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Given an array where numbers are in range from 1 to n6, which sorting algorithm can be used to sort these number in linear time?
- a)Not possible to sort in linear time
- b)Radix Sort
- c)Counting Sort
- d)Quick Sort
Correct answer is option 'B'. Can you explain this answer?
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Given an array where numbers are in range from 1 to n6, which sorting ...
See Radix Sort for explanation.
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Given an array where numbers are in range from 1 to n6, which sorting ...
Radix Sort for Linear Time Sorting
Radix Sort is a sorting algorithm that can sort numbers in linear time. It works by sorting the numbers based on their individual digits, starting from the least significant digit and moving towards the most significant digit. Radix sort has a time complexity of O(kn), where k is the number of digits in the largest number.
Steps for Radix Sort Algorithm
The steps involved in the Radix Sort algorithm are as follows:
1. Find the maximum number in the array.
2. Determine the number of digits in the maximum number.
3. Starting from the least significant digit, sort the numbers based on that digit using Counting Sort.
4. Repeat step 3 for all digits, moving towards the most significant digit.
5. The final sorted array is obtained.
Advantages of Radix Sort Algorithm
1. It has a time complexity of O(kn), which is linear.
2. It can sort numbers in any base, not just base 10.
3. It is a stable sort, which means that the order of equal elements is preserved.
Disadvantages of Radix Sort Algorithm
1. It requires extra space to store the intermediate arrays.
2. It is not suitable for sorting large numbers with many digits, as the time complexity increases with the number of digits.
Conclusion
Radix Sort is a suitable algorithm for sorting numbers in linear time. It works by sorting the numbers based on their individual digits, starting from the least significant digit and moving towards the most significant digit. Radix sort has a time complexity of O(kn), where k is the number of digits in the largest number.
Radix Sort is a sorting algorithm that can sort numbers in linear time. It works by sorting the numbers based on their individual digits, starting from the least significant digit and moving towards the most significant digit. Radix sort has a time complexity of O(kn), where k is the number of digits in the largest number.
Steps for Radix Sort Algorithm
The steps involved in the Radix Sort algorithm are as follows:
1. Find the maximum number in the array.
2. Determine the number of digits in the maximum number.
3. Starting from the least significant digit, sort the numbers based on that digit using Counting Sort.
4. Repeat step 3 for all digits, moving towards the most significant digit.
5. The final sorted array is obtained.
Advantages of Radix Sort Algorithm
1. It has a time complexity of O(kn), which is linear.
2. It can sort numbers in any base, not just base 10.
3. It is a stable sort, which means that the order of equal elements is preserved.
Disadvantages of Radix Sort Algorithm
1. It requires extra space to store the intermediate arrays.
2. It is not suitable for sorting large numbers with many digits, as the time complexity increases with the number of digits.
Conclusion
Radix Sort is a suitable algorithm for sorting numbers in linear time. It works by sorting the numbers based on their individual digits, starting from the least significant digit and moving towards the most significant digit. Radix sort has a time complexity of O(kn), where k is the number of digits in the largest number.
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