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The first such input is smaller than all previous inputs that are in the subset and the sum of inputs in the subset is more than T/2 otherwise the input also is less than T/2 and it would fit in the set. Such a sum greater than T/2 is obviously more than OPT/2.
Every integer greater than 20161 can be written as the sum of two abundant numbers. The largest even number that is not the sum of two abundant numbers is 46. [5] An abundant number which is not a semiperfect number is called a weird number. [6] An abundant number with abundance 1 is called a quasiperfect number, although none have yet been found.
For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.
Therefore the POF is 1/(3e), which is unbounded. Alice has two items with values 1 and e, for some small e>0. George has two items with value e. The capacity is 1. The maximum sum is 1, attained by giving Alice the item with value 1 and George nothing. But the max-min allocation gives both agents value e. Therefore the POF is 1/(2e), which is ...
Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum.) This conjecture is called "weak" because if Goldbach's strong conjecture (concerning sums of two primes) is proven, then this would also be true. For if every even number greater than 4 is the sum of two odd primes ...
The algorithm performs summation with two accumulators: sum holds the sum, and c accumulates the parts not assimilated into sum, to nudge the low-order part of sum the next time around. Thus the summation proceeds with "guard digits" in c , which is better than not having any, but is not as good as performing the calculations with double the ...
If-then-else flow diagram A nested if–then–else flow diagram. In computer science, conditionals (that is, conditional statements, conditional expressions and conditional constructs) are programming language constructs that perform different computations or actions or return different values depending on the value of a Boolean expression, called a condition.
condition: An expression which is evaluated as a boolean value. expression 1, expression 2: Expressions with values of any type. If the condition is evaluated to true, the expression 1 will be evaluated. If the condition is evaluated to false, the expression 2 will be evaluated.