【UVa】11456 - Trainsorting

Problem here

Problem

Erin is an engineer. She drives trains. She also arranges the cars within each train. She prefers to 
put the cars in decreasing order of weight, with the heaviest car at the front of the train. 
Unfortunately, sorting train cars is not easy. One cannot simply pick up a car and place it somewhere 
else. It is impractical to insert a car within an existing train. A car may only be added to the beginning 
and end of the train. 
Cars arrive at the train station in a predetermined order. When each car arrives, Erin can add it 
to the beginning or end of her train, or refuse to add it at all. The resulting train should be as long as 
possible, but the cars within it must be ordered by weight. 
Given the weights of the cars in the order in which they arrive, what is the longest train that Erin 
can make?

INPUT

The first line is the number of test cases to follow. The test cases follow, one after another; the format 
of each test case is the following: 
The first line contains an integer 0 ≤ n ≤ 2000, the number of cars. Each of the following n lines 
contains a non-negative integer giving the weight of a car. No two cars have the same weight.

OUTPUT

Output a single integer giving the number of cars in the longest train that can be made with the given 
restrictions.

SAMPLE

input

1 
3 
1 
2 
3

output

3

Solution

LIS + LDS -1 
這裡-1因為LIS和LDS的起點會重複

#include <iostream>
#include <vector>
#include "memory.h"
using namespace std;

int train[2000];
int len[2000];
int len2[2000];
int tn;

int main(){
    int t;
    while(cin >> t){
        while(t--){
            cin >> tn;
            for(int i = tn-1; i >= 0; i--){
                len[i] = 1;
                len2[i] = 1;
                int tmp;
                cin >> tmp;
                train[i] = tmp;
            }
            for(int i = 0; i < tn; i++){
                for(int j = i+1; j < tn; j++){
                    if(train[i] < train[j]){
                        len[j] = max(len[j], len[i]+1);
                    }
                    if(train[i] > train[j]){
                        len2[j] = max(len2[j], len2[i]+1);
                    }
                }
            }
            int result = 0;
            for(int i = 0; i < tn; i++){
                result = max(result, len[i]+len2[i]-1);
            }
            cout << result << endl;
        }
    }

    return 0;
}