Switchboard rings: Boss receipt
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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
distances. A graph is a set of points joined by paths. Here, paths go in one direction. Start at point 0. For each point, find the fewest paths you must follow to reach it. Record these distances in point order: 0, 1, 2, and so on. The distance to point 0 is 0. Record -1 for a point you cannot reach. A graph with no points gives an emptydistances. - Multiply each number in
distancesby its position, counting from 1: the first number by 1, the second by 2, and so on. - Add those products. Store the sum in
weightedTotal. - Complete
switchboardRingsBossReceiptso it returnsweightedTotal. Return it, do not print it.
Example
If links is [[0, 1, 1, 1, 0, 1], [0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, 1], [1, 1, 0, 1, 1, 1], [0, 0, 1, 0, 0, 0], [0, 0, 1, 1, 0, 1]], then distances is [0, 1, 1, 1, 2, 1] and switchboardRingsBossReceipt returns 25.
Rules
- If
distancesis empty, return 0.
Test data
TEST DATA 1: links is [[0, 0, 1, 0, 0, 0], [0, 1, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 1, 0, 1], [0, 1, 0, 0, 0, 1]].
TEST DATA 2: links is [[0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 1, 1], [0, 0, 1, 1, 0]].
Examples
Input: links = [[0,0,1,0,0,0],[0,1,1,1,0,0],[0,1,0,0,1,0],[0,0,0,0,0,1],[1,0,0,1,0,1],[0,1,0,0,0,1]] Output: 47
distances is [0, 2, 1, 3, 2, 3]. Multiply by positions that start at 1: 1 * (0) + 2 * (2) + 3 * (1) + 4 * (3) + 5 * (2) + 6 * (3) = 47. Return 47.
Input: links = [[0,0,1,0,0],[0,0,0,0,0],[0,1,0,0,0],[0,0,1,1,1],[0,0,1,1,0]] Output: -2
distances is [0, 2, 1, -1, -1]. Multiply by positions that start at 1: 1 * (0) + 2 * (2) + 3 * (1) + 4 * (-1) + 5 * (-1) = -2. Return -2.
Input: links = [] Output: 0
distances is []. There are no numbers to multiply or add, so return 0.
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 distances 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.