2-sat基础题 uvalive 3211

蓝书325页的基础题

二分+2-sat

//看看会不会爆int!数组会不会少了一维！
//取物问题一定要小心先手胜利的条件
#include <bits/stdc++.h>
using namespace std;
#pragma comment(linker,"/STACK:102400000,102400000")
#define LL long long
#define ALL(a) a.begin(), a.end()
#define pb push_back
#define mk make_pair
#define fi first
#define se second
#define haha printf("haha
")
const int maxn = 5000 + 5;

struct TwoSAT{
    int n;
    vector<int> G[maxn];
    bool mark[maxn];
    int c, s[maxn];///c是表示目前dfs到的个数和已经被标记的集合s
    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 < 2 * n; i++) G[i].clear();
        memset(mark, 0, sizeof(mark));
    }

    void add_edge(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 < 2 * n; i += 2){
            if (!mark[i] && !mark[i + 1]){
                c = 0;
                if (!dfs(i)){
                    while (c) mark[s[--c]] = false;
                    if (!dfs(i + 1)) return false;
                }
            }
        }
        return true;
    }
};

TwoSAT sat;
int n;
int E[maxn], L[maxn];
int ti[maxn][2];

bool test(int p){
    sat.init(n);
    for (int i = 0; i < n; i++){
        for (int x = 0; x < 2; x++){
            for (int j = i + 1; j < n; j++){
                for (int y = 0; y < 2; y++){
                    if (abs(ti[i][x] - ti[j][y]) < p){
                        ///那就说明不成立，因此要建立成立的边
                        sat.add_edge(i, x ^ 1, j, y ^ 1);
                    }
                }
            }
        }
    }
    return sat.solve();
}

int main(){
    while (scanf("%d", &n) == 1){
        int lb = 0, rb = 0;
        for (int i = 0; i < n; i++){
            scanf("%d%d", E + i, L + i);
            ti[i][0] = E[i], ti[i][1] = L[i];
            rb = max(rb, max(E[i], L[i]));
        }
        rb++;
        while (lb < rb - 1){
            int mid = (lb + rb) / 2;
            if (test(mid)) lb = mid;
            else rb = mid;
        }
        printf("%d
",lb);
    }
    return 0;
}