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Answer :
Final answer:
To estimate the running time for a problem size of 5000, we can use the ratio of the running times to the problem sizes for the given inputs. The estimated running time for a problem size of 5000 is 8.9 seconds. The algorithm is linear as the running time increases linearly with the problem size.
Explanation:
To estimate the running time for a problem size of 5000, we can use the ratio of the running times to the problem sizes for the given inputs. Let's calculate the ratio for the problem sizes 1000 to 4000:
- Ratio for 2000: 20 seconds / 5 seconds = 4
- Ratio for 3000: 45 seconds / 20 seconds = 2.25
- Ratio for 4000: 80 seconds / 45 seconds = 1.78
We can use this ratio to estimate the running time for a problem size of 5000:
Ratio for 5000: (1.78) * 5 seconds = 8.9 seconds
Based on the estimated running time, we can conclude that the algorithm is linear as the running time increases linearly with the problem size.
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