Introduction to Algorithms learning Notes--The 8th chapter linear time Sequencing

Any sort of comparison algorithm, the worst-case operating time limit is Ω (NLGN)

Count sort

Assuming that each of the N input elements is an integer between 0 and K, K is an integer, and when K=o (N), the run time of the count sort is θ (n)

1 //input Array A[1..N], holding the sorted result array B[1..N], temporary storage C[0..K]2counting-SORT (a,b,k)3  fori←0to K4      Doc[i]←05  forj←1To Length[a]6      Doc[a[j]]←c[a[j]]+17  fori←1to K8      Doc[i]←c[i]+c[i-1]9  forJ←length[a] Downto1Ten      DoB[c[a[j]]]←a[j] Onec[a[j]]←c[a[j]]-1

Base sort

Assuming that the length is N of array A, each element has a D-digit number, where the 1th bit is the lowest, and the D-bit is the highest bit

1 radix-SORT (a,d)2 for i←1 to D3do      use a stable sort to sort array a on digit I

Bucket sort

Assuming that the input is produced by a random process, the process distributes the elements evenly across the interval [0,1]

1bucket-SORT (A)2 N←length[a]3  fori←1To N4      DoInsert a[i] into List B[floor (Na[i])5  fori←0to n16      Dosort list B[i] with insertion sort7Concatenate the lists b[0],b[1]... b[n-1] TogetherinchOrder

Introduction to Algorithms learning Notes--The 8th chapter linear time Sequencing