4.4 Can you prevent contamination?ðŸ§ª

Score: 25pts

Time Limit: 5.00 sec

A biotech research lab has multiple research stations. The head scientist must travel to each station, collect samples, and return to the main lab located in the initial station. However, due to specific sample contamination concerns, the order in which the stations are visited can influence the overall contamination risk. The goal is to minimize the contamination risk. The contamination risk between two stations is influenced by both distance and the type of samples collected at each station. Additionally, a contamination multiplier factor increases risk as the journey progresses. You must determine the route that minimizes the total contamination risk, visiting each station exactly once and returning to the main lab, while considering contamination progression during the journey.

Constraints

Number of stations(n) <= 15

Distance between any two stations(x): 0 <= x <= 1000

Contamination Multiplier: a positive integer

Distance between any two stations(x): 0 <= x <= 1000

Contamination Multiplier: a positive integer

Input Format

1. â€˜nâ€™: number of stations

2. Matrix where â€˜matrix[i][j]â€™ represents the contamination risk between station i and station j.

2. Matrix where â€˜matrix[i][j]â€™ represents the contamination risk between station i and station j.

Output Format

The minimum total contamination risk for the optimal route, considering the contamination multiplier.

Example 1

Input:

4

0 20 42 25

20 0 30 34

42 30 0 10

25 34 10 0

Output:

110

Explanation:

Explore all routes through bit-masking. For each path, the contamination risk between stations is calculated and multiplied by a depth-based contamination multiplier, which increases as the journey progresses. The minimum total contamination risk is 110, which is found by choosing the optimal route that minimizes contamination buildup while considering the multiplier effect.

4

0 20 42 25

20 0 30 34

42 30 0 10

25 34 10 0

Output:

110

Explanation:

Explore all routes through bit-masking. For each path, the contamination risk between stations is calculated and multiplied by a depth-based contamination multiplier, which increases as the journey progresses. The minimum total contamination risk is 110, which is found by choosing the optimal route that minimizes contamination buildup while considering the multiplier effect.