UVALive3713-Astronauts (2-Sat)

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Task A, Task B, and task C3 are assigned to N astronauts, and each of them is assigned a task. Assume that the average age of N astronauts is X. Only those older than X can receive task a. Only those younger than X can receive Task B. Task C is not limited. M hates each other and therefore cannot assign the same task. Determine whether the task plan can be found.

Idea: Use XI to represent the allocation plan of the I-th astronaut. If the age is greater than or equal to X, you can select a (xi = true) and C (XI + 1 = false). If the age is light rain X, you can select B (xi = true) and C (XI + 1 = false ). Consider an annoying pair of Astronauts. If they do not belong to the same category, they can be Xi v XJ, that is, either of them must be true. If they belong to the same category, use two statements to represent Xi v XJ and ,~ Xi v ~ XJ, that is, the former indicates true, and the latter indicates false.

Code:

#include<cstdio>#include<vector>#include<cstring>#include<algorithm>using namespace std;const int maxn = 100005;struct TwoSAT {    int n;    vector<int> G[maxn*2];    bool mark[maxn*2];    int S[maxn*2], c;    bool dfs(int x) {        if (mark[x^1]) return false;        if (mark[x]) return true;        mark[x] = true;        S[c++] = x;        for (int i = 0; i < G[x].size(); i++)            if (!dfs(G[x][i])) return false;        return true;    }    void init(int n) {        this->n = n;        for (int i = 0; i < n*2; i++)             G[i].clear();        memset(mark, 0, sizeof(mark));    }        //x = xval or y = yval    void add_clause(int x, int xval, int y, int yval) {        x = x * 2 + xval;        y = y * 2 + yval;        G[x^1].push_back(y);        G[y^1].push_back(x);    }    bool solve() {        for(int i = 0; i < n*2; i += 2)            if(!mark[i] && !mark[i+1]) {                c = 0;                if(!dfs(i)) {                    while(c > 0) mark[S[--c]] = false;                    if(!dfs(i+1)) return false;                }            }        return true;    }};TwoSAT solver;int n, m, total_age, age[maxn];int is_young(int x) {    return age[x] * n < total_age;}int main() {    while(scanf("%d%d", &n, &m) == 2 && n) {        total_age = 0;        for(int i = 0; i < n; i++) {             scanf("%d", &age[i]);             total_age += age[i];         }        solver.init(n);        for(int i = 0; i < m; i++) {            int a, b;            scanf("%d%d", &a, &b);             a--;             b--;            if(a == b) continue;            solver.add_clause(a, 1, b, 1);            if(is_young(a) == is_young(b))                 solver.add_clause(a, 0, b, 0);         }        if(!solver.solve()) printf("No solution.\n");        else {            for(int i = 0; i < n; i++)                if(solver.mark[i*2]) printf("C\n");                 else if(is_young(i)) printf("B\n");                 else printf("A\n");         }    }    return 0;}

UVALive3713-Astronauts (2-Sat)