C Programming Arrays Sorting

Sorting Bubble Sort Bubble sort sinks heaviest element to bottom causing the lighter elements to bubble up. Bubble step is as follow: 1

2 3

Start from the first element in the array, compare adjacent pair of elements. Swap if required to push the lighter of the pair one position up. Repeat the comparison of next pair until 1st and 2nd element have been compared.

Sorting is accomplished by repeating bubble operation n times.

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C Programming

February 21, 2011

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C Programming Arrays Sorting

Sorting Bubble Step 7

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R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

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C Programming Arrays Sorting

Sorting Code for Bubble Sort void bubbleSort ( int a [ ] , int n) { i n t i , j , temp ; f o r ( i = n −1; i > 0 ; i −−) // E x e c u t e b u b b l e o p e r a t i o n n t i m e s f o r ( j = 1 ; j a [ j ] ) { temp = a [ j − 1 ] ; a [ j −1] = a [ j ] ; a [ j ] = temp ; } }

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

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C Programming Arrays Sorting

Sorting Putting All Together #i n c l u d e #i n c l u d e < s t d i o . h> #d e f i n e N 10 i n t main ( ) { i n t a [N ] ; i n t n = s i z e o f ( a )/ s i z e o f ( a [ 0 ] ) ; generate (a , n ); p r i n t f ( ” U n s o r t e d i n p u t \n” ) ; printArray (a , n ); bubbleSort (a , n ) ; p r i n t f ( ” S o r t e d o u t p u t \n” ) ; printArray (a , n ); }

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

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C Programming Arrays Sorting

Sorting Insertion Sort Based on the act of picking cards and arranging the hand in sorted order. Initially, only the first element of the array is in sorted order. The input element is compared element-wise with sorted part of the array. If the input is smaller than the current element of the sorted part, consider the next element of sorted part. Else position for the input element is found.

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

3/5

C Programming Arrays Sorting

Sorting Insertion Step 5

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hole created here

drop 2

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R. K. Ghosh (IIT-Kanpur)

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C Programming

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February 21, 2011

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C Programming Arrays Sorting

Sorting Code for Insertion Insertion step should be performed by each element starting from first. Insertion step at stage i is as follow: /∗ I n s e r t i o n s t e p a s s u m i n g a [ 0 ,

. . . , i −1] f o r m s s o r t e d p a r t ∗/

x = a [ i ] ; // Save n e x t u n s o r t e d e l e m e n t j = i −1; // Get i n d e x o f l a s t e l e m e n t o f s o r t e d p a r t w h i l e ( x < a [ j ] && j >= 0 ) { a [ j +1] = a [ j ] ; // S h i f t t h e l a r g e r e l e m e n t t o r i g h t j −−; // Get i n d e x o f n e x t l a r g e s t i n s o r t e d p a r t } a [ j +1] = x ; // Drop i n p u t e l e m e n t i n c u r r e n t p o s i t i o n

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

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C Programming Arrays Sorting

Sorting Insertion Sort insertionSort ( int a [] , int i , j , x ; for ( i = 1; i < n ; x = a[ i ]; j = i −1; while ( x < a [ j ] a [ j +1] = a [ j j −−; } a [ j +1] = x ; } }

R. K. Ghosh (IIT-Kanpur)

int n) { i ++) {

&& j >= 0 ) { ];

C Programming

February 21, 2011

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C Programming Arrays Sorting

Sorting Putting All Together #i n c l u d e < s t d i o . h> #i n c l u d e #d e f i n e N 10 i n t main ( ) { i n t a [N ] ; i n t n = s i z e o f ( a )/ s i z e o f ( a [ 0 ] ) ; generate (a , n ); p r i n t f ( ” \ n U n s o r t e d i n p u t \n” ) ; printArray (a , n ); insertionSort (a , n ); p r i n t f ( ” \n\ n S o r t e d o u t p u t \n” ) ; printArray (a , n ); }

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

3/5

C Programming Arrays Sorting

Sorting Counting Sort For each element count the number of other elements which are greater.

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R. K. Ghosh (IIT-Kanpur)

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C Programming

February 21, 2011

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C Programming Arrays Sorting

Sorting Counting Sort void countingSort ( int a [ ] , int n) { i n t j , k , b [ n ] , cnt [ n ] ; f o r ( j = 0 ; j < n ; j ++) cnt [ j ] = 0; // C o u n t e r s

initialized

f o r ( j = 0 ; j < n ; j ++) { f o r ( k = 0 ; k < n ; k++) { if (a[ j ] < a[k ]) // a [ k ] s h d c n t [ k ]++; i f ( a [ j ] == a [ k ] && k > j ) // c n t [ k ]++; // } } /∗ R e m a i n i n g p a r t o f f u n c t i o n a p p e a r s

appear a f t e r a [ j ] m a i n t a i n r e l a t i v e pos . of equal elements

i n n e x t s l i d e ∗/

}

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

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C Programming Arrays Sorting

Sorting Counting Sort (contd.) /∗ P l a c i n g a [ j ] i n p o s i t i o n a [ c n t [ j ] ] c o m p l e t e s s o r t i n g . ∗/ f o r ( j = 0 ; j < n ; j ++) b [ cnt [ j ] ] = a [ j ] ;

// Use t e m p o r a r y a r r a y

f o r ( j = 0 ; j < n ; j ++) a[ j ] = b[ j ];

// T r a n s f e r b a c k

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

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C Programming Arrays Sorting

Searching Linear Search Another very frequently used operation. Sequential search: look at each element from the beginning and match with the target x. Returns index of matched element if x is found. Returns -1 if x is does not occur.

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

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C Programming Arrays Sorting

Searching Code for Linear Search int sequentialSearch ( int a [] , int i ;

int n , int x) {

f o r ( i = 0 ; i < n ; i ++) i f ( a [ i ] == x ) b r e a k ; i f ( i < n) return i ; else r e t u r n −1 }

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

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C Programming Arrays Sorting

Searching Code for Linear Search #d e f i n e N 10 i n t main ( ) { i n t a [ ] = {0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10}; int x , i ; i n t n = s i z e o f ( a )/ s i z e o f ( a [ 0 ] ) ; p r i n t f (” Enter t a r g e t element : ” ) ; s c a n f ( ”%d” , &x ) ; i = sequentialSearch (a , n , x ); i f ( i == −1) p r i n t f ( ”%d i s n o t f o u n d ! \ n” , x ) ; else p r i n t f ( ”%d f o u n d a t p o s i t i o n %d \n” , x , i ) ; }

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

4/5

C Programming Arrays Sorting

Searching Binary Search l

search element x=12

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R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

4/5

C Programming Arrays Sorting

Searching Binary Search int binarySearch ( int a [ ] , int l , int h , int x) { i n t m; w h i l e ( l i n t main ( ) { i n t a [N] = {0 , 1 , 2 , 3 , 5 , 6 , 8 , 9 , 11 , 12}; i n t n = s i z e o f ( a )/ s i z e o f ( a [ 0 ] ) ; int i , x ; p r i n t f ( ” E n t e r t h e number t o be s e a r c h e d : ” ) ; s c a n f ( ”%d” , &x ) ; p r i n t f ( ” I n p u t \n” ) ; printArray (a , n ); i = b i n a r y S e a r c h ( a , 0 , n −1 , x ) ; i f ( i == −1) p r i n t f ( ”%d i s n o t f o u n d ! \ n” , x ) ; else p r i n t f ( ”%d f o u n d a t p o s i t i o n %d \n” , x , i ) ; }

R. K. Ghosh (IIT-Kanpur)

C Programming

February 21, 2011

4/5