Practical Algorithm analysis and programming chapt 2 sequential statistics algorithm and Median

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• 2.1 Algorithm for sequential statistics (Algorithm for Finding small elements I)

In N element sets, the I-th sequence is used for statistics, that is, the I-th element.

Median, that is, the nth/2th small element.

2.1 Ordered Statistics Algorithm (Algorithm for Finding small elements I)

You can use the division and control method. Refer to the quick sorting method:

Set the I-th small element to S

Divide:

A [0... n]

Central region = A [0]

Divide the set into a [0... j], a [J + 1... n], so that all elements in the previous set are less than limit, and all elements in the next set are greater than limit

Conquer:

If (S <= substring), Recursively search in range 1

If (S> recursive), recursive search in range 2

Combine:

None

# Include <iostream> Int Split ( Int Arr [],Int Lo, Int Hi ){ Int Role = arr [lo]; Int Pos = lo; For ( Int I = lo + 1; I <= Hi; ++ I ){ If (ARR [I] <strong & Pos <I) {++ Pos; STD: swap (ARR [POS], arr [I]) ;}} STD :: swap (ARR [lo], arr [POS]); Return Pos ;} Int Find_ith ( Int Arr [],Int Lo, Int Hi, Int K ){ Int Mid; If (Lo  If (K <= mid) {find_ith (ARR, lo, mid, k );} Else   If (K> mid) {find_ith (ARR, Mid + 1, hi, k );}} Return Arr [k];} Int Main (){ Int Arr [10] = {10, 20, 34, 4, 14, 8, 7, 73, 54, 5 }; For ( Int I = 0; I <10; ++ I) {STD: cout <" The "<I + 1 <" Th small element is: "<Find_ith (ARR, 0, 9, I) <" \ N ";} System (" Pause "); Return 0 ;}

Algorithm complexity analysis: O (nlogn)

Find an algorithm with linear time complexity for small I elements. For details, see algorithm design skills and analysis P110.

 

Application of the median of 2.2

 

 

 

 

 

 

 

[Proof]

 

[Example] optimal location of Oil Pipes
Professor Olay is consulting an oil company that plans to build a pipeline from east to west. The rolling pipeline will go through an oil field with N wells. Each well has a tubing along the shortest path directly connected to the main pipe (or south or north ).

 

 

 

 

 

 

 

Determine the X and Y coordinates of each well. How can Professor Olay choose the optimal position of the Main Pipe (even if the sum of the length of each nozzle is the smallest ?)

[Analysis] determining the optimal position of the upper pipeline is actually finding the median of Y coordinates of N wells;

 

Application of weighted median: