# UVALive-5906 Smoking Gun (differential constrained system + topological sequencing)

Source: Internet
Author: User

The main topic: give n personal coordinates and m to hear the order of gunfire, ask if there is a shooting order to meet the m conditions, is a or how much?

Problem-solving ideas: A typical differential constraint system, set I personal firing time for TI
Suppose a hears a B's gunshot, and then hears the C gunshot.
Then we need to meet a condition.
TB + DIS (A, b) <= tc + DIS (a,c) (this is supposed to be divided by the Sonic, but omitted here)
By this inequality constructs the edge, the concrete construction does not say, understands the differential restraint system the metropolis constructs, if not, proves that you do not know very much
Then judge, if there is a ring, that the condition cannot be fully established
In the case of conditions, topology, if the topology fails, indicating that there are multiple shooting order, if successful, there is only one

``#include <cstdio>#include <cstring>#include <iostream>#include <map>#include <vector>#include <cmath>#include <queue>#include <set>using namespace STD;#define N#define M 1010structnode{stringSintx, y;} Node[n];structedge{intU, V, next;DoubleC;} E[M]; Map<string,int>Name vector<int>Vec[n]; Set<int>Tuopu;intN, m, tot;intHead[n];CharStr1[n], Str2[n], str3[n];voidAddedge (intUintVDoublec) {e[tot].u = u; E[TOT].V = v; E[TOT].C = C; E[tot].next = Head[u]; Head[u] = tot++;}DoubleDistanceintIintj) {intx = node[i].x-node[j].x;inty = node[i].y-node[j].y;return sqrt(1.0* x * x +1.0* y * y);}voidInit () {scanf("%d%d", &n, &m);    Name.clear (); Tuopu.clear ();stringS1, S2, S3;intx, y; for(inti =1; I <= N; i++) {Cin>> node[i].s >> node[i].x >> node[i].y;         NAME[NODE[I].S] = i;    Vec[i].clear (); }memset(Head,-1,sizeof(head)); tot =0;//U + dist1 <= v + dist2     for(inti =0; I < m; i++) {scanf('%s heard%s firing before%s ', str1, str2, STR3); S1 = str1; s2 = str2; s3 = STR3;DoubleDist1 = Distance (Name[s2], name[s1]);DoubleDist2 = Distance (Name[s3], name[s1]);intU = name[s2];intv = name[s3];        Tuopu.insert (U);        Tuopu.insert (v);    Addedge (V, U, dist2-dist1); }}#define INF 0x3f3f3f3f#define ESP 1e-8DoubleD[n];BOOLVis[n];intIn[n], cnt[n];BOOLSPFA (ints) {memset(CNT,0,sizeof(CNT));memset(Vis,0,sizeof(VIS)); for(inti =1; I <= N; i++) D[i] = INF; Queue<int>Q; D[s] =0; Q.push (s); while(! Q.empty ()) {intU = Q.front (); Q.pop (); for(inti = Head[u]; ~i; i = e[i].next) {intv = e[i].v;if(D[v] > D[u] + ESP + e[i].c) {D[v] = D[u] + e[i].c;if(!vis[v]) {Vis[v] =true; Q.push (v);if(++cnt[v] >= N)return false; }}} Vis[u] =false; } for(inti =1; I <= N; i++)if(D[i] <-ESP)            {Vec[i].push_back (s);            in[s]++;        Tuopu.erase (s); }return true;}voidSolve () {memset(In,0,sizeof(in)); for(inti =1; I <= N; i++)if(!SPFA (i)) {printf("impossible\n");return; } Queue<int>Ans while(Tuopu.size ()) {if(Tuopu.size () >1) {printf("unknown\n");return; }intt = *tuopu.begin ();        Ans.push (t); Tuopu.erase (t); for(inti =0; I < vec[t].size (); i++) {--in[vec[t][i]];if(In[vec[t][i]] = =0) Tuopu.insert (Vec[t][i]); }    }cout<< Node[ans.front ()].s; Ans.pop (); while(!ans.empty ()) {cout<<" "<< Node[ans.front ()].s;    Ans.pop (); }printf("\ n");}intMain () {intTestscanf("%d", &test); while(test--)        {init ();    Solve (); }return 0;}``

UVALive-5906 Smoking Gun (differential constrained system + topological sequencing)

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