洛谷 [P3623] 免费道路

有 k 条特殊边的生成树

我们发现有一些边是必须的,如果把所有的水泥路都加入并查集,再枚举鹅卵石路,如果这条路能再次加入并查集,说明这条路是必须的
水泥路同样
这样就把必需边求出来了,剩下就可以随意加边了

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cstring>
using namespace std;
const int MAXN = 100005;
int init() {
    int rv = 0, fh = 1;
    char c = getchar();
    while(c < '0' || c > '9') {
        if(c == '-') fh = -1;
        c = getchar();
    }
    while(c >= '0' && c <= '9') {
        rv = (rv<<1) + (rv<<3) + c - '0';
        c = getchar();
    }
    return fh * rv;
}
int n, m, nume, head[MAXN], fa[MAXN], k, cnt, ans[MAXN], ind;
struct edge{
    int to, nxt, opt;
}e[MAXN << 1];
void adde(int from, int to, int opt) {
    e[++nume].to = to;
    e[nume].nxt = head[from];
    head[from] = nume;
    e[nume].opt = opt;
}
int find(int x) {
    if(x != fa[x]) return fa[x] = find(fa[x]);
    return fa[x];
}
void merge(int x, int y) {
    int r1 = find(x), r2 = find(y);
    if(r1 != r2) {
        fa[r1] = r2;
    }
}
void input() {
    for(int i = 1; i <= n; i++) fa[i] = i;
}
bool chk() {
    for(int i = 2; i <= n; i++) if(find(i) != find(1)) return 0;
    return 1;
}
int main() {
    n = init(); m = init(); k = init();
    input();
    for(int i = 1; i <= m; i++) {
        int u = init(), v = init(), opt = init();
        adde(u, v, opt); adde(v, u, opt);
        if(opt == 1) merge(u, v);
    }
    for(int i = 1; i <= m * 2; i += 2) {
        if(e[i].opt == 0) {
            int r1 = find(e[i].to), r2 = find(e[((i - 1) ^ 1) + 1].to);
            if(r1 != r2) {
                fa[r1] = r2;
                ans[++cnt] = i;
                ind++;
            }
        }
    }
    if(cnt > k || !chk()) {
        printf("no solution\n"); 
        return 0;
    }
    input();
    for(int i = 1; i <= nume; i += 2) {
        if(e[i].opt == 0) merge(e[i].to, e[((i - 1) ^ 1) + 1].to);
    }
    for(int i = 1; i <= m * 2; i += 2) {
        if(e[i].opt == 1) {
            int r1 = find(e[i].to), r2 = find(e[((i - 1) ^ 1) + 1].to);
            if(r1 != r2) {
                fa[r1] = r2;
                ans[++cnt] = i;
            }
        }
    }
    if(!chk()) {
        printf("no solution\n"); 
        return 0;
    }
    input();
    for(int i = 1; i <= cnt; i++) {
        int t = ans[i];
        merge(e[t].to, e[((t - 1) ^ 1) + 1].to);
    }
    for(int i = 1; i <= nume; i += 2) {
        if(ind == k) break;
        if(e[i].opt == 0) {
            int r1 = find(e[i].to), r2 = find(e[((i - 1) ^ 1) + 1].to);
            if(r1 != r2) {
                fa[r1] = r2;
                ans[++cnt] = i;
                ind++;
            }
        }
    }
    if(ind != k) {
        printf("no solution\n"); 
        return 0;
    }
    for(int i = 1; i <= nume; i += 2) {
        if(e[i].opt == 1) {
            int r1 = find(e[i].to), r2 = find(e[((i - 1) ^ 1) + 1].to);
            if(r1 != r2) {
                fa[r1] = r2;
                ans[++cnt] = i;
            }
        }
    }
    sort(ans + 1, ans + cnt + 1);
    for(int i = 1 ; i <= cnt; i++) {
        int t = ans[i];
        printf("%d %d %d\n", e[((t - 1) ^ 1) + 1].to, e[t].to, e[t].opt);
    }
    return 0;
}