Dispatch order: Positive proof strip
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Inputs
links is a square table of 0s and 1s. Points are numbered from 0. A 1 at links[a][b] means a one-way path goes from point a to point b. A 0 means no path.
Your tasks
- Create a list
taskOrder. Each point in this graph is a task. A path from task a to task b means a must happen before b. Put all tasks with no paths coming into them in a queue, in number order. A queue serves the task at its front first. Remove that task, record its number, and remove its outgoing paths. Check its next tasks in number order. Add a task to the back of the queue as soon as it has no paths left coming in. If you cannot record every task, the rules contain a loop: use an emptytaskOrderinstead. - Create a list
positiveValuesthat keeps only the numbers intaskOrderthat are greater than 0, in the same order. - Complete
dispatchOrderPositiveProofStripso it returnspositiveValues. Return it, do not print it.
Example
If links is [[1, 0, 1, 0, 1, 1], [1, 1, 1, 1, 0, 0], [1, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 0], [1, 1, 0, 1, 0, 1], [1, 1, 1, 1, 0, 1]], then taskOrder is [] and dispatchOrderPositiveProofStrip returns [].
Rules
- If no number is greater than 0, return [].
Test data
TEST DATA 1: links is [[1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 0], [1, 0, 0, 1, 1, 0]].
TEST DATA 2: links is [[0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [0, 1, 1, 0, 0], [0, 1, 1, 0, 0], [0, 1, 0, 0, 0]].
Examples
Input: links = [[1,0,0,0,0,1],[0,0,0,0,0,0],[1,0,1,1,0,0],[0,0,0,1,0,0],[0,1,1,0,0,0],[1,0,0,1,1,0]] Output: []
taskOrder is []. Keep only numbers greater than 0, without changing their order. Return [].
Input: links = [[0,0,1,0,0],[0,1,0,0,0],[0,1,1,0,0],[0,1,1,0,0],[0,1,0,0,0]] Output: []
taskOrder is []. Keep only numbers greater than 0, without changing their order. Return [].
Input: links = [] Output: []
taskOrder is []. Keep only numbers greater than 0, without changing their order. Return [].
Input limits
- 0 <= input size <= 16.
- Answers fit in a signed 32-bit integer: -2,147,483,648 through 2,147,483,647.
- Input numbers have no decimal part. They range from -1,000,000 to 1,000,000. Follow any extra input rules in task 1.
- The graph has at most 16 points. Its table has the same number of rows and columns. Link entries are 0 or 1; cost entries are 0 through 13.
Efficiency goal
Big-O describes how the work or memory needed grows as the input gets larger.
Efficiency goal: time O(V^2); extra memory, including the helper list, O(n). n is the input length; V is the number of graph points. These labels describe how work and memory grow with the input.
Practice focus
Build taskOrder first, then return exactly what the tasks ask for. Follow the order, keep repeated values when the rule says so, and check the empty case.