【luogu P1993 小K的农场】 题解
题目链接:https://www.luogu.org/problemnew/show/P1993
1.差分约束:
对于a - b <= c 有一条 b——>a 权值为c
对于a - b >= c 有一条 a——>b 权值为-c
对于一个差分约束系统,若存在负环则无解
2.dfs版SPFA判负环
#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define ri register
using namespace std;
const int maxn = 100000 + 10;
const int inf = 0x7fffffff;
int n, m, dis[maxn], vis[maxn];
queue<int> q;
struct edge{
int from, to, next, len;
}e[maxn<<2];
int head[maxn], cnt;
void add(int u, int v, int w)
{
e[++cnt].from = u;
e[cnt].len = w;
e[cnt].next = head[u];
e[cnt].to = v;
head[u] = cnt;
}
bool SPFA(int now)
{
vis[now] = 1;
for(int i = head[now]; i != -1; i = e[i].next)
{
if(dis[e[i].to] > dis[now] + e[i].len)
{
dis[e[i].to] = dis[now] + e[i].len;
if(!vis[e[i].to])
{
if(!SPFA(e[i].to)) return 0;
}
else return 0;
}
}
vis[now] = 0;
return 1;
}
int main()
{
memset(head, -1, sizeof(head));
scanf("%d%d",&n,&m);
for(ri int i = 1; i <= n; i++)
{
add(0, i, 0);dis[i] = inf;
}
for(ri int i = 1; i <= m; i++)
{
int u, v, w, opt;
scanf("%d",&opt);
if(opt == 1)
{
scanf("%d%d%d",&u,&v,&w);
add(u, v, -w);
}
if(opt == 2)
{
scanf("%d%d%d",&u,&v,&w);
add(v, u, w);
}
if(opt == 3)
{
scanf("%d%d",&u,&v);
add(v, u, 0);
add(u, v, 0);
}
}
if(!SPFA(0))
printf("No\n");
else
printf("Yes\n");
return 0;
}
隐约雷鸣,阴霾天空,但盼风雨来,能留你在此。
隐约雷鸣,阴霾天空,即使天无雨,我亦留此地。
![](https://images.cnblogs.com/cnblogs_com/MisakaAzusa/1169114/o_a0c3752e09f79052b15f108c0cf3d7ca7acbd5b0.gif)