CF1108F题解

传送门：https://codeforces.com/problemset/problem/1108/F

求出最小生成树后处理出任意两点间边的最大值，这里可以用倍增或者树刨。然后用不在生成树上的边去替换，如果边权和边两端点路径最大边值相同则最小生成树不唯一，需要将边权$+1$。实现比较简单，写了一遍就过了。

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#include <bits/stdc++.h>

using namespace std;

inline int read() {
    char c;
    bool flag = false;
    while ((c = getchar()) < '0' || c > '9') if (c == '-') flag = true;
    int res = c - '0';
    while ((c = getchar()) >= '0' && c <= '9') res = (res << 3) + (res << 1) + c - '0';
    return flag ? -res : res;
}

const int N = 2e5 + 1;

int Max[N][22], fa[N][22], head[N], cnt, ff[N], dep[N];

struct Edge {
    int v, next, w;
} e[N * 2];

void add(int u, int v, int w) {
    e[cnt].v = v;
    e[cnt].w = w;
    e[cnt].next = head[u];
    head[u] = cnt++;
}

int get(int x) { return x == ff[x] ? x : ff[x] = get(ff[x]); }

struct E {
    int u, v, w, use;

    bool operator<(const E &o) const { return w < o.w; }
} edge[N];

void dfs(int x, int f) {
    dep[x] = dep[f] + 1;
    fa[x][0] = f;
    for (int i = 1; i <= 20; ++i) {
        fa[x][i] = fa[fa[x][i - 1]][i - 1];
        Max[x][i] = max(Max[x][i - 1], Max[fa[x][i - 1]][i - 1]);
    }
    for (int i = head[x]; ~i; i = e[i].next) {
        int y = e[i].v;
        if (y == f) continue;
        Max[y][0] = e[i].w;
        dfs(y, x);
    }
}

int getMax(int x, int y) {
    int ans = 0;
    if (dep[x] > dep[y]) swap(x, y);
    for (int i = 21; i >= 0; --i) if (dep[fa[y][i]] >= dep[x]) ans = max(ans, Max[y][i]), y = fa[y][i];
    if (x == y) return ans;
    for (int i = 21; i >= 0; --i)
        if (fa[x][i] != fa[y][i])
            ans = max(ans, max(Max[x][i],
                               Max[y][i])), x = fa[x][i], y = fa[y][i];
    return max(ans, max(Max[x][0], Max[y][0]));
}

int main() {
    int ans = 0;
    memset(head, -1, sizeof head);
    int n = read(), m = read();
    for (int i = 1; i <= n; ++i) ff[i] = i;
    for (int i = 1; i <= m; ++i) edge[i].u = read(), edge[i].v = read(), edge[i].w = read();
    sort(edge + 1, edge + m + 1);
    for (int i = 1; i <= m; ++i) {
        int u = edge[i].u, v = edge[i].v, w = edge[i].w;
        if (get(u) != get(v)) {
            ff[get(u)] = get(v);
            add(u, v, w);
            add(v, u, w);
            edge[i].use = 1;
        }
    }
    dfs(1, 0);
    for (int i = 1; i <= m; ++i) if (!edge[i].use) if (edge[i].w == getMax(edge[i].u, edge[i].v)) ++ans;
    printf("%d", ans);
    return 0;
}