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Linear search:
Serching the element sequentially(one by one).
Binary search: Serching the element with the condition of
binary
search tree(ordered array).
If (k=middle element) then return the position
Else if(k
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Linear Search
int sequentialsearch(int k,int a[],int n){int i=0;
while(i
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Binary Search
int binarysearch(int k,int a[],int n)
{
Int lower=0,upper=n-1,i;
While(upper>=lower){
mid=(upper+lower)/2;
if(k==a[mid])
{
i=mid;
break;
}
else
{
if(k
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Selection sort
Original Array
After Pass1
After Pass2sorted unsorted
After Pass3
After Pass4
After Pass5
23 78 45 8 32 56
8 78 45 23 32 56
8 23 45 78 32 56
8 23 32 78 45 56
8 23 32 45 78 56
8 23 32 45 56 78
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Bubble sortFirst pass:
( 514 2 8 )( 154 2 8 ),( 1 542 8 )( 1 452 8 ), Swap since 5 >
4( 1 4 528 )( 1 4 258 ), Swap since 5 > 2( 1 4 2 58)( 1 4 2
58).
Second Pass:
( 142 5 8 )
( 142 5 8 )( 1 425 8 )( 1 245 8 ), Swap since 4 > 2( 1 2 458
)( 1 2 458 )( 1 2 4 58)( 1 2 4 58)
Third Pass:
( 124 5 8 )( 124 5 8 )( 1 245 8 )( 1 245 8 )( 1 2 458 )( 1 2 458
)( 1 2 4 58)( 1 2 4 58)
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Insertion sort Eg:playing cards.
Inserting the elemnt in their correct positions.
A sorting algorithm that inserts each item in theproper place
into an initially empty list by comparing itwith each item in the
list
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Insertion sortVoid insertionsort(int a[],int n){
Int i=0,j,temp;While(i
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Routine for conquer part
Void merge(int A[],int lower1,int upper1,int
lower2,intupper2)
{
int p,q,j,n;
int d[100];
p=lower1;q=lower2;n=0;
while((p
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Heap Sort Heap?
Structure property
Heap order propertyApply rule2 from right most non leaf node at
bottom
level for heap sort.
Bring down the root node and delete it to add into an
output array.
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Routine for heap sortint n;int a[100];void heapsort(){int
I,t,m;for(i=n/2,i>=1,i--)
restoreheapdown(i);m=n;while(n>1){t=a[1];a[1]=a[n];
a[n]=t;n=n-1;restoreheapdown(1);}n=m;}
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QUICK SORT By picking a pivot element.
Left array must be less than pivot and right array must
be greater than pivot(divide). Recursively solve.(conquer)
Then merge.
void qsort(int a[] int left int right)
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void qsort(int a[],int left,int right){
int pivot,temp,i,j;pivot=left;if(left
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RADIX SORTdef: sorts data with integer keys by grouping keys by
theindividual digits which share the same significant positionand
value.
LSD radix sort (comparing LSD) MSD radix sort (comparing MSD)Eg:
170, 45, 75, 90, 802, 2, 24, 66Sorting by least significant digit
(1s place) gives:170, 90, 802, 2, 24, 45, 75, 66
Sorting by next digit (10s place) gives:802, 2, 24, 45, 66, 170,
75, 90Sorting by most significant digit (100s place) gives:2, 24,
45, 66, 75, 90, 170, 802
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CASE ANANLYSIS
sorting method best average worst
Quick sort nlogn nlogn n^2
Merge sort nlogn nlogn nlogn Heap sort nlogn nlogn nlogn
Insertion sort n^2 n^2 n^2
Selection n^2 n^2 n^2
Bubble n n^2 n^2
