Worked Examples: Correctness of Algorithms

These examples are designed to step through the logical process of applying the algorithmic concepts.

Example 1: Sum Array

❓ Problem: Invariant for code summing array A.

💡 Solution: At start of loop i, 'sum' equals sum of A[0..i-1].

Example 2: Max Finding

❓ Problem: Invariant for Finding Max.

💡 Solution: 'max' holds largest value in A[0..i-1].

Example 3: Selection Sort

❓ Problem: State Invariant.

💡 Solution: Subarray A[0..i-1] contains the i smallest elements in sorted order.

Example 4: Binary Search

❓ Problem: State Invariant.

💡 Solution: If target exists, it is in A[low..high].

Example 5: Termination

❓ Problem: Why does Binary Search terminate?

💡 Solution: Range size (high-low) decreases strictly monotonically.

Example 6: Bubble Sort

❓ Problem: State Invariant (Outer loop).

💡 Solution: Subarray A[n-i..n] contains the i largest elements in sorted order.