34 views

Count paths in matrix that visit each number exactly once [duplicate]

Let's say we are given matrix of size $N \leq 21 \text{ by } M \leq 21$ each element of the matrix is either $-1$ or number in the interval $[0, 20]$. We want to count the number of paths that start ...
939 views

Calculating greatest common divisor and least common multiple modulo prime number

I'm trying to solve pretty complex problem with number theory and set of numbers. To make the problem more clear we are going to define $GCD(a, b)$ as the greates number that divides both $a$ and $b$...
161 views

Count arrays with size n, sum k and largest element m

I'm trying to solve pretty complex problem with combinatorics. Namely, we have given three numbers N, K, M. Now we want to count how many different arrays of integers are there with length N, sum K ...
253 views

Obtain data structure able to do reverse range updates

For given array $A$ of size $N$, note that the array is going to be permutation of the numbers from 1 to N, each number will be there exactly once, we want to obtain data structure being able to ...
181 views

Sort binary matrix by swapping columns to make subrectangle of ones with maximum size

We have given binary matrix (matrix containing only 1 and 0) of size $n\cdot m$. We want to order the matrix such that the biggest rectangle containing only ones is with maximum size. For example if ...
180 views

For given set of integers, find and count the pairs with maximum value of bitwise or

Let's say we have given set of integers $A = \{x_1, x_2, x_3, x_4, \dots, x_n\}$, consisting of exactly $n$ values, all of them positive integers. Now the problem is to find the maximum value of ...
74 views

Minimum number of deleting palindromes to delete whole string

Let's say we have given array $A$ of size $n$. Our goal is to delete the whole array with minimum steps. In one step we can choose substring (consecutive elements from the string) and delete it only ...
63 views

Is it possible to make data structure that will find MEX and support modification queries

Let's say we have given array of $n$ elements, now we want to create data structure that will allow us to get the MEX of its elements, MEX meaning the smallest positive integer that is not present in ...
57 views

Given a tree find path that maximizes the median of the costs of edges

We have given tree with $N$ nodes and $N-1$ edges, such that each edges is assigned positive weight. We need to find path of length between $L$ and $R$ inclusively, with maximum cost. Cost of a path ...
46 views

Count submatrices with only zeros for each element of the matrix

Let's say we have given matrix of size $N \cdot M$, only with zeros and ones. For each element in the matrix, we want to count subrectangles that are covering this element and are made only of zeros. ...