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The time complexity of an algorithm is given by T(n) = 5n^2 + 3n + 2. What is the dominant term in this equation?
- a)5n^2
- b)3n
- c)2
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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The time complexity of an algorithm is given by T(n) = 5n^2 + 3n + 2. ...
Time Complexity of an Algorithm:
The time complexity of an algorithm measures how the running time of the algorithm increases with the size of the input. It provides an estimation of the number of operations or steps required to solve a problem as a function of the input size.
Given Time Complexity Function:
T(n) = 5n^2 - 3n + 2
Dominant Term:
The dominant term in the time complexity equation is the term that grows the fastest as the input size increases. It represents the most significant factor that contributes to the overall time complexity of the algorithm.
Calculating the Dominant Term:
To determine the dominant term in the given time complexity equation, we need to analyze the growth rates of each term.
1. 5n^2: This term represents the highest power of n (n^2). As the input size increases, the impact of this term becomes more significant compared to the other terms.
2. -3n: This term represents the linear term (n). Although it is multiplied by a constant (-3), its growth rate is slower than the quadratic term (n^2).
3. 2: This term is a constant and does not depend on the input size. It has no impact on the time complexity as the input size increases.
Conclusion:
Based on the analysis, the dominant term in the given time complexity equation T(n) = 5n^2 - 3n + 2 is 5n^2. It grows the fastest and has the most significant impact on the overall time complexity of the algorithm as the input size increases.
Therefore, the correct answer is option 'A' - 5n^2.
The time complexity of an algorithm measures how the running time of the algorithm increases with the size of the input. It provides an estimation of the number of operations or steps required to solve a problem as a function of the input size.
Given Time Complexity Function:
T(n) = 5n^2 - 3n + 2
Dominant Term:
The dominant term in the time complexity equation is the term that grows the fastest as the input size increases. It represents the most significant factor that contributes to the overall time complexity of the algorithm.
Calculating the Dominant Term:
To determine the dominant term in the given time complexity equation, we need to analyze the growth rates of each term.
1. 5n^2: This term represents the highest power of n (n^2). As the input size increases, the impact of this term becomes more significant compared to the other terms.
2. -3n: This term represents the linear term (n). Although it is multiplied by a constant (-3), its growth rate is slower than the quadratic term (n^2).
3. 2: This term is a constant and does not depend on the input size. It has no impact on the time complexity as the input size increases.
Conclusion:
Based on the analysis, the dominant term in the given time complexity equation T(n) = 5n^2 - 3n + 2 is 5n^2. It grows the fastest and has the most significant impact on the overall time complexity of the algorithm as the input size increases.
Therefore, the correct answer is option 'A' - 5n^2.
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Community Answer
The time complexity of an algorithm is given by T(n) = 5n^2 + 3n + 2. ...
In the given equation, 5n^2 has the highest power of n. Hence, it is the dominant term.
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The time complexity of an algorithm is given by T(n) = 5n^2 + 3n + 2. What is the dominant term in this equation?a)5n^2b)3nc)2d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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