1 条题解

  • 1
    @ 2023-2-18 18:46:12
    #include <bits/stdc++.h>
    using namespace std;
    const int MAXN = 100000 + 5;
    int n, q;
    vector<int> e[MAXN];
    int init_color[MAXN]; // 初始颜色
    int ans[MAXN];        // 最终答案
    // 每个点的:父节点、深度、大小、重子节点
    int fa[MAXN], dep[MAXN], siz[MAXN], hson[MAXN];
    void dfs_build(int u, int fat)
    {
        hson[u] = 0;
        siz[u] = 1;
        for (int i = 0; i < e[u].size(); i++)
        {
            int v = e[u][i];
            if (v == fat)
                continue;
            dep[v] = dep[u] + 1;
            fa[v] = u;
            dfs_build(v, u);
            siz[u] += siz[v];
            if (siz[v] > siz[hson[u]])
                hson[u] = v;
        }
    }
    // 每个点的:所在链的链顶、重边优先的 dfs 序、dfs序对应的节点编号
    int tot, top[MAXN], dfn[MAXN], rnk[MAXN];
    void dfs_div(int u, int fa)
    {
        dfn[u] = ++tot;
        rnk[tot] = u;
        if (hson[u])
        {
            top[hson[u]] = top[u];
            dfs_div(hson[u], u);
            for (int i = 0; i < e[u].size(); i++)
            {
                int v = e[u][i];
                if (v == fa || v == hson[u])
                    continue;
                top[v] = v;
                dfs_div(v, u);
            }
        }
    }
    struct Res
    {
        // 左边颜色,右边颜色,颜色段数
        int lcolor, rcolor, sum;
    };
    struct SegTree
    {
        int sum[4 * MAXN];    // 有多少段颜色
        int lazy[4 * MAXN];   // 延迟染色,0 表示没有染色
        int lcolor[4 * MAXN]; // 区间左端点颜色
        int rcolor[4 * MAXN]; // 区间右端点颜色
        void up(int now)
        {
            sum[now] = sum[now * 2] + sum[now * 2 + 1];
            lcolor[now] = lcolor[now * 2];
            rcolor[now] = rcolor[now * 2 + 1];
            if (rcolor[now * 2] == lcolor[now * 2 + 1])
                sum[now]--;
        }
        void down(int now, int l, int r)
        {
            if (l == r || lazy[now] == 0)
                return;
            sum[now * 2] = 1;
            sum[now * 2 + 1] = 1;
            lazy[now * 2] = lazy[now];
            lcolor[now * 2] = lazy[now];
            rcolor[now * 2] = lazy[now];
            lazy[now * 2 + 1] = lazy[now];
            lcolor[now * 2 + 1] = lazy[now];
            rcolor[now * 2 + 1] = lazy[now];
            lazy[now] = 0;
        }
        void build(int now, int l, int r)
        {
            lazy[now] = 0;
            if (l == r)
            {
                sum[now] = 1;
                lcolor[now] = rcolor[now] = init_color[rnk[l]];
                return;
            }
            int mid = (l + r) / 2;
            build(now * 2, l, mid);
            build(now * 2 + 1, mid + 1, r);
            up(now);
        }
        // x~y 染成 z 色
        void update(int now, int l, int r, int x, int y, int z)
        {
            if (x <= l && r <= y)
            {
                sum[now] = 1;
                lcolor[now] = rcolor[now] = z;
                lazy[now] = z;
                return;
            }
            down(now, l, r);
            int mid = (l + r) / 2;
            if (x <= mid)
                update(now * 2, l, mid, x, y, z);
            if (y >= mid + 1)
                update(now * 2 + 1, mid + 1, r, x, y, z);
            up(now);
        }
        Res query(int now, int l, int r, int x, int y)
        {
            if (x <= l && r <= y)
                return (Res){lcolor[now], rcolor[now], sum[now]};
            down(now, l, r);
            int mid = (l + r) / 2;
            Res res = {0, 0, 0};
            Res lRes = {0, 0, 0};
            Res rRes = {0, 0, 0};
            if (x <= mid)
            {
                lRes = query(now * 2, l, mid, x, y);
                res = lRes;
            }
            if (y >= mid + 1)
            {
                rRes = query(now * 2 + 1, mid + 1, r, x, y);
                if (res.lcolor == 0)
                    res.lcolor = rRes.lcolor;
                res.rcolor = rRes.rcolor;
                res.sum += rRes.sum;
            }
            // 左右都有涉及,并且中间颜色一样,段数就少一段
            if (lRes.sum > 0 && rRes.sum > 0 && lRes.rcolor == rRes.lcolor)
                res.sum--;
            return res;
        }
    } st;
    // u~v路径上查询颜色段数
    int query(int u, int v)
    {
        int res = 0;
        int ulast = -1; // u上一段最后的颜色
        int vlast = -1; // v上一段最后的颜色
        while (top[u] != top[v])
        {
            if (dep[top[u]] < dep[top[v]])
            {
                // v~top[v] 计入答案中
                Res now = st.query(1, 1, tot, dfn[top[v]], dfn[v]);
                res += now.sum;
                if (now.rcolor == vlast)
                    res--;
                vlast = now.lcolor;
                v = fa[top[v]];
            }
            else
            {
                // u~top[u] 计入答案中
                Res now = st.query(1, 1, tot, dfn[top[u]], dfn[u]);
                res += now.sum;
                if (now.rcolor == ulast)
                    res--;
                ulast = now.lcolor;
                u = fa[top[u]];
            }
        }
        if (dep[u] > dep[v])
        {
            swap(u, v);
            swap(ulast, vlast);
        }
        Res now = st.query(1, 1, tot, dfn[u], dfn[v]);
        res += now.sum;
        if (now.lcolor == ulast)
            res--;
        if (now.rcolor == vlast)
            res--;
        return max(res, 1);
    }
    
    void update(int u, int v, int z)
    {
        while (top[u] != top[v])
        {
            if (dep[top[u]] < dep[top[v]])
            {
                // v~top[v] 计入答案中
                st.update(1, 1, tot, dfn[top[v]], dfn[v], z);
                v = fa[top[v]];
            }
            else
            {
                // u~top[u] 计入答案中
                st.update(1, 1, tot, dfn[top[u]], dfn[u],z);
                u = fa[top[u]];
            }
        }
        if (dep[u] > dep[v])
            swap(u, v);
        st.update(1, 1, tot, dfn[u], dfn[v],z);
    }
    int main()
    {
        ios::sync_with_stdio(false);
        cin.tie(0);
        cin >> n >> q;
        for (int i = 1; i <= n; i++)
            cin >> init_color[i];
        for (int i = 1; i <= n - 1; i++)
        {
            int u, v;
            cin >> u >> v;
            e[u].push_back(v);
            e[v].push_back(u);
        }
        dep[1] = 1;
        fa[1] = 0;
        dfs_build(1, 0);
        tot = 0;
        top[1] = 1;
        dfs_div(1, 0);
        /*
        for(int i=1;i<=tot;i++)
            cout<<dfn[i]<<" ";
        cout<<endl;
        */
        //--------
        st.build(1, 1, tot);
        while (q--)
        {
            char op;
            int a, b, c;
            cin >> op;
            if (op == 'C')
            {
                cin >> a >> b >> c;
                update(a, b, c);
            }
            else if (op == 'Q')
            {
                cin >> a >> b;
                cout << query(a, b) << "\n";
            }
        }
        return 0;
    }
    
    
    • 1

    信息

    ID
    793
    时间
    1000ms
    内存
    512MiB
    难度
    7
    标签
    递交数
    37
    已通过
    10
    上传者