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If the variable has a signed integer type, a program may make the assumption that a variable always contains a positive value. An integer overflow can cause the value to wrap and become negative, which violates the program's assumption and may lead to unexpected behavior (for example, 8-bit integer addition of 127 + 1 results in −128, a two's ...
Reducing and re-arranging the coefficients by adding multiples of as necessary, we can assume < (in fact, this is the unique such satisfying the equation and inequalities). Similarly we take u , v {\displaystyle u,v} satisfying N − k = u a + v b {\displaystyle N-k=ua+vb} and 0 ≤ u < b {\displaystyle 0\leq u<b} .
Coin values can be modeled by a set of n distinct positive integer values (whole numbers), arranged in increasing order as w 1 through w n.The problem is: given an amount W, also a positive integer, to find a set of non-negative (positive or zero) integers {x 1, x 2, ..., x n}, with each x j representing how often the coin with value w j is used, which minimize the total number of coins f(W)
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S 1 and S 2 such that the sum of the numbers in S 1 equals the sum of the numbers in S 2.
Kummer's theorem states that the number of carries involved in adding two numbers in base is equal to the exponent of the highest power of dividing a certain binomial coefficient. When several random numbers of many digits are added, the statistics of the carry digits bears an unexpected connection with Eulerian numbers and the statistics of ...
There are two main reasons for using integer variables when modeling problems as a linear program: The integer variables represent quantities that can only be integer. For example, it is not possible to build 3.7 cars. The integer variables represent decisions (e.g. whether to include an edge in a graph) and so should only take on the value 0 or 1.
Every natural number not exceeding one billion is either a harshad number or the sum of two harshad numbers. Conditional to a technical hypothesis on the zeros of certain Dedekind zeta functions , Sanna proved that there exists a positive integer k {\displaystyle k} such that every natural number is the sum of at most k {\displaystyle k ...
Declarative solutions are easier to understand than imperative solutions, [12] and there has been a long-term trend from imperative to declarative methods. [13] [14] Formula calculators are part of this trend. Many software tools for the general user, such as spreadsheets, are declarative. Formula calculators are examples of such tools.