time limit per test3 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
Recently Irina arrived to one of the most famous cities of Berland — the Berlatov city. There are n showplaces in the city, numbered from 1 to n, and some of them are connected by one-directional roads. The roads in Berlatov are designed in a way such that there are no cyclic routes between showplaces.
Initially Irina stands at the showplace 1, and the endpoint of her journey is the showplace n. Naturally, Irina wants to visit as much showplaces as she can during her journey. However, Irina’s stay in Berlatov is limited and she can’t be there for more than T time units.
Help Irina determine how many showplaces she may visit during her journey from showplace 1 to showplace n within a time not exceeding T. It is guaranteed that there is at least one route from showplace 1 to showplace n such that Irina will spend no more than T time units passing it.
Input
The first line of the input contains three integers n, m and T (2 ≤ n ≤ 5000, 1 ≤ m ≤ 5000, 1 ≤ T ≤ 109) — the number of showplaces, the number of roads between them and the time of Irina’s stay in Berlatov respectively.
The next m lines describes roads in Berlatov. i-th of them contains 3 integers ui, vi, ti (1 ≤ ui, vi ≤ n, ui ≠ vi, 1 ≤ ti ≤ 109), meaning that there is a road starting from showplace ui and leading to showplace vi, and Irina spends ti time units to pass it. It is guaranteed that the roads do not form cyclic routes.
It is guaranteed, that there is at most one road between each pair of showplaces.
Output
Print the single integer k (2 ≤ k ≤ n) — the maximum number of showplaces that Irina can visit during her journey from showplace 1 to showplace n within time not exceeding T, in the first line.
Print k distinct integers in the second line — indices of showplaces that Irina will visit on her route, in the order of encountering them.
If there are multiple answers, print any of them.
Examples
input
4 3 13
1 2 5
2 3 7
2 4 8
output
3
1 2 4
input
6 6 7
1 2 2
1 3 3
3 6 3
2 4 2
4 6 2
6 5 1
output
4
1 2 4 6
input
5 5 6
1 3 3
3 5 3
1 2 2
2 4 3
4 5 2
output
3
1 3 5
【题解】
记忆化搜搜。
设f[i][j]表示到达i这个点时,已经走过j个点所花费的最少时间。
用这个来做记忆化搜索即可。
从1号节点开始。
f初始化为一个很大的数。
输出方案的技巧可以膜拜一下。
#include <cstdio>
#include <cstring>
#include <vector>
#include <cstdlib>
using namespace std;
const int MAXN = 5500;
const long long INF = 1e15;
int n, m, ans = 0, xulie[MAXN], num = 0;
long long t;
long long f[MAXN][MAXN];
vector <int> a[MAXN];
vector <long long> w[MAXN];
bool oa = false;
bool dfs(int x, int num, long long cost)//把dfs设置为一个bool型,用于判断是否到达了n号节点且更新了答案。
{
if (f[x][num] <= cost)
return false;//如果没有比原来的优就不用继续搜了。
f[x][num] = cost;
if (x == n)
{
if (cost <= t && num > ans)
{
ans = num;
xulie[num] = x;
return true;
}
return false;
}
bool can = false;
int len = a[x].size();
for (int i = 0; i <= len - 1; i++)
{
int y = a[x][i];
if (dfs(y, num + 1, cost + w[x][i]))
{
xulie[num] = x;
can = true;
}
}
return can;
}
int main()
{
//freopen("F:\rush.txt", "r", stdin);
scanf("%d%d%I64d", &n, &m, &t);
for (int i = 1; i <= m; i++)
{
int x, y;
long long z;
scanf("%d%d%I64d", &x, &y, &z);
a[x].push_back(y);
w[x].push_back(z);
}
memset(f, 127 / 3, sizeof(f));
int len = a[1].size();
xulie[1] = 1;
for (int i = 0; i <= len - 1; i++)
{
int y = a[1][i];
dfs(y, 2, w[1][i]);
}
printf("%d
", ans);
for (int i = 1; i <= ans - 1; i++)
printf("%d ", xulie[i]);
printf("%d
", xulie[ans]);
return 0;
}