radix sort -...
TRANSCRIPT
Radix Sort
Radix Sort
45834 6283 56323 92634 78332 55111
Radix Sort
45834 6283 56323 92634 78332 55111
Radix Sort
45834 6283 56323 92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
45834 6283 56323 92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
45834
6283 56323 92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
45834
6283 56323 92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
45834
6283 56323 92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283
56323 92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283
56323 92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283
56323 92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634 78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
78332 55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
78332
55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
78332
55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
78332
55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
7833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
7833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
7833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
78332
55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
78332
55111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
7833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
7833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323
92634
7833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
45834
6283 56323
92634
7833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
45834
6283 56323
92634
7833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
45834
6283 56323
92634
7833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323 926347833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
458346283 56323 926347833255111
0:1:2:3:4:5:6:7:8:9:
Radix Sort
45834
6283
563239263478332
551110:1:2:3:4:5:6:7:8:9:
Radix Sort
0:1:2:3:4:5:6:7:8:9:
9263478332 45834 62835632355111
Radix Sort
0:1:2:3:4:5:6:7:8:9:
92634
78332
45834
6283
56323
55111
Radix Sort
0:1:2:3:4:5:6:7:8:9:
9263456323 78332 45834628355111
Radix Sort
0:1:2:3:4:5:6:7:8:9:
92634
78332
45834563236283
55111
Radix Sort
0:1:2:3:4:5:6:7:8:9:
5632345834 6283 783325511192634
Radix Sort
0:1:2:3:4:5:6:7:8:9:
6283
4583456323
78332
55111
92634
Radix Sort
0:1:2:3:4:5:6:7:8:9:
7833255111 56323 92634458346283
Radix Sort
Example shows working from LSD to MSD. Is radix sort correct working from MSD to LSD?
Radix Sort
Example shows working from LSD to MSD. Is radix sort correct working from MSD to LSD?
No! Here is a counter-example:
72 27
Radix Sort
Example shows working from LSD to MSD. Is radix sort correct working from MSD to LSD?
No! Here is a counter-example:
72
272:...7:
Radix Sort
Example shows working from LSD to MSD. Is radix sort correct working from MSD to LSD?
No! Here is a counter-example:
27 72
Radix Sort
Example shows working from LSD to MSD. Is radix sort correct working from MSD to LSD?
No! Here is a counter-example:
27
722:...7:
Radix Sort
Example shows working from LSD to MSD. Is radix sort correct working from MSD to LSD?
No! Here is a counter-example - numbers not increasing:
72 27
Radix SortCan we prove that radix sort is correct when working from LSD to MSD?
Radix SortCan we prove that radix sort is correct when working from LSD to MSD?
Yes! By induction on the digit being sorted
Radix SortCan we prove that radix sort is correct when working from LSD to MSD?
Yes! By induction on the digit being sorted
Base step: After 1st step – all numbers in order on LSD
Radix SortCan we prove that radix sort is correct when working from LSD to MSD?
Yes! By induction on the digit being sorted
Base step: After 1st step – all numbers in order on LSD
Induction step: suppose (P) after k th step that all numbers are
in non-decreasing order on k least significant digits.
Radix SortCan we prove that radix sort is correct when working from LSD to MSD?
Yes! By induction on the digit being sorted
Base step: After 1st step – all numbers in order on LSD
Induction step: suppose (P) after k th step that all numbers are
in non-decreasing order on k least significant digits. Consider a queue on the k+1
st step where at least two numbers are out of order in the k least significant digits. For example,
572 527 5495: (k=2)
Radix SortCan we prove that radix sort is correct when working from LSD to MSD?
Yes! By induction on the digit being sorted
Base step: After 1st step – all numbers in order on LSD
Induction step: suppose (P) after k th step that all numbers are
in non-decreasing order on k least significant digits. Consider a queue on the k+1
st step where at least two numbers are out of order in the k least significant digits. For example,
The numbers in that queue are in the same order they were in the list following the k
th step. But that is a violation of (P). Hence, all numbers in a queue are in non-decreasing order.
572 527 5495: (k=2)
Radix SortCan we prove that radix sort is correct when working from LSD to MSD?
Yes! By induction on the digit being sorted
Base step: After 1st step – all numbers in order on LSD
Induction step: suppose (P) after k th step that all numbers are
in non-decreasing order on k least significant digits. Consider a queue on the k+1
st step where at least two numbers are out of order in the k least significant digits. For example,
The numbers in that queue are in the same order they were in the list following the k
th step. But that is a violation of (P). Hence, all numbers in a queue are in non-decreasing order. Since assembling the list after the k+1
st step is by increasing queue rank (k+1
st digit) all numbers in the list are in non- decreasing order.
572 527 5495: (k=2)