P1986 元旦晚会

模板题，不讲太多。

---

同样是两个式子：

\[a[r] - a[l] \geq k \]

和

\[0 \leq a[i] - a[i - 1] \leq 1 \]

建边之后，从0点为起点找最长路就对了。

差分约束差不多也就学到这里了。

代码：

#include<cstdio>
#include<cstring>
#include<queue>

const int maxn = 30005, maxm = 5005;
// s[r] - s[l - 1] >= k
// dist[v] >= dist[u] + e[i].weight
// longest path problem
// 0 <= s[i] - s[i - 1] <= 1
// s[i] - s[i - 1] >= 0
// s[i - 1] - s[i] >= -1
struct Edges
{
    int next, to, weight;
} e[maxm << 2];
int head[maxn], tot;
int n, m; 
std::queue<int> q;
bool vis[maxn];
int dist[maxn];
int read()
{
    int ans = 0, s = 1;
    char ch = getchar();
    while(ch > '9' || ch < '0')
    {
        if(ch == '-') s = -1;
        ch = getchar();
    }
    while(ch >= '0' && ch <= '9')
    {
        ans = ans * 10 + ch - '0';
        ch = getchar();
    }
    return s * ans;
}
void link(int u, int v, int w)
{
    e[++tot] = (Edges){head[u], v, w};
    head[u] = tot;
}
void spfa(int s)
{
    for(int i = 0; i <= n; i++) dist[i] = -19260817;
    dist[s] = 0;
    q.push(s); vis[s] = true;
    while(!q.empty())
    {
        int u = q.front(); q.pop(); vis[u] = false;
        for(int i = head[u]; i; i = e[i].next)
        {
            int v = e[i].to;
            if(dist[u] + e[i].weight > dist[v])
            {
                dist[v] = dist[u] + e[i].weight;
                if(!vis[v])
                {
                    q.push(v); vis[v] = true;
                }
            }
        }
    }
}
int main()
{
    n = read(), m = read();
    while(m--)
    {
        int l = read(), r = read(), k = read();
        link(l - 1, r, k);
    }
    for(int i = 1; i <= n; i++)
    {
        link(i - 1, i, 0);
        link(i, i - 1, -1);
    }
    spfa(0);
    printf("%d\n", dist[n]);
    return 0;
}