Here is my code for a "check roulette" game that decides who in the party will pay the bill at a restaurant
names_string = input("Give me everybody's names, separated by a comma. ")
names = names_string.split(", ")
number = len(names)
roulette_number = random.randint(0,number - 1)
print((names[roulette_number]),"is going to buy the meal today!")
my question is, why did i have to add the -1 in the randint function to select the roulette number? why wouldn't it just be roulette_number = random.randint(0,number)?
You did -1 because number is the length of the list names suppose you names are
["Sam", "Jack"]
then the number variable will store 2, but the available index are only 0 and 1, this is beacuse list follow 0-based indexing.
So by doing -1 we ensure that our random integer is always in the list index range.
This is because random.randint(a, b) returns a random integer N such that a <= N <= b. See the documentation here.
To see why this is a problem, assume (as in Harsh's example) that you have two names: names = ["Sam", "Jack"].
You'll call random.randint(0, 2), which will return one of 0, 1, or 2. But there are only two names in your array, with indexes 0 and 1. If roulette_number is 2, you'll get an exception when accessing the non-existent array member.
You have several options:
If you're using Python 3.x, you can use random.randrange() instead, which excludes the final value from the results. See the documentation here. That is: random.randrange(0, 2) will return 0 or 1.
You can (as you did) subtract one from the count, giving you (in the 2-item example) random.randint(0, 1), which will return 0 or 1.
(Generally, don't do this one) You can call random.randint(1, count), which will (in the same 2-item example) return 1 or 2. Then you subtract the result from the array indexer: names[roulette - 1], giving you index 0 or index 1. I mention this option for completeness. It's not idiomatic (Python devs are used to zero-based thinking), and you'll likely confuse anyone reading your code.
Related
I am looking for a least time-complex algorithm that would solve a variant of the perfect sum problem (initially: finding all variable size subset combinations from an array [*] of integers of size n that sum to a specific number x) where the subset combination size is of a fixed size k and return the possible combinations without direct and also indirect (when there's a combination containing the exact same elements from another in another order) duplicates.
I'm aware this problem is NP-hard, so I am not expecting a perfect general solution but something that could at least run in a reasonable time in my case, with n close to 1000 and k around 10
Things I have tried so far:
Finding a combination, then doing successive modifications on it and its modifications
Let's assume I have an array such as:
s = [1,2,3,3,4,5,6,9]
So I have n = 8, and I'd like x = 10 for k = 3
I found thanks to some obscure method (bruteforce?) a subset [3,3,4]
From this subset I'm finding other possible combinations by taking two elements out of it and replacing them with other elements that sum the same, i.e. (3, 3) can be replaced by (1, 5) since both got the same sum and the replacing numbers are not already in use. So I obtain another subset [1,5,4], then I repeat the process for all the obtained subsets... indefinitely?
The main issue as suggested here is that it's hard to determine when it's done and this method is rather chaotic. I imagined some variants of this method but they really are work in progress
Iterating through the set to list all k long combinations that sum to x
Pretty self explanatory. This is a naive method that do not work well in my case since I have a pretty large n and a k that is not small enough to avoid a catastrophically big number of combinations (the magnitude of the number of combinations is 10^27!)
I experimented several mechanism related to setting an area of research instead of stupidly iterating through all possibilities, but it's rather complicated and still work in progress
What would you suggest? (Snippets can be in any language, but I prefer C++)
[*] To clear the doubt about whether or not the base collection can contain duplicates, I used the term "array" instead of "set" to be more precise. The collection can contain duplicate integers in my case and quite much, with 70 different integers for 1000 elements (counts rounded), for example
With reasonable sum limit this problem might be solved using extension of dynamic programming approach for subset sum problem or coin change problem with predetermined number of coins. Note that we can count all variants in pseudopolynomial time O(x*n), but output size might grow exponentially, so generation of all variants might be a problem.
Make 3d array, list or vector with outer dimension x-1 for example: A[][][]. Every element A[p] of this list contains list of possible subsets with sum p.
We can walk through all elements (call current element item) of initial "set" (I noticed repeating elements in your example, so it is not true set).
Now scan A[] list from the last entry to the beginning. (This trick helps to avoid repeating usage of the same item).
If A[i - item] contains subsets with size < k, we can add all these subsets to A[i] appending item.
After full scan A[x] will contain subsets of size k and less, having sum x, and we can filter only those of size k
Example of output of my quick-made Delphi program for the next data:
Lst := [1,2,3,3,4,5,6,7];
k := 3;
sum := 10;
3 3 4
2 3 5 //distinct 3's
2 3 5
1 4 5
1 3 6
1 3 6 //distinct 3's
1 2 7
To exclude variants with distinct repeated elements (if needed), we can use non-first occurence only for subsets already containing the first occurence of item (so 3 3 4 will be valid while the second 2 3 5 won't be generated)
I literally translate my Delphi code into C++ (weird, I think :)
int main()
{
vector<vector<vector<int>>> A;
vector<int> Lst = { 1, 2, 3, 3, 4, 5, 6, 7 };
int k = 3;
int sum = 10;
A.push_back({ {0} }); //fictive array to make non-empty variant
for (int i = 0; i < sum; i++)
A.push_back({{}});
for (int item : Lst) {
for (int i = sum; i >= item; i--) {
for (int j = 0; j < A[i - item].size(); j++)
if (A[i - item][j].size() < k + 1 &&
A[i - item][j].size() > 0) {
vector<int> t = A[i - item][j];
t.push_back(item);
A[i].push_back(t); //add new variant including current item
}
}
}
//output needed variants
for (int i = 0; i < A[sum].size(); i++)
if (A[sum][i].size() == k + 1) {
for (int j = 1; j < A[sum][i].size(); j++) //excluding fictive 0
cout << A[sum][i][j] << " ";
cout << endl;
}
}
Here is a complete solution in Python. Translation to C++ is left to the reader.
Like the usual subset sum, generation of the doubly linked summary of the solutions is pseudo-polynomial. It is O(count_values * distinct_sums * depths_of_sums). However actually iterating through them can be exponential. But using generators the way I did avoids using a lot of memory to generate that list, even if it can take a long time to run.
from collections import namedtuple
# This is a doubly linked list.
# (value, tail) will be one group of solutions. (next_answer) is another.
SumPath = namedtuple('SumPath', 'value tail next_answer')
def fixed_sum_paths (array, target, count):
# First find counts of values to handle duplications.
value_repeats = {}
for value in array:
if value in value_repeats:
value_repeats[value] += 1
else:
value_repeats[value] = 1
# paths[depth][x] will be all subsets of size depth that sum to x.
paths = [{} for i in range(count+1)]
# First we add the empty set.
paths[0][0] = SumPath(value=None, tail=None, next_answer=None)
# Now we start adding values to it.
for value, repeats in value_repeats.items():
# Reversed depth avoids seeing paths we will find using this value.
for depth in reversed(range(len(paths))):
for result, path in paths[depth].items():
for i in range(1, repeats+1):
if count < i + depth:
# Do not fill in too deep.
break
result += value
if result in paths[depth+i]:
path = SumPath(
value=value,
tail=path,
next_answer=paths[depth+i][result]
)
else:
path = SumPath(
value=value,
tail=path,
next_answer=None
)
paths[depth+i][result] = path
# Subtle bug fix, a path for value, value
# should not lead to value, other_value because
# we already inserted that first.
path = SumPath(
value=value,
tail=path.tail,
next_answer=None
)
return paths[count][target]
def path_iter(paths):
if paths.value is None:
# We are the tail
yield []
else:
while paths is not None:
value = paths.value
for answer in path_iter(paths.tail):
answer.append(value)
yield answer
paths = paths.next_answer
def fixed_sums (array, target, count):
paths = fixed_sum_paths(array, target, count)
return path_iter(paths)
for path in fixed_sums([1,2,3,3,4,5,6,9], 10, 3):
print(path)
Incidentally for your example, here are the solutions:
[1, 3, 6]
[1, 4, 5]
[2, 3, 5]
[3, 3, 4]
You should first sort the so called array. Secondly, you should determine if the problem is actually solvable, to save time... So what you do is you take the last k elements and see if the sum of those is larger or equal to the x value, if it is smaller, you are done it is not possible to do something like that.... If it is actually equal yes you are also done there is no other permutations.... O(n) feels nice doesn't it?? If it is larger, than you got a lot of work to do..... You need to store all the permutations in an seperate array.... Then you go ahead and replace the smallest of the k numbers with the smallest element in the array.... If this is still larger than x then you do it for the second and third and so on until you get something smaller than x. Once you reach a point where you have the sum smaller than x, you can go ahead and start to increase the value of the last position you stopped at until you hit x.... Once you hit x that is your combination.... Then you can go ahead and get the previous element so if you had 1,1,5, 6 in your thingy, you can go ahead and grab the 1 as well, add it to your smallest element, 5 to get 6, next you check, can you write this number 6 as a combination of two values, you stop once you hit the value.... Then you can repeat for the others as well.... You problem can be solved in O(n!) time in the worst case.... I would not suggest that you 10^27 combinations, meaning you have more than 10^27 elements, mhmmm bad idea do you even have that much space??? That's like 3bits for the header and 8 bits for each integer you would need 9.8765*10^25 terabytes just to store that clossal array, more memory than a supercomputer, you should worry about whether your computer can even store this monster rather than if you can solve the problem, that many combinations even if you find a quadratic solution it would crash your computer, and you know what quadratic is a long way off from O(n!)...
A brute force method using recursion might look like this...
For example, given variables set, x, k, the following pseudo code might work:
setSumStructure find(int[] set, int x, int k, int setIdx)
{
int sz = set.length - setIdx;
if (sz < x) return null;
if (sz == x) check sum of set[setIdx] -> set[set.size] == k. if it does, return the set together with the sum, else return null;
for (int i = setIdx; i < set.size - (k - 1); i++)
filter(find (set, x - set[i], k - 1, i + 1));
return filteredSets;
}
From a given array (call it numbers[]), i want another array (results[]) which contains all sum possibilities between elements of the first array.
For example, if I have numbers[] = {1,3,5}, results[] will be {1,3,5,4,8,6,9,0}.
there are 2^n possibilities.
It doesn't matter if a number appears two times because results[] will be a set
I did it for sum of pairs or triplet, and it's very easy. But I don't understand how it works when we sum 0, 1, 2 or n numbers.
This is what I did for pairs :
std::unordered_set<int> pairPossibilities(std::vector<int> &numbers) {
std::unordered_set<int> results;
for(int i=0;i<numbers.size()-1;i++) {
for(int j=i+1;j<numbers.size();j++) {
results.insert(numbers.at(i)+numbers.at(j));
}
}
return results;
}
Also, assuming that the numbers[] is sorted, is there any possibility to sort results[] while we fill it ?
Thanks!
This can be done with Dynamic Programming (DP) in O(n*W) where W = sum{numbers}.
This is basically the same solution of Subset Sum Problem, exploiting the fact that the problem has optimal substructure.
DP[i, 0] = true
DP[-1, w] = false w != 0
DP[i, w] = DP[i-1, w] OR DP[i-1, w - numbers[i]]
Start by following the above solution to find DP[n, sum{numbers}].
As a result, you will get:
DP[n , w] = true if and only if w can be constructed from numbers
Following on from the Dynamic Programming answer, You could go with a recursive solution, and then use memoization to cache the results, top-down approach in contrast to Amit's bottom-up.
vector<int> subsetSum(vector<int>& nums)
{
vector<int> ans;
generateSubsetSum(ans,0,nums,0);
return ans;
}
void generateSubsetSum(vector<int>& ans, int sum, vector<int>& nums, int i)
{
if(i == nums.size() )
{
ans.push_back(sum);
return;
}
generateSubsetSum(ans,sum + nums[i],nums,i + 1);
generateSubsetSum(ans,sum,nums,i + 1);
}
Result is : {9 4 6 1 8 3 5 0} for the set {1,3,5}
This simply picks the first number at the first index i adds it to the sum and recurses. Once it returns, the second branch follows, sum, without the nums[i] added. To memoize this you would have a cache to store sum at i.
I would do something like this (seems easier) [I wanted to put this in comment but can't write the shifting and removing an elem at a time - you might need a linked list]
1 3 5
3 5
-----
4 8
1 3 5
5
-----
6
1 3 5
3 5
5
------
9
Add 0 to the list in the end.
Another way to solve this is create a subset arrays of vector of elements then sum up each array's vector's data.
e.g
1 3 5 = {1, 3} + {1,5} + {3,5} + {1,3,5} after removing sets of single element.
Keep in mind that it is always easier said than done. A single tiny mistake along the implemented algorithm would take a lot of time in debug to find it out. =]]
There has to be a binary chop version, as well. This one is a bit heavy-handed and relies on that set of answers you mention to filter repeated results:
Split the list into 2,
and generate the list of sums for each half
by recursion:
the minimum state is either
2 entries, with 1 result,
or 3 entries with 3 results
alternatively, take it down to 1 entry with 0 results, if you insist
Then combine the 2 halves:
All the returned entries from both halves are legitimate results
There are 4 additional result sets to add to the output result by combining:
The first half inputs vs the second half inputs
The first half outputs vs the second half inputs
The first half inputs vs the second half outputs
The first half outputs vs the second half outputs
Note that the outputs of the two halves may have some elements in common, but they should be treated separately for these combines.
The inputs can be scrubbed from the returned outputs of each recursion if the inputs are legitimate final results. If they are they can either be added back in at the top-level stage or returned by the bottom level stage and not considered again in the combining.
You could use a bitfield instead of a set to filter out the duplicates. There are reasonably efficient ways of stepping through a bitfield to find all the set bits. The max size of the bitfield is the sum of all the inputs.
There is no intelligence here, but lots of opportunity for parallel processing within the recursion and combine steps.
I have a problem, I want to generate a table of 4 columns and 1 line, and with integers in the range 0 to 9, without repeating and are random each time it is run.
arrives to this, but I have a problem I always generates a 0 in the first element. And i dont know how to put a limit of 0-9
anyone who can help me?
Code of Function:
function [ n ] = generar( )
n = [-1 -1 -1 -1];
for i = 1:4
r=abs(i);
dig=floor((r-floor(r))*randn);
while find (n == dig)
r=r+1;
dig=dig+floor(r-randn);
end
n(i)=dig;
end
end
And the results:
generar()
ans =
0 3 9 6
generar()
ans =
0 2 4 8
I dont know if this post is a duplicate, but i need help with my specific problem.
So assuming you want matlab, because the code you supplied is matlab, you can simply do this:
randperm(10, 4) - 1
This will give you 4 unique random numbers from 0-9.
Another way of getting there is randsample(n, k) where n is an integer, then a random sample of size k will be drawn from the population 1:n (as a column vector). So for your case, you would get the result by:
randsample(10, 4)' - 1
It draws 4 random numbers from the population without replacement and all with same weights. This might be slower than randperm(10, 4) - 1 as its real strength comes with the ability to pass over population vectors for more sophisticated examples.
Alternatively one can call it with randsample(pop, k) where pop is the population-vector of which you want to draw a random sample of size k. So for your case, one would do:
randsample(0:9, 4)
The result will have the same singleton dimension as the population-vector, which in this case is a row vector.
Just to offer another solution and get you in touch with randsample().
I have a list of integers and I need to find out the range it falls in. I have a list of ranges which might be of size 2 to 15 at the maximum. Currently for every integer,I check through the list of ranges and find its location. But this takes a lot of time as the list of integers I needed to check includes few thousands.
//list of integers
val numList : List[(Int,Int)] = List((1,4),(6,20),(8,15),(9,15),(23,27),(21,25))
//list of ranges
val rangesList:List[(Int,Int)] = List((1,5),(5,10),(15,30))
def checkRegions(numPos:(Int,Int),posList:List[(Int,Int)]){
val loop = new Breaks()
loop.breakable {
for (va <- 0 until posList.length) {
if (numPos._1 >= posList(va)._1 && numPos._2 <= (posList(va)._2)) {
//i save "va"
loop.break()
}
}
}
}
Currently for every integer in numList I go through the rangesList to find its range and save its range location. Is there any faster/better way approach to this issue?
Update: It's actually a list of tuples that is compared against a list of ranges.
First of all, using apply on a List is problematic, since it takes linear run time.
List(1,2,3)(2) has to traverse the whole list to finally get the last element at index 2.
If you want your code to be efficient, you should either find a way around it or choose another data structure. Data structures like IndexedSeq have constant time indexing.
You should also avoid breaks, as to my knowledge, it works via exceptions and that is not a good practice. There are always ways around it.
You can do something like this:
val numList : List[(Int,Int)] = List((1,4),(6,20),(8,15),(9,15),(23,27),(21,25))
val rangeList:List[(Int,Int)] = List((1,5),(5,10),(15,30))
def getRegions(numList: List[(Int,Int)], rangeList:List[(Int,Int)]) = {
val indexedRangeList = rangeList.zipWithIndex
numList.map{case (a,b) => indexedRangeList
.find{case ((min, max), index) => a >= min && b <= max}.fold(-1)(_._2)}
}
And use it like this:
getRegions(numList, rangeList)
//yields List(0, -1, -1, -1, 2, 2)
I chose to yield -1 when no range matches. The key thing is that you zip the ranges with the index beforehand. Therefore we know at each range, what index this range has and are never using apply.
If you use this method to get the indices to again access the ranges in rangeList via apply, you should consider changing to IndexedSeq.
The apply will of course only be costly when the number ranges gets big. If, as you mentioned, it is only 2-15, then it is no problem. I just want to give you the general idea.
One approach includes the use of parallel collections with par, and also indexWhere which delivers the index of the first item in a collection that holds a condition.
For readability consider this predicate for checking interval inclusion,
def isIn( n: (Int,Int), r: (Int,Int) ) = (r._1 <= n._1 && n._2 <= r._2)
Thus,
val indexes = numList.par.map {n => rangesList.indexWhere(r => isIn(n,r))}
indexes: ParVector(0, -1, -1, -1, 2, 2)
delivers, for each number, the index in the ranges collection where it is included. Value -1 indicates the condition did not hold.
For associating numbers with range indexes, consider this,
numList zip indexes
res: List(((1,4), 0), ((6,20),-1), ((8,15),-1),
((9,15),-1), ((23,27),2), ((21,25),2))
Parallel collections may prove more efficient that the non parallel counterpart for performing computations on a very large number of items.
I was trying to write a program for the problem I mentioned above, the numbers (i.e the lists) can be of unequal length, I was not able to figure out a way to do this other than the most commonly thought of approach i.e
reverse list-1
reverse list-2
find the sum and store it in a new list represented by list-3
reverse the list.
The complexity of this should be of the O(n+m). Is there anyway to reduce it, or do it better?
Ideally the first thing I would do is store the numbers in reverse digit order, so 43,712 is stored as:
2 -> 1 -> 7 -> 3 -> 4
It makes arithmetic operations much easier.
Displaying a number can be done either iteratively or more simply with a recursive algorithm. Note: all this assumes singly-linked lists.
Edit: But you've since stated you have no choice in the storage format. As such, your best bet is to reverse both the lists, do the addition and then reverse the result.
You can do better without list reversal. WLOG I'll assume that both lists have equal length (prepend with 0 if necessary).
Start the addition from left to right (from most significant to least significant digit). You have three cases, depending of the sum of two digits:
= 9: keep the nine and increase a counter
< 9: write counter x nine, write sum, reset counter
9: increase last digit, write counter x zero, write sum (modulo 10), reset counter
I'll work on the following example:
2 568 794 +
1 438 204
--------- =
4 006 998
Add 2 + 1 = 3: case 3.
list = (3), counter = 0
Add 5 + 4 = 9: case 1
list = (3), counter = 1
Add 6 + 4 = 9: case 1
list = (3), counter = 2
Add 8 + 8 = 16: case 3
list = (4, 0, 0, 6), counter = 0
Add 7 + 2 = 9: case 1
list = (4, 0, 0, 6), counter = 1
Add 9 + 0 = 9: case 1
list = (4, 0, 0, 6), counter = 2
Add 4 + 4 = 8: case 2
list = (4, 0, 0, 6, 9, 9, 8), counter = 0
If you can use a doubly-linked list then you can quickly traverse to the end of each list, and then just work your way back, adding the numbers at each point and add that to a new list.
You will need to determine which list is longer, and add up based on the length of the shorter list, and then just finish summing and adding the longer list.
But, you will have some issues with the fact that the sum may go over one digit, so if that happens you will need to keep track of the overflow and add that to the next node.
I don't think of a better solution to the problem as stated. The root problem is that you have to process the list elements in the reverse order. In theory you could implement the algorithm recursively, avoiding the need for explicit reversal steps. But that requires O(max(m,n)) stack space, and would most likely be slower.
But I think that is really saying that you've chosen a poor representation. If you represent the numbers as doubly linked lists of int or arrays of int (with an explicit size), the complexity will be O(max(m,n)) with a smaller constant of proportionality.
Note: O(max(m,n)) and O(m+n) are both abuses of O notation. Strictly speaking, O is a defined in terms of a limit as a single variable goes to infinity. Looked at it this way, O(max(m,n)) and O(m+n) both reduce to O(m) or O(n). However, I understand what you are trying to say :-).
The only potential optimization, which would come at the cost of some code clarity, would be to combine the initial reversals into a single loop. You then go from O(n+m+m) to O(m+m), although the steps inside the loop are costlier.