Search results
Results from the WOW.Com Content Network
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.
The longest increasing subsequence problem is closely related to the longest common subsequence problem, which has a quadratic time dynamic programming solution: the longest increasing subsequence of a sequence is the longest common subsequence of and , where is the result of sorting.
It is easy to find a threshold value θ, the smallest value such that the edges of weight θ form a 2-connected graph. Then θ provides a valid lower bound on the bottleneck TSP weight, for the bottleneck TSP is itself a 2-connected graph and necessarily contains an edge of weight at least θ .
Let A be the sum of the negative values and B the sum of the positive values; the number of different possible sums is at most B-A, so the total runtime is in (()). For example, if all input values are positive and bounded by some constant C , then B is at most N C , so the time required is O ( N 2 C ) {\displaystyle O(N^{2}C)} .
The maximum sum is 1, attained by giving one agent the item with value 1 and the other agent nothing. But the max-min allocation gives each agent value at least e, so the sum must be at most 3e. 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 ...
Binary search: assuming the array is sorted, check the middle value of the current search range, then if the value is lesser check the lower range, and if the value is greater check the upper range. Block sort uses two variants: one which finds the first position to insert a value in the sorted array, and one which finds the last position.
Initialize an element m and a counter c with c = 0; For each element x of the input sequence: If c = 0, then assign m = x and c = 1; else if m = x, then assign c = c + 1; else assign c = c − 1; Return m; Even when the input sequence has no majority, the algorithm will report one of the sequence elements as its result.
Consider finding a shortest path for traveling between two cities by car, as illustrated in Figure 1. Such an example is likely to exhibit optimal substructure. That is, if the shortest route from Seattle to Los Angeles passes through Portland and then Sacramento, then the shortest route from Portland to Los Angeles must pass through Sacramento too.