Tag:Differential constraint system
Article From:https://www.cnblogs.com/cangT-Tlan/p/9063621.html
Time Limit: 1000MS   Memory Limit: 65536K
Total Submissions: 13706   Accepted: 6581


Like everyone else, cows like to stand close to their friends when queuing for feed. FJ has N (2 <= N <= 1,000) cows numbered 1..N standing along a straight line waiting for feed. The cows are standing in the same order as they are numbered, and since they can be rather pushy, it is possible that two or more cows can line up at exactly the same location (that is, if we think of each cow as being located at some coordinate on a number line, then it is possible for two or more cows to share the same coordinate). 

Some cows like each other and want to be within a certain distance of each other in line. Some really dislike each other and want to be separated by at least a certain distance. A list of ML (1 <= ML <= 10,000) constraints describes which cows like each other and the maximum distance by which they may be separated; a subsequent list of MD constraints (1 <= MD <= 10,000) tells which cows dislike each other and the minimum distance by which they must be separated. 

Your job is to compute, if possible, the maximum possible distance between cow 1 and cow N that satisfies the distance constraints.


Line 1: Three space-separated integers: N, ML, and MD. 

Lines 2..ML+1: Each line contains three space-separated positive integers: A, B, and D, with 1 <= A < B <= N. Cows A and B must be at most D (1 <= D <= 1,000,000) apart. 

Lines ML+2..ML+MD+1: Each line contains three space-separated positive integers: A, B, and D, with 1 <= A < B <= N. Cows A and B must be at least D (1 <= D <= 1,000,000) apart.


Line 1: A single integer. If no line-up is possible, output -1. If cows 1 and N can be arbitrarily far apart, output -2. Otherwise output the greatest possible distance between cows 1 and N.

Sample Input

4 2 1
1 3 10
2 4 20
2 3 3

Sample Output



Explanation of the sample: 

There are 4 cows. Cows #1 and #3 must be no more than 10 units apart, cows #2 and #4 must be no more than 20 units apart, and cows #2 and #3 dislike each other and must be no fewer than 3 units apart. 

The best layout, in terms of coordinates on a number line, is to put cow #1 at 0, cow #2 at 7, cow #3 at 10, and cow #4 at 27.


USACO 2005 December Gold
Idea: differential constraint system.
The distance between u and V D is less than or equal to D, that is, V – u < = D. (2) the distance from u to V is greater than or equal to D, that is, u – V > = D. (3) a cow corresponds to a position, that is, u – V ≫ = 0.
Then the constraint relation can be listed and transformed into the shortest path problem. It
#define MAXN 1001000
using namespace std;
int n,ml,md,tot,flag;
int vis[MAXN],dis[MAXN],cnt[MAXN];
int to[MAXN],net[MAXN],cap[MAXN],head[MAXN]; 
void add(int u,int v,int w){ 
void spfa(){
        int now=que.front();
        for(int i=head[now];i;i=net[i])
                    if(++cnt[to[i]]>n){ printf("-1");exit(0); }
    if(dis[n]==2139062143)    printf("-2");
    else printf("%d",dis[n]);exit(0);
int main(){
    for(int i=1;i<=ml;i++){
        int a,b,d;
    for(int i=1;i<=md;i++){
        int a,b,d;
    for(int i=1;i<=n;i++)    add(i,i-1,0);


Link of this Article: POJ Layout

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