be simultaneously active. The precise value of
this limit depends upon the Python distribution, but a typical default
value is 1000. If this limit is reached, the Python interpreter
raises a RuntimeError with a message, maximum recursion depth exceeded.
Michael T. Goodrich (2013), Data Structures and Algorithms in Python, Wiley
To change the default value do:
import sys
sys.setrecursionlimit(1000000)
here is one more approach to solve above problem
def maximum(L):
if len(L) == 1:
return L[0]
else:
return max(L[0],maximum(L[1:]))
so example input and output:
L= [2,4,6,23,1,46]
print maximum(L)
produces
46
The basic approach is this.
If the list contains only a single element, that element is the max. Return it immediately.
Otherwise, the list contains multiple elements. Either the first element in the list is the maximum, or it is not.
The maximum of the first element is simply the first element in the list.
Recursively call Max on the rest (all but first element) to find the maximum of those elements.
Compare the results from step 3 and 4. The result is the number that is greater. Return it.
Right now you have some syntax errors. For example, you have two else clauses for a single if, and the indentation looks funny. You can only have one else for an if block. But if you follow these instructions, you should have a working algorithm.
def Max(lis,maxx=-float("inf")):
if len(lis) == 1: #only one element in lis
return maxx if maxx>lis[0] else lis[0] #return lis[0] if it's greater than maxx
else:
m=lis[0] if lis[0]>maxx else maxx # m = max(lis[0],maxx)
return Max(lis[1:],m) #call Max with lis[1:] and pass 'm' too
print Max([1,2,39,4,5,6,7,8]) #prints 39
print Max([1,2,3,4,5,6,7,8]) #prints 8
These solutions fail after certain list size.
This is a better version:
def maximum2(a, n):
if n == 1:
return a[0]
x = maximum2(a[n//2:], n - n//2)
return x if x > a[0] else a[0]
def maximum(a):
return maximum2(a, len(a))
maximum(range(99999))
>>> 99998
One simple way would be to sort the list first then use indexing.
Here's a function that would work:
a = [1,233,12,34]
def find_max(a):
return sorted(a)[-1]
def find_max(my_list, max):
if len(my_list) <= 1:
return max
else:
if my_list[0] > max:
return find_max(my_list[1:], my_list[0])
else:
return find_max(my_list[1:], max)
if __name__ == '__main__':
my_list = [1, 5, 16, 9, 20, 40, 5]
print(find_max(my_list, my_list[0]))
def find_max(arr):
"""find maximum number in array by recursion"""
if arr == []: # if its an empty array
return 0
if len(arr) == 1: # if array has only one element
return arr[0]
else: # get max of first item compared to other items recursively
return max(arr[0], find_max(arr[1:])) # 1: means all other excluding 0th element
def main():
print(find_max([2,3,5,6,7,1])) # will print max - 7
if __name__ == "__main__":
main()
You can also do it in this way:
def maximum(data, start, stop):
if start >= stop:
return data[start]
else:
if data[start] >= data[stop - 1]:
return maximum(data, start, stop - 1)
else:
return maximum(data, start + 1, stop)
def recursiveMax(a):
if len(a) == 1:
return a[0]
else:
return a[0] if a[0] > recursiveMax(a[1:]) else recursiveMax(a[1:])
Test:
print(recursiveMax([1, 2, 15, 6, 3, 2, 9]))
print(recursiveMax([98, 2, 1, 1, 1, 1, ]))
TLDR; This code will also work when the list passed to the function is empty!
#jam's answer is amazing. However, I found some problems with the conditions, I think #Blender was hinting at it.
That code will fail in the case when the list passed to the function is empty. There are two base cases:
When the list is empty -> return None
When the list has one item -> return list[0]
And then the recursive case ... to reduce any other case into the base case.
def recursive_max(arr):
if len(arr) == 0:
return None
elif len(arr) == 1:
return arr[0]
else:
maxItem = recursive_max(arr[1:])
return maxItem if maxItem > arr[0] else arr[0]
Here is my answer, with a one line of code :))
def max_value(n_list):
return n_list[0] if len(n_list) == 1 else max(n_list[0], max_value(n_list[1:]))
def getMaxNumber(numbers):
return 'N.A' if len(numbers) == 0 else max(numbers)