Finding the maximum: how it works

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

1. Which is the best way to start a maximum search on a list of values?

A Set Max to the first value in the list

B Set Max to the last value you check

2. Max is 14 and the next value is 9. What happens to Max?

A Max becomes 9

B Max stays 14

3. Max is 14 and the next value is 20. What happens to Max?

A Max becomes 20

B Max stays 14

4. Which line correctly replaces the maximum when a larger value is found?

A IF Num < Max THEN Max ← Num

B IF Num > Max THEN Max ← Num

5. The values are -5, -2, -9. Max is set to 0 before the loop. What is the result?

A Max stays 0, which is wrong because 0 is not in the data

B Max becomes -2, which is correct

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1Max ← Numbers[1]		AMax ← Num
2IF Numbers[Index] > Max THEN Max ← Numbers[Index]		BStarting Max at 0 fails when all values are negative. Max would stay 0, which is not in the list. Start with Max ← Numbers[1].
3Compare each later value with the largest so far by looping from the second item to the last		CReplace the largest value so far when a later value is bigger
4Keep the largest value seen so far in a variable which is updated when a bigger value is found		DStart the maximum with the first value in the list, so it is a real value from the data
5Max ← 0 FOR Index ← 1 TO 5 IF Numbers[Index] > Max THEN Max ← Numbers[Index] NEXT Index		EFOR Index ← 2 TO 5
6IF Num < Max THEN Max ← Num		FThe wrong comparison is used. < finds a smaller value, so this finds the minimum. It should be IF Num > Max.

Definitions

IF Num > Max THEN Max ← Num

Fill in the Blanks

Complete each line of code by filling in the missing parts.

Max ← Numbers[_]

Max ← Numbers[1] FOR Index ← _ TO 5

FOR Index ← 2 TO 5 IF Numbers[Index] _ Max THEN Max ← Numbers[Index]

IF Numbers[Index] > Max THEN Max ← Numbers[_____] ENDIF

NEXT Index OUTPUT "Largest: ", ___

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A Max ← Scores[1]

B FOR i = 2 TO 5

C IF Scores[i] > Max THEN

D Max ← Scores[i]

E ENDIF

F NEXT i

Question 2

A Max ← 0

B FOR i ← 2 TO 6

C IF Ages[i] > Max THEN

D Max ← Ages[i]

E ENDIF

F NEXT i

Question 3

A Max ← Weights[1]

B FOR i ← 2 TO 6

C IF Weights[i] > Max THEN

D Max ← i

E ENDIF

F NEXT i

Question 4

A Max ← Heights[1]

B FOR i ← 2 TO 8

C IF Heights[i] < Max THEN

D Max ← Heights[i]

E ENDIF

F NEXT i

Question 5

A Highest ← Temp[1]

B FOR n ← 2 TO 7

C IF Temp[n] > Highest THEN

D Highest ← Temp[1]

E ENDIF

F NEXT n

Answer Key

Finding the maximum: how it works

Section A: Quick Questions

A — Set Max to the first value in the list

B — Max stays 14

A — Max becomes 20

B — IF Num > Max THEN Max ← Num

A — Max stays 0, which is wrong because 0 is not in the data

Section B: Match the Pairs

Max ← Numbers[1] → Start the maximum with the first value in the list, so it is a real value from the data

IF Numbers[Index] > Max THEN Max ← Numbers[Index] → Replace the largest value so far when a later value is bigger

Compare each later value with the largest so far by looping from the second item to the last → FOR Index ← 2 TO 5

Keep the largest value seen so far in a variable which is updated when a bigger value is found → Max ← Num

Max ← 0 FOR Index ← 1 TO 5 IF Numbers[Index] > Max THEN Max ← Numbers[Index] NEXT Index → Starting Max at 0 fails when all values are negative. Max would stay 0, which is not in the list. Start with Max ← Numbers[1].

IF Num < Max THEN Max ← Num → The wrong comparison is used. < finds a smaller value, so this finds the minimum. It should be IF Num > Max.

Section C: Definitions

IF Num > Max THEN Max ← Num — Keep the largest value seen so far in Max. Start Max with the first value, then replace it whenever a later value is larger. Starting at 0 can fail if all values are negative.

Section D: Fill in the Blanks

Max ← Numbers[1]

Max ← Numbers[1]
FOR Index ← 2 TO 5

FOR Index ← 2 TO 5
   IF Numbers[Index] > Max THEN
      Max ← Numbers[Index]

IF Numbers[Index] > Max THEN
   Max ← Numbers[Index]
ENDIF

NEXT Index
OUTPUT "Largest: ", Max

Section E: Spot the Error

B — A FOR loop in Cambridge pseudocode sets its counter with the assignment arrow ←, not =. It should be FOR i ← 2 TO 5. The loop starts at 2 because Scores[1] is already in Max.

A — Starting Max at 0 can fail. If every value is negative, none will beat 0 and the wrong answer stays in Max. Max should start with the first value, Max ← Ages[1].

D — This stores the index i in Max, not the value found at that position. It should be Max ← Weights[i].

C — The < operator replaces Max with smaller values, so this finds the minimum. To find the maximum, the test must be Heights[i] > Max.

D — Highest is reset to the first value every time instead of the larger value just found. It should be Highest ← Temp[n].