© Peter Andreae

CS4HS

Algorithms

• Searching for an item in a list• Sorting a list• Searching for a word in text• Analysing Networks.

© Peter Andreae

CS4HS

Searching in a list.

• “Find the name ‘Stevens, D’ in the list”• What algorithm should you use?• Linear Search for target item

from position 1 to position 300if item at the position is target, exit with “found”

exit with “not found”• Binary Search

lower ← 1, upper ← 300, while (lower ≤ upper)

position ← (upper + lower)/2if target is at position: exit with “found”if target < item at position: upper = position-1if target > item at position: lower = position + 1

exit with “not found”

© Peter Andreae

CS4HS

Searching in a list.

• Interpolation Search for target itemlower ← 1, upper ← 300, while (lower ≤ upper)

position ← compute estimate of position of target based on items at lower and upper

if target = item at position: exit with “found”if target < item at position: upper = position-1if target > item at position: lower = position + 1

exit with “not found”

fraction ← (target – item@lower)/(item@upper – item@lower) position ← lower + fraction ∗ (upper-lower)

© Peter Andreae

CS4HS

Sorting a list of items?

• Which algorithm did you use?• Insertion Sort

• insert each item in turn into its right place in the growing list• Selection Sort

• Repeatedly find the smallest (or largest) and put it next in the sorted list• Radix Sort

• Put items in piles based on the first letter• Sort each pile

• Quick Sort• Separate into lists of the smaller items and larger items,

(by comparing each item to the first item – “pivot”)• Sort each list

• Merge Sort• Lay out items as a sequence of of one item lists• Repeatedly merge adjacent lists into larger lists.

© Peter Andreae

CS4HS

Analysing Networks

• Minimum “Spanning Trees”• How could I connect all these towns by fibre optic cables at the minimum cost!

(cost might depend on distance, terrain, and land ownership)

• Shortest Path from here to there• How does Google maps find the shortest path in the network of roads?• How do the NPC’s in games work out where to go?

• Lots more “graph” algorithms• Articulation Points

• critical nodes that would disconnect the network• Maximum Flow

• given a network of railways/pipes/… with maximum capacities, what is the maximum amount of freight/oil/… that can be pushed through the network from A to B.

© Peter Andreae

CS4HS

Find Minimum Spanning Tree.

6

4

5

9

4

1

5

83

7

3

8

976

6

9

25

2

35

7

6

4

1

8 3

4

9

5

2

8

8

5

7

927

5

4 67

3

2

3

5

984

26

2

5 33 4

45

2

7

8

6

98

62

3

7

2

9

© Peter Andreae

CS4HS

Minimum Spanning Tree

• How did you do it?

• Prim’s Algorithm:• Build connected subset outwards,

always adding the smallest edge to an unconnected node

• Kruskal’s Algorithm:• Add the next smallest edge that doesn’t make a loop

(have to keep track of the connected subsets)

© Peter Andreae

CS4HS

Find shortest path in graph.

6

4

5

9

4

1

5

83

7

3

8

976

6

9

25

2

35

7

6

4

1

8 3

4

9

5

2

8

8

5

7

927

5

4 67

3

2

3

5

984

26

2

5 33 4

4

5

2

7

8

6

98

62

Start

End

3

7

© Peter Andreae

CS4HS

Shortest Path

• How did you do it?

• Dijkstra’s Algorithm:• Build connected subset outwards,

always adding the edge for the shortest PATH to unconnected node • Stop when you reach the goal

• A* search Algorithm:• Same as Dijkstra, but have heuristic look ahead to aim towards goal.