POJ 2983 差分约束系统
2016-04-30 00:25
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题目
Is the Information Reliable?Time Limit: 3000MS Memory Limit: 131072K
Total Submissions: 12490 Accepted: 3930
Description
The galaxy war between the Empire Draco and the Commonwealth of Zibu broke out 3 years ago. Draco established a line of defense called Grot. Grot is a straight line with N defense stations. Because of the cooperation of the stations, Zibu’s Marine Glory cannot march any further but stay outside the line.
A mystery Information Group X benefits form selling information to both sides of the war. Today you the administrator of Zibu’s Intelligence Department got a piece of information about Grot’s defense stations’ arrangement from Information Group X. Your task is to determine whether the information is reliable.
The information consists of M tips. Each tip is either precise or vague.
Precise tip is in the form of P A B X, means defense station A is X light-years north of defense station B.
Vague tip is in the form of V A B, means defense station A is in the north of defense station B, at least 1 light-year, but the precise distance is unknown.
Input
There are several test cases in the input. Each test case starts with two integers N (0 < N ≤ 1000) and M (1 ≤ M ≤ 100000).The next M line each describe a tip, either in precise form or vague form.
Output
Output one line for each test case in the input. Output “Reliable” if It is possible to arrange N defense stations satisfying all the M tips, otherwise output “Unreliable”.
Sample Input
3 4
P 1 2 1
P 2 3 1
V 1 3
P 1 3 1
5 5
V 1 2
V 2 3
V 3 4
V 4 5
V 3 5
Sample Output
Unreliable
Reliable
题意
给出两个指令,P A B X ,表示a在b的前面x米。V A B ,A在B前面不知道多少米。问这些信息有没有矛盾
题解
有d[a]-d[b]=X
这个结果可以用两个不等式表示
d[a]-d[b]>=x&&d[a]-d[b]<=x
a至少在b前1米
即d[a]>=d[b]+1
按这些约束条件进行Bllman-ford
*用c++提交AC,用G++提交RE
#define _CRT_SECURE_NO_WARNINGS #include <iostream> #include <cstdio> #include <cstring> #include <algorithm> #include <stack> #include <string> #include <set> #include <cmath> #include <map> #include <queue> #include <sstream> #include <vector> #include <iomanip> #define m0(a) memset(a,0,sizeof(a)) #define mm(a) memset(a,0x3f,sizeof(a)) #define m_1(a) memset(a,-1,sizeof(a)) #define f(i,a,b) for(i = a;i<=b;i++) #define fi(i,a,b) for(i = a;i>=b;i--) #define lowbit(a) ((a)&(-a)) #define FFR freopen("data.in","r",stdin) #define FFW freopen("data.out","w",stdout) #define INF 0x3f3f3f3f typedef long long ll; typedef long double ld; const ld PI = acos(-1.0); using namespace std; #define SIZE ( ) struct Edge { int u, v, k; }; struct Edge1 { Edge edge[100000 + 10]; int cnt; void push_back(int u, int v, int k) { edge[cnt].u = u; edge[cnt].v = v; edge[cnt].k = k; cnt++; } }; Edge1 G; int d[1234]; int main() { //ios_base::sync_with_stdio(false); cin.tie(0); int n, m; while (~scanf("%d%d",&n,&m)) { char s[5]; int i,j; G.cnt = 0; f(i, 1, m) { scanf("%s", s); if ('P' == s[0]) { int u, v, k; scanf("%d%d%d", &u, &v, &k); G.push_back(u, v, -k); G.push_back(v, u, k); } else { int u, v; scanf("%d%d", &u, &v); G.push_back(u, v, -1); } } m0(d); int ok = 0; f(i, 1, n) { ok = 0; f(j, 0, G.cnt - 1) { if(d[G.edge[j].v] > d[G.edge[j].u] + G.edge[j].k){ d[G.edge[j].v] = d[G.edge[j].u] + G.edge[j].k; ok = 1; } } if(!ok){ ok = 1; break; } } if (i<=n) printf("Reliable\n"); else printf("Unreliable\n"); } return 0; }
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