Array Applications

2 © tjEE 1910 – Winter 2016

Array Applications

• Sorting

• Want to put the contents of an array in order

• Selection Sort

• Bubble Sort

• Insertion Sort

• Quicksort

• Quickersort

3 © tjEE 1910 – Winter 2016

Array Applications

• Bubble Sort - conceptual

• Sort an array of numbers into ascending or descending order• Split the list into 2 parts: sorted and unsorted

• Find the smallest(largest) element in the unsorted part of the list

• Move that element to the end of the sorted list

• Move the sort boundary up by 1 element

sortboundary

sorted unsorted

4 © tjEE 1910 – Winter 2016

Array Applications

• Bubble Sort - conceptual

sortboundary

sorted unsorted

sortboundary

sorted unsorted

5 © tjEE 1910 – Winter 2016

Array Applications

• Bubble Sort – implementation

• How do we find the smallest(largest) element in the unsorted list?• Bubble it up to the beginning of the list

• Compare 2 side by side elements• If in correct order, small large(large small), leave them

alone

• If not in correct order, swap them

-2 -1 3 1 8 9 2 3

sortboundary

sorted unsorted

6 © tjEE 1910 – Winter 2016

Array Applications

• Bubble Sort – implementation

-1 3 1 8 9 2 3

sorted unsorted

-1 3 1 8 9 2 3

sorted unsorted

-1 3 1 8 2 9 3

sorted unsorted

-1 3 1 2 8 9 3

sorted unsorted

-1 3 1 2 8 9 3

sorted unsorted

-1 1 3 2 8 9 3

sorted unsorted

swap

swap

swap

Shift boundary

7 © tjEE 1910 – Winter 2016

Array Applications

• Bubble Sort – implementationBubble Sort

bdry = 0bdry ++

bub = lastbub --

ary[bub] <ary[bub – 1]

swap

y

bdry< last

bub >bdry

y

y

n

n

n

8 © tjEE 1910 – Winter 2016

Array Applications

• Bubble Sort – implementationBubble Sort

bdry = 0bdry ++

bub = lastbub --

ary[bub] <ary[bub – 1]

swap

y

bdry< last

bub >bdry

y

y

n

n

n

void bubbleSort(int myArray[], int last){// local variablesint tmp;int bdry;int bub;

// outer loopfor(bdry = 0; bdry < last; bdry++){

// inner loopfor(bub = last; bub > bdry; bub--){

if(myArray[bub] < myArray[bub – 1]){tmp = myArray[bub];myArray[bub] = myArray[bub – 1];myArray[bub – 1] = tmp;

} // end if} // end inner

} // end outerreturn;

} // end bubbleSort

9 © tjEE 1910 – Winter 2016

Array Applications

• Bubble Sort

• Efficiency - Bubble sort takes

• N outer loops

• (N-1)! inner loops

• and a maximum of (N-1)! exchanges

10 © tjEE 1910 – Winter 2016

Array Applications

• Searching

• Want to determine if and where something is in an array

• Sequential Search

• Binary Search

11 © tjEE 1910 – Winter 2016

Array Applications

• Sequential Search

• Check each array value for the item you are looking for

• Takes a maximum of N checks

12 © tjEE 1910 – Winter 2016

Array Applications

• Binary Search

• Requires the data to be sorted

• Reduces the number of checks to log2N+1

• N = 1M, 20 checks

mid lastfirst

13 © tjEE 1910 – Winter 2016

Array Applications

• Binary Search

• Find the mid point between first and last(indexes)

• Compare the target with the value at mid

• If value is greater than mid set first to mid + 1

• If value is less than mid set last to mid -1

• If value = target return the index

mid lastfirst

14 © tjEE 1910 – Winter 2016

Array Applications

• Binary Search – looking for 5

1 2 3 4 5 7 8 9 10 11 12 13

mid lastfirst

1 2 3 4 5 7 8 9 10 11 12 13

mid lastfirst

1 2 3 4 5 7 8 9 10 11 12 13

firstmid

last

target < mid

Set last to mid-1Reset mid

target > mid

Set first to mid+1Reset mid

target > mid

Set first to mid+1Reset mid

1 2 3 4 5 7 8 9 10 11 12 13

first, mid, last

target = midreturn mid

15 © tjEE 1910 – Winter 2016

Array Applications

• Binary Search – looking for 6

1 2 3 4 5 7 8 9 10 11 12 13

mid lastfirst

1 2 3 4 5 7 8 9 10 11 12 13

mid lastfirst

1 2 3 4 5 7 8 9 10 11 12 13

firstmid

last

target < mid

Set last to mid-1Reset mid

target > mid

Set first to mid+1Reset mid

target > mid

Set first to mid+1Reset mid

1 2 3 4 5 7 8 9 10 11 12 13

first, mid, last

target > midSet first to mid+1

first > lastSTOP – not found1 2 3 4 5 7 8 9 10 11 12 13

last first

16 © tjEE 1910 – Winter 2016

Array Applications

• Binary Search – implementation

Binary Search

first <= last

first = 0last = end

target >ary[mid]

mid =(first + last)/2

target <ary[mid]

first = mid + 1

first = mid + 1first = last + 1*locn = midfound = 1

y

yy

n

n

n

17 © tjEE 1910 – Winter 2016

Array Applications

• Binary Search – implementation

int binarySearch(int myArray[], int end, int target, int* locn){// Binary Search Function//// Inputs: Array to sort, index of last element,// value to search for, pointer to location// to store the index of the value if found// Outputs: Returns 1 if value found, 0 if not// Modifies the value corresponding to the pointer//// local variablesint first;int mid;int last;

// algorithmfirst = 0;last = end;

while(first <= last){// calculate midmid = (first + last)/2;

// check valueif(target > myArray[mid])

// upper halffirst = mid + 1;

else if(target < myArray[mid])// lower halflast = mid - 1;

else// foundfirst = last + 1;

} // end while

// set value of index// using a pointer to allow multiple returns*locn = mid;

// set return to 1 if found, 0 if not foundreturn (target == myArray[mid]);

}