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2023-2024年USACO首次月考题目出炉！白金级第三题真题及解析

Category: 国际竞赛, 翰林严选, 计算机国际竞赛 Date: 2024年1月2日上午11:29

2023-2024赛季的USACO考试已于12月18日正式结束，晋级赛的最新试题也已经公布。近日，USACO官方公布了2023-2024赛季首场月赛的晋级分数线。如果没有晋级，12月可以当做一个练手+熟悉赛制的环节，1、2月的月赛持续发力，USACO可以重复挑战。

今天给大家分享白金级试题和解析，参赛的同学来看看解题思路，没参赛的同学来看看难度如何？

USACO 2023年12月白金级第三题

**Note：The memory limit for this problem is 512MB, twice the default.**

Bessie has taken on a new job as a train dispatcher! There are two train stations：A and B. Due to budget constraints, there is only a single track connecting the stations. If a train departs a station at time t, then it will arrive at the other station at time t+T(1≤T≤10¹²).

There are N (1≤N≤5000) trains whose departure times need to be scheduled. The i th train must leave station s_iat time t_i or later (s_i∈{A,B},0≤t_i≤10¹²). It is not permitted to have trains going in opposite directions along the track at the same time (since they would crash). However, it is permitted to have many trains on the track going in the same direction at the same time (assume trains have negligible size).

Help Bessie schedule the departure times of all trains such that there are no crashes and the total delay is minimized. If train i is scheduled to leave at time a_i≥s_i, the total delay is defined as

INPUT FORMAT (pipe stdin)：

The first line contains N and T.

Then N lines follow, where the ith line contains the station s_i,
and time t_icorresponding to the ith train.

OUTPUT FORMAT (pipe stdout)：

The minimum possible total delay over all valid schedules.

SAMPLE INPUT：

1 95
B 63

SAMPLE OUTPUT：

The only train leaves on time.

SAMPLE INPUT：

4 1
B 3
B 2
A 1
A 3

SAMPLE OUTPUT：

1
There are two optimal schedules. One option is to have trains 2,3,4 leave on time and train 1 leave after a one-minute delay. Another is to have trains 1,2,3 leave on time and train 4 leave after a one-minute delay.

SAMPLE INPUT：

4 10
A 1
B 2
A 3
A 21

SAMPLE OUTPUT：

13
The optimal schedule is to have trains 1and 3 leave on time, train 2 leave at time 13, and train 4 leave at time 23. The total delay is 0+11+0+2=13.

SAMPLE INPUT：

8 125000000000
B 17108575619
B 57117098303
A 42515717584
B 26473500855
A 108514697534
B 110763448122
B 117731666682
A 29117227954

SAMPLE OUTPUT：

548047356974

SCORING：

Inputs 5-6： N≤15
Inputs 7-10： N≤100
Inputs 11-14： N≤500
Inputs 15-18： N≤2000
Inputs 19-24： No additional constraints
Problem credits： Brandon Wang

部分代码截图：