combinatorics

问题 I have a doubt in how did the author reach the intuition behind the formula to calculate the (m + n -2)C n-1 in this problem - https://www.geeksforgeeks.org/count-possible-paths-top-left-bottom-right-nxm-matrix/ Please scroll down to solution by using combinatorics. Particularly talking, I don't understand how the below code was developed for what is basically a nCr for (int i = n; i < (m + n - 1); i++) { path *= i; path /= (i - n + 1); } I mean, if I put values into it, I get it. But, if you

问题 I have a doubt in how did the author reach the intuition behind the formula to calculate the (m + n -2)C n-1 in this problem - https://www.geeksforgeeks.org/count-possible-paths-top-left-bottom-right-nxm-matrix/ Please scroll down to solution by using combinatorics. Particularly talking, I don't understand how the below code was developed for what is basically a nCr for (int i = n; i < (m + n - 1); i++) { path *= i; path /= (i - n + 1); } I mean, if I put values into it, I get it. But, if you

来源： https://stackoverflow.com/questions/62397126/efficient-algorithm-to-find-the-sum-of-all-concatenated-pairs

来源： https://stackoverflow.com/questions/62344469/find-all-combinations-of-n-positive-numbers-adding-up-to-k-in-python

来源： https://stackoverflow.com/questions/62344469/find-all-combinations-of-n-positive-numbers-adding-up-to-k-in-python

来源： https://stackoverflow.com/questions/62344469/find-all-combinations-of-n-positive-numbers-adding-up-to-k-in-python

问题 From python's Documentation: https://docs.python.org/2/library/itertools.html#itertools.combinations see combinations_with_replacement: "# combinations_with_replacement('ABC', 2) --> AA AB AC BB BC CC" I'd like to use the same function, with the bonus of generating "BA", "CA", and "CB". 回答1: itertools.product is definitely the method you're looking for here. As the documentation states, it is effectively a compact for loop; product(A,B) is equivalent to ((x, y) for x in A for y in B) product

问题 I was looking for a Python library function which computes multinomial coefficients. I could not find any such function in any of the standard libraries. For binomial coefficients (of which multinomial coefficients are a generalization) there is scipy.special.binom and also scipy.misc.comb. Also, numpy.random.multinomial draws samples from a multinomial distribution, and sympy.ntheory.multinomial.multinomial_coefficients returns a dictionary related to multinomial coefficients. However, I

问题 I have an assignment problem where I'm trying to allocate a number of tasks with a known expected cost (runtime in seconds) to X parallel workers, subject to the constraint that each worker receives the same number of tasks (save for remainders), so that the total expected runtime per worker is roughly equal. I'm using a data frame that defines the tasks to be executed, and for each task I can calculate a pretty accurate expected cost (runtime in seconds). E.g. something like this: library(

问题 I have a counting algorithm for which I am trying to get a general big-o description. It is horribly nested and horribly exponential. Here it is: 1. For each T_i in T 2. For k = 1 to max_k 3. For each of 2^k*(n choose k) items 4. For each t in T_i 5. check if the item is in t...etc. Here is a line-by-line idea of each running time This is a simple partitioning and I'm going to just give it a constant c1. max_k is a small number, always less than n, perhaps around 4 or 5. I will use k below.