Algorithm: UVA 1391 Astronauts (2-sat + output scheme)

"The main effect of the topic"

There are n astronauts who, by age, are younger than the average age, and older than the average age are experienced astronauts.

Now to allocate them to a,b,c three space stations, where a station only experienced astronauts to go, and B station is only young to go, C station can go.

M is a nuisance to the astronauts and cannot allow them to work on the same space station.

The output of each astronaut should be assigned to which space station, if not the output no solution.

Ideas

For each astronaut, he has only two places to go: C or non-C (if Young is B, sophisticated is a), so it is two to choose one, you can think of 2-sat decision problem.

When the edge is built, it can be divided into good condition plus edge. And then there's the template set.

Code

#include <iostream> #include <queue> #include <cstdio> #include <cstring> #define WHITE-1  
    
    
#define RED 1 #define BLUE 0 using namespace std;  
const int INF = 0X3F3F3F3F;  
const int MAXN = 100010;  
const int VN = MAXN*2;  
    
const int EN = VN*5;  
int n, m;  
int AGE[MAXN];  
    
int sum;  
    struct graph{int size, HEAD[VN]; Struct{int u, V, next;  
    E[en];  
    void Init () {size=0; memset (Head,-1, sizeof (head));}  
        void Addedge (int u, int v) {e[size].u = u;  
        E[SIZE].V = v;  
        E[size].next = Head[u];  
    Head[u] = size++;  
    
}}g, G1;  
        Class tow_sat{Public:bool Check () {SCC ();  
        for (int i=0; i<n; ++i) if (belong[i] = = Belong[i+n]) return false;  
    return true;  
        } void Toposort () {g1.init ();  
        memset (indeg, 0, sizeof (INDEG)); for (int i=0; i<n; ++i) {Opp[beLong[i]] = belong[i+n];  
        Opp[belong[i+n]] = belong[i];  
            for (int e=0; e<g.size; ++e) {int u = belong[g.e[e].u];  
            int v = belong[g.e[e].v];  
            if (u==v) continue;  
            ++indeg[u];  
        G1.addedge (V, u);  
        } queue<int>que;  
        memset (color, white, sizeof (color));  
            
        for (int i=1; i<=bcnt; ++i) if (!indeg[i)) Que.push (i);  
            while (!que.empty ()) {int u = que.front ();  
            Que.pop ();  
            if (Color[u]!= white) continue;  
            Color[u] = RED;  
            Color[opp[u]] = BLUE; for (int e=g1.head[u]; e!=-1; e=g1. E[e].next) {int v=g1.  
                E[E].V;  
            if (--indeg[v] = = 0) que.push (v); }//output for (int i=0; i<n; ++i) {if (color[belong[i)] = = RED) {if (Age[i]*n < sum) puts ("B");  
            Else puts ("A");  
            }else{puts ("C");  
        }} private:void Tarjan (const int u) {int V;  
        Dfn[u] = low[u] = ++idx;  
        Instack[u] = true;  
        sta[top++] = u;  
            for (int e=g.head[u]; E!=-1 e=g.e[e].next) {v = g.e[e].v;  
            if (dfn[v] = = 1) Tarjan (v), Low[u]=min (Low[u), low[v]);  
        else if (Instack[v]) low[u]=min (Low[u], dfn[v]);  
            } if (low[u] = = Dfn[u]) {++bcnt;  
                do{V=sta[--top];  
                INSTACK[V] = false;  
            BELONG[V] = bcnt;  
        }while (U!= v);  
        } void SCC () {idx = bcnt = top = 0;  
        memset (instack, 0, sizeof (instack));  
        memset (DFN,-1, sizeof (DFN));  
for (int i=0; i<2*n; ++i) if (dfn[i] = = 1)                Tarjan (i);  
    } private:int idx, top, bcnt;  
    int LOW[VN],DFN[VN],BELONG[VN],STA[VN];  
    BOOL INSTACK[VN];  
int COLOR[VN], indeg[vn], OPP[VN];  
    
}sat;  
        int main () {while (~scanf ("%d%d", &n, &m) && n+m) {sum = 0;  
            for (int i=0; i<n; ++i) {scanf ("%d", &age[i]);  
    
        Sum + + age[i];  
        } g.init ();  
        int A, B;  
            for (int i=0; i<m; ++i) {scanf ("%d%d", &a, &b); --a;  
            --b;  
                if (Age[a]*n < sum && age[b]*n < sum) {//small, small G.addedge (A, b+n);  
                G.addedge (a+n, b);  
                G.addedge (b, a+n);  
            G.addedge (B+n, a);  
                }else if (Age[a]*n < sum && age[b]*n >= sum) {//small, large G.addedge (a+n, b);  
            G.addedge (B+n, a); }else if (age[a]*n >= sum &&  
                Age[b]*n < sum) {//large, small G.addedge (a+n, b);  
            G.addedge (B+n, a);  
                }else{//Large, large G.addedge (A, b+n);  
                G.addedge (a+n, b);  
                G.addedge (b, a+n);  
            G.addedge (B+n, a);  
        } if (!sat.check ()) puts ("No solution.");  
    else Sat.toposort ();  
return 0; }

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