Algorithms and Data Structures Objective To review the fundamental algorithms and data structures that are commonly used in programs To see how to use and implement these algorithms and data structures in different languages and to see what language and library support exists for them Sorting and Searching Arrays and Vectors Lists Hash Tables Generic programming This material comes from chapter 2 of Brian Kernighan and Rob Pike The Practice of Programming Topics Binary Search Quicksort Big Oh Vectors Lists Hash Tables C C Java Perl Linear Search typdef struct Nameval Nameval struct Nameval char name int value HTML characters e g AElig is a ligature of A and E values are Unicode ISO10646 encoding Nameval htmlchars Aelig 0x00c6 Aacute 0x00c1 Acirc 0x00c2 zeta 0x03b6 Linear Search lookup sequential search for name in tab return index int lookup char name Nameval tab int ntab int i for i 0 i ntab i if strcmp name tab i name 0 return i return 1 no match Binary Search lookup binary search for name in tab return index or 1 if not found int lookup char name Nameval tab int ntab int low high mid cmp low 0 high ntab 1 while low hight mid low high 2 cmp strcmp name tab mid name if cmp 0 high mid 1 else if cmp 0 low mid 1 else found match return mid return 1 no match Quicksort pick one element of the array pivot partition the other elements into two groups those less than the pivot those that are greater than or equal to the pivot recursively sort each group Partition p unexamined last i p 0 n 1 p 1 last p 0 p unexamined i p last n 1 p n 1 Quicksort quicksort sort v 0 v n 1 into increasing order void quicksort int v int n int i last if n 1 nothing to do return swap v 0 rand n move pivot element to v 0 last 0 for i 1 i n i partition if v i v 0 swap v last i swap v 0 last restore pivot quicksort v last recursively sort each part quicksort v last 1 n last 1 Swap swap interchange v i and v j void swap int v int i int j int temp temp v i v i v j v j temp Libraries C qsort C sort algorithm library from STL java util collections sort perl sort qsort strings char str N qsort str N sizeof str 0 scmp scmp string compare of p1 and p2 int scmp const void p1 const void p2 char v1 v2 v1 char p1 v2 char p2 return strcmp v1 v2 qsort int int arr N qsort arr N sizeof arr 0 icmp icmp integer compare of p1 and p2 int icmp const void p1 const void p2 int v1 v2 v1 int p1 v2 int p2 if v1 v2 return 1 else if v1 v2 return 0 else return 1 Big Oh Notation O 1 O log n O n O nlog n O n2 O n3 O 2n Name constant logarithmic linear n log n quadratic cubic exponential Example array index binary search string comparison quicksort mergesort insertion sort matrix multiplication set partitioning It is more precise to use for order classes Timing Unix time command jjohnson ws56 lec1 time sign usr share dict words sort squash temptime 0 11user 0 01system 0 00 27elapsed 43 CPU 0avgtext 0avgdata 0maxresident k 0inputs 0outputs 91major 13minor pagefaults 0swaps clock counting cycles nlog n vs n2 Growing Arrays Arrays provide O 1 access and insertion time Sorted arrays provide O log n search time and O n insertion time have to move elements If the number of elements in an array is not known ahead of time it may be necessary to resize the array Involves dynamic memory allocation and copying To minimize the cost it is best to resize in chunks Growing Arrays in C typedef struct Nameval Nameval struct Nameval char name int value struct NVtab int nval current number of values int max allocated number of values Nameval nameval array of name value pairs enum NVINIT 1 NVGROW 2 Growing Arrays addname add new name and value to nvtab int addname Nameval newname Nameval nvp if nvtab nameval NULL first time nvtab nameval Nameval malloc NVINIT sizeof Nameval if nvtab nameval NULL return 1 nvtab max NVINIT nvtab nval 0 else if nvtab nval nvtab max grow nvp Nameval realloc nvtab nameval NVGROW nvtab max sizeof Nameval if nvp NULL return 1 nvtab max NVGROW nvtab nameval nvp nvtab nameval nvtab nval newname return nvtab nval Lists A sequence of elements Space is allocate for each new element and consecutive elements are linked together with a pointer O 1 time to insert at front O n to append unless pointer to last element kept O n traversal time head NULL data 1 data 2 data 3 data 4 Lists in C typedef struct Nameval Nameval struct Nameval char name int value Nameval next in list newitem create new item from name and value Nameval newitem char name int value Nameval newp newp Nameval emalloc sizeof Nameval newp name name newp value value newp next NULL return newp Lists in C addfront add newp to front of listp Nameval addfront Nameval listp Nameval newp newp next listp return newp nvlist addfront nvlist newitem smiley 0x263A Prepend Element in Front of List addend add newp to end of listp Nameval addend Nameval listp Nameval newp Nameval p if listp NULL return newp for p listp p NULL p p next p next newp return listp Append Element to Back of List addend add newp to end of listp Nameval addend Nameval listp Nameval newp Nameval p if listp NULL return newp for p listp p NULL p p next p next newp return listp Lookup Element in List lookup sequential search for name in listp Nameval lookup Nameval listp char name for listp NULL listp listp next if strcmp name listp name 0 return listp return NULL no match Apply Function to Elements in List apply execute fn for each element of listp void apply Nameval listp void fn Nameval void void arg for listp NULL listp listp next fn listp arg call the function void fn Nameval void is a pointer to a void function of two arguments the first argument is a pointer to a Nameval and the second is a generic pointer Print Elements of a List printnv print name and value using format in arg void printnv Nameval p void arg char fmt fmt char arg printf fmt p name p value apply nvlist printnv s x n Count Elements of a List inccounter increment counter arg void inccounter Nameval p void arg int ip p is unused ip int arg ip int n n 0 apply nvlist inccounter n printf d elements in nvlist n n Free Elements in List freeall free all elements of listp void freeall Nameval listp Nameval next for listp NULL listp next next listp next assumes name is freed elsewhere free listp for listp NULL listp listp next free …