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This problem can be solved use several different algorithmic techniques, including brute force, divide and conquer, dynamic programming, and reduction to shortest paths. If the array contains all non-positive numbers, then a solution is any subarray of size 1 containing the maximal value of the array (or the empty subarray, if it is allowed). The maximal subarray problem was proposed by Ulf Grenander in 1977 as a simplified model for maximal likelihood estimate of shapes in digitized pictures. There is some evidence that no significantly faster algorithm exists; an algorithm that solves the two-dimensional maximal subarray problem in O(n3−ε) time, for any ε>0, would imply a similarly fast algorithm for the all-pairs shortest paths problem. Grenander derived an algorithm that solves the one-dimensional problem in O(n2) time, better the brute force working time of O(n3).