Sorting. Sorted Original. index. index
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1 1 Unt 16 Sortng
2 2 Sortng Sortng requres us to move data around wthn an array Allows users to see and organze data more effcently Behnd the scenes t allows more effectve searchng of data There are MANY sortng algorthms out there, we wll focus on two smple ones Lst ndex Lst ndex Orgnal Sorted
3 3 Bubble Sort Man Idea: Keep comparng neghbors, movng larger tem up and smaller tem down untl largest tem s at the top. Repeat on lst of sze n-1 Have one loop to count each pass, (a.k.a. ) to dentfy whch ndex we need to stop at Have an nner loop start at the lowest ndex and count up to the stoppng locaton comparng neghborng elements and advancng the larger of the neghbors Lst Lst Lst Lst Lst Lst Orgnal After Pass After Pass After Pass After Pass After Pass 5
4 4 Bubble Sort Algorthm vod bsort(nt mylst[], nt sze) { nt, ; for(=... ){ for(=... ){ f(mylst[] > mylst[+1]) { swap(mylst[], mylst[+1]) } } } } Pass 1 Pass 2 Pass n swap no swap swap no swap swap swap swap swap swap swap
5 5 Bubble Sort Value Courtesy of wkpeda.org Lst Index
6 6 Selecton Sort Selecton sort does away wth the many swaps and ust records where the mn or max value s and performs one swap at the end The lst/array can agan be thought of n two parts Sorted Unsorted The problem starts wth the whole array unsorted and slowly the sorted porton grows We could fnd the max and put t at the end of the lst or we could fnd the mn and put t at the start of the lst Just for varaton let's choose the mn approach
7 7 Selecton Sort Algorthm vod ssort(nt mylst[], nt sze) { for(=...){ nt mn = ; for(=... ){ f(mylst[] < mylst[mn]) { mn = } } swap(mylst[], mylst[mn]) } Pass 1 Pass 2 Pass n-2 mn=0 mn=1 mn= mn= mn= mn= mn=1 mn=1 mn=1 mn=5 swap mn= mn= mn= swap
8 Selecton Sort 8 Value Courtesy of wkpeda.org Lst Index
9 OPERATIONS ON A SORTED ARRAY 9
10 10 Inserton to a Sorted Array Another opton rather than sortng an unordered array us to always nsert new data nto the correct locaton of the array See example below To nsert, we must Iterate untl we fnd the approprate locaton to place the new value Make room for the new value by shftng the remanng tems back a spot nsert(7) nsert(6) nsert(3) nsert(8) nsert(6)
11 11 Removng from a Sorted Array Erasng / removng tem at any locaton other than the very last tem requres us to copy all tems behnd the removed tem to the prevous slot To delete/remove the tem at locaton 2 requres us to move everyone else up
12 COMPLEXITY & RUNTIME 12
13 13 Tme Complexty Comng up wth AN algorthm to solve a problem s often not TOO hard Comng up wth a GOOD algorthm to solve a problem can be a bt harder We need a way to udge how "GOOD" an algorthm s For us "GOOD" wll mean how long the algorthm takes to solve the problem We wll count steps of work and come up wth an answer n terms of N, where N s the sze of the nput/problem
14 14 Recall the bubble sort Bubble Sortng How much work do our nested loops requre us to do Thnk of each step/teraton as 1 unt of tme/work Lst Orgnal Lst Pass 1 ( steps) Lst Pass 2 ( steps) Lst Pass 3 ( steps) Lst Lst Orgnal Lst s length N (N=6 for ths example) Pass 4 ( steps) Lst Pass 5 ( steps) Lst Pass 6 ( steps)
15 Run-tme 15 Complexty of Sort Algorthms Bubble Sort & Selecton Sort 2 Nested Loops Execute outer loop n tmes For each outer loop teraton, nner loop runs tmes. Tme complexty s proportonal to n 2 Other sort algorthms can run n tme proportonal to n*log 2 n N N 2 N*log2(N) N
16 16 Importance of Tme Complexty It makes the dfference between effectve and mpossble Many mportant problems currently can only be solved wth exponental run-tme algorthms (e.g. O(2 n ) tme) Usually algorthms are only practcal f they run n polynomal tme (e.g. O(n) or O(n 2 ) etc.) N O(1) O(log 2 n) O(n) O(n*log 2 n) O(n 2 ) O(2 n ) ,048, , , E , ,000,000 #NUM!
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