POJ-3237 Tree

Tree

树链剖分

树的路径边权最大值询问，其中还能使一整条路径上的值取反（正负数）

线段树维护最大值和最小值就能做到取反的时候交换，再加多一个懒标记维护一下

码量很大，但是感觉挺重复的，线段树太久没写各种崩，中途还跑去聚餐，结果回来更是崩

#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long ll;
const int maxn = 1e4 + 10;
const ll inf = (1ll << 62) - 1;
#define pii pair<int, int>
int dep[maxn], siz[maxn], hson[maxn], fa[maxn];
int dfn[maxn], rnk[maxn], top[maxn];
int id[maxn], p[maxn];
ll w[maxn];
char op[20];
vector<pii>gra[maxn];

struct node
{
    int l, r, lazy;
    ll minn, maxx;
}tr[maxn << 2];

void build(int now, int l, int r)
{
    tr[now].l = l;
    tr[now].r = r;
    tr[now].lazy = 0;
    if(l == r)
    {
        tr[now].minn = tr[now].maxx = w[id[rnk[l]]];
        return;
    }
    int mid = l + r >> 1;
    build(now << 1, l, mid);
    build(now << 1 | 1, mid + 1, r);
    tr[now].maxx = max(tr[now << 1].maxx, tr[now << 1 | 1].maxx);
    tr[now].minn = min(tr[now << 1].minn, tr[now << 1 | 1].minn);
}

inline void self(int now)
{
    swap(tr[now].maxx, tr[now].minn);
    tr[now].maxx = -tr[now].maxx;
    tr[now].minn = -tr[now].minn;
}

inline void push_down(int now)
{
    if(tr[now].lazy)
    {
        int lson = now << 1;
        int rson = now << 1 | 1;
        self(lson);
        self(rson);
        tr[lson].lazy ^= 1;
        tr[rson].lazy ^= 1;
        tr[now].lazy = 0;
    }
}

inline void push_up(int now)
{
    tr[now].minn = min(tr[now << 1].minn, tr[now << 1 | 1].minn);
    tr[now].maxx = max(tr[now << 1].maxx, tr[now << 1 | 1].maxx);
}

void change(int now, int x, ll val)
{
    if(tr[now].l == tr[now].r)
    {
        tr[now].minn = val;
        tr[now].maxx = val;
        return;
    }
    push_down(now);
    int mid = tr[now].l + tr[now].r >> 1;
    if(x <= mid)
        change(now << 1, x, val);
    else
        change(now << 1 | 1, x, val);
    push_up(now);
}

void update_n(int now, int L, int R)
{
    if(L <= tr[now].l && tr[now].r <= R)
    {
        self(now);
        tr[now].lazy ^= 1;
        return;
    }
    push_down(now);
    int mid = tr[now].l + tr[now].r >> 1;
    if(L <= mid) update_n(now << 1, L, R);
    if(R > mid) update_n(now << 1 | 1, L, R);
    push_up(now);
}

ll query(int now, int L, int R)
{
    if(L <= tr[now].l && tr[now].r <= R)
        return tr[now].maxx;
    push_down(now);
    int mid = tr[now].l + tr[now].r >> 1;
    ll ans = -inf;
    if(L <= mid)
        ans = max(ans, query(now << 1, L, R));
    if(R > mid)
        ans = max(ans, query(now << 1 | 1, L, R));
    return ans;
}

void dfs1(int now, int pre, int d)
{
    hson[now] = 0;
    siz[now] = 1;
    dep[now] = d;
    fa[now] = pre;
    for(int i=0; i<gra[now].size(); i++)
    {
        int nex = gra[now][i].first;
        int x = gra[now][i].second;
        if(nex == pre) continue;
        id[nex] = x;
        p[x] = nex;
        dfs1(nex, now, d + 1);
        siz[now] += siz[nex];
        if(siz[hson[now]] < siz[nex])
            hson[now] = nex;
    }
}

int tp = 0;
void dfs2(int now, int t)
{
    top[now] = t;
    tp++;
    dfn[now] = tp;
    rnk[tp] = now;
    if(hson[now])
    {
        dfs2(hson[now], t);
        for(int i=0; i<gra[now].size(); i++)
        {
            int nex = gra[now][i].first;
            if(nex == fa[now] || nex == hson[now]) continue;
            dfs2(nex, nex);
        }
    }    
}

void init(int n, int rt)
{
    tp = 0;
    dfs1(rt, rt, 1);
    dfs2(rt, rt);
    for(int i=0; i<=n; i++) gra[i].clear();
    build(1, 1, n);
}

void LCA_n(int a, int b)
{
    while(top[a] != top[b])
    {
        if(dep[top[a]] < dep[top[b]]) swap(a, b);
        update_n(1, dfn[top[a]], dfn[a]);
        a = fa[top[a]];
    }
    if(dfn[a] > dfn[b]) swap(a, b);
    if(a != b) update_n(1, dfn[a] + 1, dfn[b]);
}

ll solve(int a, int b)
{
    ll ans = -inf;
    while(top[a] != top[b])
    {
        if(dep[top[a]] < dep[top[b]]) swap(a, b);
        ans = max(ans, query(1, dfn[top[a]], dfn[a]));
        a = fa[top[a]];
    }
    if(dfn[a] > dfn[b]) swap(a, b);
    if(a != b) ans = max(ans, query(1, dfn[a] + 1, dfn[b]));
    if(ans == -inf) ans = 0;
    return ans;
}

int main()
{
    int t;
    scanf("%d", &t);
    while(t--)
    {
        int n;
        scanf("%d", &n);
        for(int i=1; i<n; i++)
        {
            int x, y;
            scanf("%d%d%lld", &x, &y, &w[i]);
            gra[x].push_back(make_pair(y, i));
            gra[y].push_back(make_pair(x, i));
        }
        init(n, 1);
        while(1)
        {
            scanf("%s", op);
            if(op[0] == 'D') 
                break;
            else if(op[0] == 'C')
            {
                int i;
                ll v;
                scanf("%d%lld", &i, &v);
                change(1, dfn[p[i]], v);
            }
            else if(op[0] == 'N')
            {
                int a, b;
                scanf("%d%d", &a, &b);
                LCA_n(a, b);
            }
            else
            {
                int a, b;
                scanf("%d%d", &a, &b);
                printf("%lld\n", solve(a, b));
            }
        }
    }
    return 0;
}