Finding the max. value in a list

Which of the following flowcharts correctly represents an algorithm for finding the maximum value—labeled max—in a list L? (Note: More than one flowchart may be correct.)

For example:

• if L = [1, 2, 3, 4, 5], the algorithm should output 5.
• if L = [5, 4, 3, 2, 1], the algorithm should output 5.
• if L = [1, 3, 2, 5, 4], the algorithm should output 5.
• if L = [5, 6], the algorithm should output 6.

You can consider that the list L:

• Is non-empty and contains at least two elements.
• Is indexed starting from 0.

Choose the correct flowchart from the options below:

• Flowchart in Figure 1 (a)
• Flowchart in Figure 1 (b)
• Flowchart in Figure 1 (c)
• Flowchart in Figure 1 (d)
• Flowchart in Figure 1 (e)

Figure 1 groups the five candidate flowcharts for comparison.

graph LR
    accTitle: Maximum-value candidate A
    accDescr: The maximum starts at the first list value, the index starts at one, and larger later values replace the maximum.
    A((Start)) --> IN[/L/]
    IN --> B[Set max to<br>first element]
    B --> C[Set i to 1]
    C --> D{"Is i<br>less than<br>L length?"}
    D -- No --> E[/Output max/]
    D -- Yes --> F{"Is L[i]<br>greater<br>than max?"}
    F -- Yes --> G["Set max<br>to L[i]"]
    F -- No --> H[Increment i by 1]
    G --> H
    H --> D
    E --> I((End))

(a) Candidate A.

graph LR
    accTitle: Maximum-value candidate B
    accDescr: The maximum starts at the first list value, the index starts at zero, and each larger value replaces the maximum.
    A((Start)) --> IN[/L/]
    IN --> B[Set max to<br>first element]
    B --> C[Set i to 0]
    C --> D{"Is i<br>less than<br>L length?"}
    D -- No --> E[/Output max/]
    D -- Yes --> F{"Is L[i]<br>greater<br>than max?"}
    F -- Yes --> G["Set max<br>to L[i]"]
    F -- No --> H[Increment i by 1]
    G --> H
    H --> D
    E --> I((End))

(b) Candidate B.

graph LR
    accTitle: Maximum-value candidate C
    accDescr: The maximum starts at zero and the index at one. Until the index is greater than the list length, a larger value at the index replaces the maximum and the index increases by one.
    A((Start)) --> IN[/L/]
    IN --> B[Set max to 0]
    B --> C[Set i to 1]
    C --> D{"Is i<br>greater than<br>L length?"}
    D -- Yes --> E[/Output max/]
    D -- No --> F{"Is L[i]<br>greater<br>than max?"}
    F -- Yes --> G["Set max<br>to L[i]"]
    F -- No --> H[Increment i by 1]
    G --> H
    H --> D
    E --> I((End))

(c) Candidate C.

graph LR
    accTitle: Maximum-value candidate D
    accDescr: The maximum starts at zero and the index at zero. While the index is less than the list length, a smaller value at the index replaces the maximum and the index increases by one.
    A((Start)) --> IN[/L/]
    IN --> B[Set max to 0]
    B --> C[Set i to 0]
    C --> D{"Is i<br>less than<br>L length?"}
    D -- No --> E[/Output max/]
    D -- Yes --> F{"Is L[i]<br>less than<br>max?"}
    F -- Yes --> G["Set max to L[i]"]
    F -- No --> H[Increment i by 1]
    G --> H
    H --> D
    E --> I((End))

(d) Candidate D.

graph LR
    accTitle: Maximum-value candidate E
    accDescr: The maximum starts at the first list value and the index at one. Until the index equals the list length, a smaller value at the index replaces the maximum and the index increases by one.
    A((Start)) --> IN[/L/]
    IN --> B[Set max to<br>first element]
    B --> C[Set i to 1]
    C --> D{"Is i<br>equal to<br>L length?"}
    D -- Yes --> E[/Output max/]
    D -- No --> F{"Is L[i]<br>less than<br>max?"}
    F -- Yes --> G["Set max<br>to L[i]"]
    F -- No --> H[Increment i by 1]
    G --> H
    H --> D
    E --> I((End))

(e) Candidate E.

Figure 1: Finding the Maximum Value in a List (Question 1).