1. Algorithm Efficiency and Sorting
Chapter 10 (continued)
Algorithm Efficiency and Sorting
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2. Quicksort Alg. pseudo-code
void Quicksort(arr, low, high){
int j = partition(arr,low,high);
Quicksort(arr, low, j-1);
Quicksort(arr, j+1, high); }
int Partition(arr, low, high){
int i = low, j = high, pivot = arr[low];
0. while(i<j)
1. Increment i until (arr[i]>pivot or i>high)
2. Decrement j until (arr[j]< pivot or j<low)
3. if(i<j) swap(arr[i],arr[j])
4. swap(arr[low],arr[j])
5. return j }
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3. Quicksort Analysis quicksort is usually extremely fast in practice
Even if the worst case occurs, quicksort’s performance is acceptable for moderately large arrays
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4. Radix Sort Radix sort Analysis
Treats each data element as a character string
Strategy
Repeatedly organize the data into groups according to the ith character in each element
Analysis
Radix sort is O(n)
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5. Radix Sort Figure 10-21 A radix sort of eight integers
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6. A Comparison of Sorting Algorithms
Figure 10-22
Approximate growth rates of time required for eight sorting algorithms
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7. Summary
Order-of-magnitude analysis and Big O notation measure an algorithm’s time requirement as a function of the problem size by using a growth-rate function
To compare the inherit efficiency of algorithms
Examine their growth-rate functions when the problems are large
Consider only significant differences in growth-rate functions
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8. Summary Worst-case and average-case analyses
Worst-case analysis considers the maximum amount of work an algorithm requires on a problem of a given size
Average-case analysis considers the expected amount of work an algorithm requires on a problem of a given size
Order-of-magnitude analysis can be used to choose an implementation for an abstract data type
Selection sort, bubble sort, and insertion sort are all O(n2) algorithms
Quicksort and mergesort are two very efficient sorting algorithms
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