## How to generate non-decreasing integer n-tuples in Python?

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**This question already has answers here**:

`itertools.combinations_with_replacement`

does the job:

from itertools import combinations_with_replacement as cwr for tup in cwr(range(1, m+1), n): do_whatever_with(tup)

**Python generating all nondecreasing sequences,** You can do this using itertools.combinations_with_replacement : >>> L, N = 3,3 >>> cc = combinations_with_replacement(range(1, N+1), Number of n-digits non-decreasing integers Given an integer n > 0, which denotes the number of digits, the task to find total number of n-digit positive integers which are non-decreasing in nature. A non-decreasing integer is a one in which all the digits from left to right are in non-decreasing form. ex: 1234, 1135, ..etc.

You can try this:

def list_of_tuples(n, m): return set(tuple(sorted(tup)) for tup in product(range(1,m+1), repeat = n))

For n=3 and m=2, it results in:

{(1, 2, 2), (2, 2, 2), (1, 1, 1), (1, 1, 2)}

This is not very efficient, though, but perhaps this does not matter.

**Python,** Given a tuple, sort the list of tuples in increasing order by any key in tuple. get the last key. Python List Comprehension | Sort even-placed elements in increasing and odd-placed in decreasing order · Sort even and odd Sort even-placed elements in increasing and odd-placed in decreasing order · Sort only non-prime A tuple is created by placing all the items (elements) inside parentheses (), separated by commas. The parentheses are optional, however, it is a good practice to use them. A tuple can have any number of items and they may be of different types (integer, float, list, string, etc.). print(my_tuple) # Output: () # Tuple having integers.

Not sure that I got exactly what you're looking for, but perhaps this code snippet might work:

list_of_tuples = list(product(range(1,m+1), repeat = n)) my_set = set([tuple(sorted(t)) for t in list_of_tuples])

Using the `set`

operation you keep a single copy of each duplicate, and you're done.

**Tuples,** To create a tuple with a single element, you have to include the final comma: The comparison operators work with tuples and other sequences; Python starts by The keyword argument reverse=True tells sort to go in decreasing order. a list with one integer and I give you a plain old integer (not in a list), it won't work. Tuple Objects¶ PyTupleObject¶ This subtype of PyObject represents a Python tuple object. PyTypeObject PyTuple_Type¶ This instance of PyTypeObject represents the Python tuple type; it is the same object as tuple in the Python layer. int PyTuple_Check(PyObject *p)¶ Return true if p is a tuple object or an instance of a subtype of the tuple type.

This code could be done pretty easily with recursion, without using `itertools`

.

def non_decreasing(n, m): if n==0: return [] if n==1: return [[i] for i in range(1,m+1)] return [[i] + t for t in non_decreasing(n-1, m) for i in range(1,t[0]+1)]

Example:

In [23]: non_decreasing(2,3) Out[23]: [[1, 1], [1, 2], [2, 2], [1, 3], [2, 3], [3, 3]]

**Tuples,** Although it is not necessary, it is common to enclose tuples in parentheses: Another way to create a tuple is the built-in function tuple. With no For example, if you want to divide two integers and compute the quotient and remainder, it is Each time through the loop, Python selects the next tuple in the list and assigns the Lists and tuples are arguably Python’s most versatile, useful data types.You will find them in virtually every nontrivial Python program. Here’s what you’ll learn in this tutorial: You’ll cover the important characteristics of lists and tuples.

**Tuples,** Although it is not necessary, it is common to enclose tuples in parentheses: To create a tuple with a single element, you have to include a final comma: For example, if you want to divide two integers and compute the quotient and Each time through the loop, Python selects the next tuple in the list and assigns the A Non-Repeating Pseudo-Random Number Generator. The ideal PRNG for this problem is one which would generate a unique, random integer the first 2 32 times we call it, then repeat the same sequence the next 2 32 times it is called, ad infinitum. In other words, a repeating cycle of 2 32 values.

**List *all* the tuples!,** This is a function mapping an integer n to an infinite lazy list of tuples (lists of g(int k){ // tuple is not fully generated, if(k<n) // try all values from (0,j] for(int i=0 Chapter 10 Tuples 10.1 Tuples are immutable A tuple 1 is a sequence of values much like a list. The values stored in a tuple can be any type, and they are indexed by integers. The important difference is that tuples are immutable. Tuples are also comparable and hashable so we can sort lists of them and use tuples as key values in Python

**Non-descending Tuples,** A general solution for your problem should not create all tuples, only to throw most of them away. Additionally, one should consider the situation A number is said to be made up of non-decreasing digits if all the digits to the left of any digit is less than or equal to that digit. For example, the four-digit number $1234$ is composed of digits that are non-decreasing. Some other four-digit numbers that are composed of non-decreasing digits are $0011$, $1111$, $1112$, $1122$, $2223$.

##### Comments

- Have you considered using the built-in
`sorted`

function to sort your list of tuples? You could use the`sorted`

function to sort the tuples inside your list. Your question is unclear, so I can't help you much further. Can you provide an example of desired inout and output? - do you need
*all*of the non-decreasing tuples? - @Joel I made an edit. Is it clear now?
- Try
`sorted(list_of_tuples, key=lambda x: (x[0], x[1], x[2]))`

- Are you just looking for
`combinations_with_replacement(range(1,m+1), n)`

? (I'm not making this an answer because I think it might be a dupe, if so.) - Hi, Thanks for your answer. How efficient is this method? I want to this for large values of $n.$ Do you think it is feasible to use this method?
- @SuperMario: It's going to be more feasible than filtering the
`itertools.product`

output, but iterating over all those tuples at all is probably infeasible no matter how you generate them. - Actually, my goal is to test whether the sum of elements of the tuple is equal to their product, with m = 2n. So for various values of n, I have to generate non-decreasing tuples with each element ranging from 1 to 2n and then I want to iterate over them and check if the sum of elements of the tuple is equal to their product. I guess if it is efficient it will be better.