JDEP183H

Handout 19: Sorting

October 28, 2008

Insertion Sort

Before examining record , we assume that the preceding records have already been sorted; then we insert into its proper place among the previously sorted records.

Straight insertion. Assume that and that records have been rearranged so that

.

We compare the new value with , , …, in turn, until discovering that should be inserted between and ; then we move records , …, , up one space and put the new record into position i + 1.

Implementation.

int numbers[];

int i, j, k;

// assume that numbers[0] has already been sorted.

for (j = 1; j < numbers.length; j++) {

// find the place to insert

i = 0;

while (i < j && numbers[j] > numbers[i])

i++;

int temp = numbers[j]; // store the value first

// insertion point is i

// need to move all the other numbers by one position

for (k = j; k > i; k--)

numbers[k] = numbers[k-1];

// now the finishing touch.

numbers[i] = temp;

}

Exchange Sort

Exchange or transposition which systematically interchange pairs of elements that are out of order until no more such pairs exist.

The bubble sort. Compare and , interchanging and if the keys are out of order; then do the same to records and , and , etc. During this sequence of operations, records with the largest value will move up to become . Repetitions of the process will get the appropriate records into positions , , etc., so that all records will ultimately sorted.

Implementation.

int numbers[];

int i, j, k;

int iteration = 1;

for (j = 0; j < (numbers.length-1); j++) {

// compare it with the rest of the numbers

for (k = 0; k < (numbers.length-iteration); k++) {

if (numbers[k] > numbers[k+1]) {

// switch

int temp = numbers[k+1];

numbers[k+1] = numbers[k];

numbers[k] = temp;

}

}

iteration++;

}

Selection Sort

(1) Find the smallest value; transfer the corresponding record to the output area, then replace the value by the value “” (which is assumed to be higher than any actual value).

(2) Repeat step (1). This time the second smallest key will be selected, since the smallest key has been replaced by .

(3) Continue repeating step (i) until N records have been selected.

Requires all the input items to be present before sorting may proceed, and it generates the final outputs one by one in sequence. This is essentially the opposite of insertion, where the inputs are received sequentially but we do not know any of the final outputs until sorting is completed.

Implementation.

int numbers[];

int i, j, k;

for (j = (numbers.length-1); j >= 1; j--) {

// find the maximum between 0 and j

int maximum = numbers[0];

int maximumIndex = 0;

for (k = 0; k <= j; k++) {

if (numbers[k] > maximum) {

maximum = numbers[k];

maximumIndex = k;

}

}

// replace the records, the maximum one to the current

int temp = numbers[j];

numbers[j] = maximum;

numbers[maximumIndex] = temp;

}

* Based on Knuth (1973)