Example. Selection sort

[comp1110-1Y]
  • August 11, 2026
  • Liam O'Connor, Fabian Muehlboeck
 void selectionSort(int[] arr) { int i = 0; while(i < arr.length) { //INV : arr[0..i-1] is sorted AND for every j in // [i..arr.length-1], arr[j] >= every element // in arr[0..i-1] int currentMin = arr[i]; // could as well be always referred // to as arr[currentPos] int currentPos = i; int j = i + 1; while(j < arr.length) { //INT: arr[currentPos] is the minimum element in arr[i..j-1] if(arr[j] < currentMin) { currentMin = arr[j]; currentPos = j; } j = j + 1; } //arr[currentPos] is the minimum element in arr[i..arr.length-1] // from above, we know that it is greater than or equal to every // element in arr[0..i-1] int swap = arr[i]; arr[i] = arr[currentPos]; arr[currentPos] = swap; //therefore, swapping arr[currentPos] with arr[i] makes arr[0..i] // still sorted, and every element in arr[i+1..arr.length-1] // is >= every element in arr[0..i] . i = i + 1; } }

Context

    Understanding sorting

    [comp1110-1V]
    • Liam O'Connor

    Definition. A spec and a test suite for sorting

    [comp1110-1W]
    • March 10, 2026
    • Liam O'Connor

    Any in-place sorting algorithm, no matter how it is implemented, should satisfy the following spec:

    /** Sort an array in-place. There are two postconditions: - After executing, the array must be sorted. - After executing, the array must be some permutation of the values that existed before. (many programmers will get the former but forget the latter) @param arr the array to sort */ void sort(int[] arr)

    Assuming we had such a function, we might test it (using proper array comparison) as follows:

    void sortAndCheck (int[] toSort, int[] toCheck) { sort(toSort); assert Arrays.equal(toSort, toCheck); } void main (String[] args) { // already sorted sortAndCheck(new int[]{1,2,3,4,5,6,7,8,9}, new int[]{1,2,3,4,5,6,7,8,9}); // inversely sorted sortAndCheck(new int[]{9,8,7,6,5,4,3,2,1}, new int[]{1,2,3,4,5,6,7,8,9}); // random order sortAndCheck(new int[]{6,-5,212,42,19,0,0,5,9718}, new int[]{-5,0,0,5,6,19,42,212,9718}); // negative and inverse sortAndCheck(new int[]{-1,-2,-3,-4,-5}, new int[]{-5,-4,-3,-2,-1}); // empty sortAndCheck(new int[]{}, new int[]{}); // singleton sortAndCheck(new int[]{0}, new int[]{0}); // two sortAndCheck(new int[]{100,100}, new int[]{100,100}); }

    Definition. Quadratic sorting methods

    [comp1110-1X]
    • August 11, 2026
    • Liam O'Connor, Fabian Muehlboeck

    We demonstrated two sorting algorithms in the lecture:

    • Selection sort: We divide the array into an "unsorted zone" and a "sorted zone". The sorted zone begins empty at the start of the array, and the unsorted zone begins by occupying the whole array. Each loop iteration, we look through the unsorted zone, find the minimum, and swap it with the first element of the unsorted zone (right next to the sorted zone). This means that the sorted zone can be expanded by one element. Repeat until the unsorted zone is of size zero.
    • Bubble sort: Here, the "sorted zone" grows from the end of the array rather than the beginning. Loop through the unsorted zone comparing adjacent elements. If they are not in order, swap them. This will result in the highest element reaching the top. This means we can increase the size of the sorted zone. Repeat until all sorted.

      If we go through the unsorted zone without doing any swaps, we can immediately stop — the array is sorted. This is called an early exit trick.

    I briefly mentioned another one at the start of the workshop:

    • Insertion sort: The most popular of these three, and somewhat similar to selection sort, in that the sorted zone begins empty and grows from the left. Instead of finding the minimum, however, we take the first element from the unsorted zone and remember it (call it X) and shift everything greater than X in the sorted zone to the right one spot. Then we place X in the slot left over.

    These algorithms are called "quadratic" because they take a quadratic amount of key operations (in terms of the size of the array), in this case comparisons and moves/swaps to perform.

    While insertion sort is generally the most popular of the three, each of them have their own advantages, depending on your particular situation. On arrays:

    • Selection sort minimizes the number of times you have to move an array element.
    • Bubble sort only swaps adjacent elements and has an easy way to exit early on sorted arrays.
    • Insertion sort can minimize the number of comparisons that you do (these can become expensive on more complex data types).

    Which of these you actually get depends on the particulars of your implementation, and minor variations (say starting from the other direction) can make a huge difference for certain scenarios.

    Example. Selection sort

    [comp1110-1Y]
    • August 11, 2026
    • Liam O'Connor, Fabian Muehlboeck
     void selectionSort(int[] arr) { int i = 0; while(i < arr.length) { //INV : arr[0..i-1] is sorted AND for every j in // [i..arr.length-1], arr[j] >= every element // in arr[0..i-1] int currentMin = arr[i]; // could as well be always referred // to as arr[currentPos] int currentPos = i; int j = i + 1; while(j < arr.length) { //INT: arr[currentPos] is the minimum element in arr[i..j-1] if(arr[j] < currentMin) { currentMin = arr[j]; currentPos = j; } j = j + 1; } //arr[currentPos] is the minimum element in arr[i..arr.length-1] // from above, we know that it is greater than or equal to every // element in arr[0..i-1] int swap = arr[i]; arr[i] = arr[currentPos]; arr[currentPos] = swap; //therefore, swapping arr[currentPos] with arr[i] makes arr[0..i] // still sorted, and every element in arr[i+1..arr.length-1] // is >= every element in arr[0..i] . i = i + 1; } }

    Example. Bubble sort

    [comp1110-1Z]
    • August 11, 2026
    • Liam O'Connor

    Bubble sort swaps a lot of elements, but the key idea is that once it finds the maximum element in the unsorted part of the array, it keeps "bubbling" it up further and further, until we reach the end of the unsorted part, where a sorted array of elements larger than the new element is waiting. In that sense, it works like selection sort (either one of them could also just work in the other direction), but with more elements being moved around. We include the "early exit" trick mentioned by Definition [comp1110-1X]:

    void bubbleSort(int[] arr) { int i = arr.length - 1; while(i > 0) { // INV: arr[i..arr.length-1] is sorted, and // for every j in [0..i], arr[j] <= every element // in arr[i+1..arr.length-1] int j = 0; boolean swapped = false; while(j < i) { // INV: for every k < j, arr[k] < arr[j] // and if swapped == false, then arr[0..j-1] is sorted if(arr[j] > arr[j + 1]) { int swap = arr[j]; arr[j] = arr[j + 1]; arr[j+1] = swap; swapped = true; } j = j + 1; } // for every k < i, arr[k] < arr[i], and if // swapped == false, then arr[0..i-1] is sorted if(!swapped) { // at this point, both arr[0..i-1] and arr[i..arr.length-1] // are sorted, and we know that every element in // arr[0..i-1] is less than or equal to every element in // arr[i..arr.length-1]. hence, the whole array is sorted i = 0; } i = i - 1; } // arr[0..arr.length-1] is sorted }

    Definition. In-place

    [comp1110-20]

      An algorithm is in-place if only modifies existing structures, rather than create new ones. For example, for sorting an in-place function returns void, as they don't produce a new array, they just modify an old one. All our sorting algorithms in this section are in-place.

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