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CF662B Graph Coloring 題解 搜尋

題目連結:https://www.luogu.com.cn/problem/CF662B

題目大意:

\(n\) 個點 \(m\) 條邊,邊有顏色 —— 紅色或藍色。你可以對點進行操作,每操作一個點,與這個點相鄰的所有邊會變化顏色(紅色變藍色,藍色變紅色)。問:最少需要操作幾次能夠讓邊的顏色都一樣(並輸出最少需要操作的所有點的編號)。

解題思路:

可能存在多個連通塊。首先我需要列舉將要變成的顏色,然後對於每一個連通塊中第一個碰到的點,我列舉這個點要不要進行操作。

因為一條邊連線兩個點,這個點有沒有操作直接影響了和它相鄰的邊要不要操作。同時一個點最多操作依次(操作兩次就跟沒操作一樣了)。

所以,總的時間複雜度為 \(O(4 \cdot n)\)

示例程式碼:

#include <bits/stdc++.h>
using namespace std;
const int maxn = 100010;
struct Edge {
    int u, v, c, cc, nxt;    // cc表示原始的顏色
    Edge() {}
    Edge(int _u, int _v, int _c, int _nxt) { u = _u; v = _v; c = cc = _c; nxt = _nxt; }
} edge[maxn<<1];
int head[maxn], n, m, ecnt, tmp, sum[2];
vector<int> res[2], tmp_vec, vecs[2];
void init() {
    ecnt = 0;
    memset(head, -1, sizeof(int)*(n+1));
}
void addedge(int u, int v, int c) {
    edge[ecnt] = Edge(u, v, c, head[u]); head[u] = ecnt ++;
    edge[ecnt] = Edge(v, u, c, head[v]); head[v] = ecnt ++;
}
bool vis[maxn];
bool dfs(int u, bool paint, int c) {
    vis[u] = true;
    if (paint) {
        tmp ++;
        tmp_vec.push_back(u);
        for (int i = head[u]; i != -1; i = edge[i].nxt) {
            edge[i].c ^= 1;
            edge[i^1].c ^= 1;
        }
    }
    for (int i = head[u]; i != -1; i = edge[i].nxt) {
        int v = edge[i].v;
        if (edge[i].c != c) {
            if (vis[v]) return false;
            if (!dfs(v, true, c)) return false;
        }
        else if (!vis[v] && !dfs(v, false, c)) return false;
    }
    return true;
}
void recover(int u) {
    vis[u] = false;
    for (int i = head[u]; i != -1; i = edge[i].nxt) {
        edge[i].c = edge[i^1].c = edge[i].cc;
        int v = edge[i].v;
        if (vis[v]) recover(v);
    }
}
void handle(int u, int c, int id) {
    tmp = 0;
    int tmp1 = -1;
    for (int i = 0; i < 2; i ++) vecs[i].clear();
    tmp_vec.clear();
    if (dfs(u, true, c)) {
        tmp1 = tmp;
        for (int i = 0; i < tmp1; i ++) vecs[0].push_back(tmp_vec[i]);
    }
    recover(u);
    tmp = 0;
    int tmp2 = -1;
    tmp_vec.clear();
    if (dfs(u, false, c)) {
        tmp2 = tmp;
        for (int i = 0; i < tmp2; i ++) vecs[1].push_back(tmp_vec[i]);
    }
    if (tmp1 == -1 && tmp2 == -1 ) sum[id] = -1;
    else if (tmp2 == -1 || tmp1 != -1 && tmp1 < tmp2) {
        sum[id] += tmp1;
        for (int i = 0; i < tmp1; i ++) res[id].push_back(vecs[0][i]);
    }
    else {
        sum[id] += tmp2;
        for (int i = 0; i < tmp2; i ++) res[id].push_back(vecs[1][i]);
    }
}
int main() {
    scanf("%d%d", &n, &m);
    init();
    while (m --) {
        int u, v, c;
        char cc[2];
        scanf("%d%d%s", &u, &v, cc);
        c = (cc[0] == 'R');
        addedge(u, v, c);
    }
    for (int i = 1; i <= n && sum[0] != -1; i ++) {
        if (!vis[i]) handle(i, 0, 0);
    }
    for (int i = 1; i <= n; i ++) vis[i] = false;
    for (int i = 0; i < ecnt; i ++) edge[i].c = edge[i].cc;
    for (int i = 1; i <= n && sum[1] != -1; i ++) {
        if (!vis[i]) handle(i, 1, 1);
    }
    if (sum[0] == -1 && sum[1] == -1) puts("-1");
    else if (sum[1] == -1 || sum[0] != -1 && sum[0] < sum[1]) {
        printf("%d\n", sum[0]);
        for (int i = 0; i < sum[0]; i ++) printf("%d ", res[0][i]);
    }
    else {
        printf("%d\n", sum[1]);
        for (int i = 0; i < sum[1]; i ++) printf("%d ", res[1][i]);
    }
    return 0;
}