CSC3100 Data Structures

Programming Assignment 2

Assignment Link: http://oj.cuhk.edu.cn/contest/csc310023falla2

Access Code: 7d2x0Zs8

1 Battle Game (40% of this assignment)

1.1 Description

Imagine a group of n players that are located in different floors. The i-th player (for each i such that

1 ≤ i ≤ n, where i is an integer) is characterized by the following:

• pi

, a unique starting floor level

• hi

, a starting HP (Health Points) value

• di

, a direction of movement, either U indicating that the i-th player is going upward or D indicating

that the i-th player is going downward

All players move simultaneously at the same speed in their respective directions. When two players

meet, they engage in a battle. The player with the lower health is eliminated instantaneously, while

the other continue to move in the same direction at the same speed but with a reduced HP by 1. In a

case where two players have identical HP, they are both eliminated simultaneously after the battle.

Your task is to determine the final HP of the surviving players.

1.2 Input

The first line of input contains an integer n, representing the number of players.

The next n lines follow.

The i-th line contains three values: pi

, hi

, di – an integer representing the starting floor level for the

i-th player, an integer representing the HP value for the i-th player, and a character representing the

direction of movement for the i-th player.

1.3 Output

For each surviving player, output their remaining HP on a separate line, in the order of their input.

Sample Input 1

5

5 11 U

4 15 U

3 17 U

2 77 U

1 30 U

Sample Output 1

11

15

17

77

30

4

Sample Input 2

5

5 3 U

4 7 D

1 5 U

3 5 D

8 6 U

Sample Output 2

3

7

6

The following figures show the visual representations for both input samples in their initial positions,

respectively.

Problem Scale & Subtasks

For 100% of the test cases:

• 1 ≤ n ≤ 106

• 1 ≤ pi ≤ 108

(for each i such that 1 ≤ i ≤ n)

• 1 ≤ hi ≤ 100 (for each i such that 1 ≤ i ≤ n)

• di ∈ {U, D} (for each i such that 1 ≤ i ≤ n)

Test Case No. Constraints

1-4 n ≤ 1 000

5-8 n ≤ 10 000

9-10 No additional constraints

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2 Buried Treasure (50% of this assignment)

2.1 Description

Jack Sparrow, the legendary pirate of the Seven Seas, sets sail to an inhabited island in search of a

buried treasure. Guided by his map, he believes the treasure lies within a weird-looking trench. The

trench stretches across a width of n. For any given point from i − 1 to i on the trench’s x-coordinate,

the depth is represented by di (for each i such that 1 ≤ i ≤ n, where i is an integer).

Jack is wondering about the size of the largest treasure that could possibly fit inside the trench.

Wanting to maximize his haul, he turns to you, a trusted member of his crew, to make the calculations.

By largest, Jack means the maximum area – the product of width and height – of the rectangular

treasure chest that can be buried within the trench’s confines. For example, the following figure shows

the largest possible treasure that can fit in a trench with n = 8 and d = [6, 2, 5, 4, 5, 1, 4, 4].

Could you give these calculations a look for our legendary pirate?

2.2 Input

The first line contains an integer T, representing the number of Jack Sparrow’s queries.

The descriptions of T queries follow.

Each query is described in the following format:

• The first line contains an integer n representing the width of the trench.

• The second line contains n integers separated by a space representing the depths of the trench.

2.3 Output

Output T lines. The j-th line contains the answer to the j-th query.

Sample Input 1

2

8

6 2 5 4 5 1 4 4

3

2 7 4

Sample Output 1

12

8

6

Problem Scale & Subtasks

For 100% of the test cases:

• 1 ≤ T ≤ 10

• 1 ≤ n ≤ 106

• 1 ≤ di ≤ 106

(for each i such that 1 ≤ i ≤ n)

• The sum of n over all queries, denoted as N, does not exceed 106

in each test case.

Test Case No. Constraints

1-2 n ≤ 10

3-4 n ≤ 1 000

5-8 N ≤ 10 000

9-10 No additional constraints

Hint

Hint 1: For C/C++ and Java users, an int type stores integers range from -2,147,483,648 to 2,147,483,647.

It may be too small for this problem. You need other data types, such as long long for C/C++ and

long for Java. They store integers ranging from -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807.

Use scanf(“%lld”,&n) for C, cin>>n for C++ and n = scanner.nextLong() for Java to output the

answer query. And the other operations for long and long long are quite same as int.

Hint 2: Sailing through the vast expanse of the Seven Seas, Jack Sparrow found himself drawn to an

intriguing map. Tantalized by the prospect of hidden riches, he anchored near a mysterious island

with an unusual trench. As he examined the trench’s varying depths, he pondered the size of the

treasure that might be buried within. Carefully, he sought the counsel of a trusted crew member to

calculate the chest’s potential dimensions. Knowing the importance of this task, the crew member

took to the challenge, hoping to maximize the treasure for their legendary captain.

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