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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. If the array contains all non ...
The above algorithm provides an exact solution to SSP in the case that the input numbers are small (and non-negative). If any sum of the numbers can be specified with at most P bits, then solving the problem approximately with = is equivalent to solving it exactly.
It is a generalization of the subset sum problem. The input to the problem is a multiset of n integers and a positive integer m representing the number of subsets. The goal is to construct, from the input integers, some m subsets. The problem has several variants: Max-sum MSSP: for each subset j in 1,...,m, there is a capacity C j.
next i return sum This algorithm can also be rewritten to use the Fast2Sum algorithm: [7] function KahanSum2(input) // Prepare the accumulator. var sum = 0.0 // A running compensation for lost low-order bits. var c = 0.0 // The array input has elements indexed for i = 1 to input.length do // c is zero the first time around.
The subset sum problem is a special case of the decision and 0-1 problems where each kind of item, the weight equals the value: =. In the field of cryptography, the term knapsack problem is often used to refer specifically to the subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. [2]
In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S). In multiway number partitioning , there is an integer parameter k , and the goal is to decide whether S can be partitioned into k subsets of equal sum ...
One of the most famous algorithms for finding the majority of an array was proposed by Boyer and Moore [9] which is also known as the Boyer–Moore majority vote algorithm. Boyer and Moore proposed an algorithm to find the majority element of a string (if it has one) in O ( n ) {\displaystyle O(n)} time and using O ( 1 ) {\displaystyle O(1)} space.
The input to the algorithm is a set S of numbers, and a parameter k. The required output is a partition of S into k subsets, such that the sums in the subsets are as nearly equal as possible. Greedy algorithms process the numbers sequentially, and insert the next number into a bin in which the sum of numbers is currently smallest.