Aoj 2450 Do use segment tree【树链剖分】

树链剖分，个人因为姿势太丑就不发代码了。
维护四个域。
区间和，右端最大连续值，左端最大连续值，答案。

注意的是，2操作是一个有序的操作，因此需要求一个LCA，从某点更新到LCA，再从LCA更新到另一个点。当然也有不要LCA的方法，就是通过判断深度，不swap，直接旋转地找。

//      whn6325689//      Mr.Phoebe//      http://blog.csdn.net/u013007900#include <algorithm>#include <iostream>#include <iomanip>#include <cstring>#include <climits>#include <complex>#include <fstream>#include <cassert>#include <cstdio>#include <bitset>#include <vector>#include <deque>#include <queue>#include <stack>#include <ctime>#include <set>#include <map>#include <cmath>#include <functional>#include <numeric>#pragma comment(linker, "/STACK:1024000000,1024000000")using namespace std;#define eps 1e-9#define PI acos(-1.0)#define INF 0x3f3f3f3f#define LLINF 1LL<<62#define speed std::ios::sync_with_stdio(false);typedef long long ll;typedef unsigned long long ull;typedef long double ld;typedef pair<ll, ll> pll;typedef complex<ld> point;typedef pair<int, int> pii;typedef pair<pii, int> piii;typedef vector<int> vi;#define CLR(x,y) memset(x,y,sizeof(x))#define CPY(x,y) memcpy(x,y,sizeof(x))#define clr(a,x,size) memset(a,x,sizeof(a[0])*(size))#define cpy(a,x,size) memcpy(a,x,sizeof(a[0])*(size))#define debug(a) cout << #a" = " << (a) << endl;#define debugarry(a, n) for (int i = 0; i<(n); i++) { cout << #a"[" << i << "] = " << (a)[i] << endl; }#define mp(x,y) make_pair(x,y)#define pb(x) push_back(x)#define lowbit(x) (x&(-x))#define MID(x,y) (x+((y-x)>>1))#define getidx(l,r) (l+r | l!=r)#define ls getidx(l,mid)#define rs getidx(mid+1,r)#define lson l,mid#define rson mid+1,rtemplate<class T>inline bool read(T &n){    T x = 0, tmp = 1;    char c = getchar();    while((c<'0' || c > '9') && c != '-' && c != EOF) c = getchar();    if(c == EOF) return false;    if(c == '-') c = getchar(), tmp = -1;    while(c >= '0' && c <= '9') x *= 10, x += (c - '0'),c = getchar();    n = x*tmp;    return true;}template <class T>inline void write(T n){    if(n<0)    {        putchar('-');        n = -n;    }    int len = 0,data[20];    while(n)    {        data[len++] = n%10;        n /= 10;    }    if(!len) data[len++] = 0;    while(len--) putchar(data[len]+48);}//-----------------------------------const int MAXN = 200020;struct Node{    ll sumv, suml, sumr, maxv;    ll sett;    Node()    {        sumv = 0;        sett = INF;        suml = sumr = maxv = -INF;    }    void setv(ll x, ll num)    {        sett = x;        sumv = x*num;        if(x >= 0)            suml = sumr = maxv = sumv;        else            suml = sumr = maxv = x;    }    Node operator + (const Node &rhs) const    {        Node c;        c.sett = INF;        c.sumv = sumv + rhs.sumv;        c.suml = max(suml, sumv+rhs.suml);        c.sumr = max(sumr+rhs.sumv, rhs.sumr);        c.maxv = max(maxv, rhs.maxv);        c.maxv = max(c.maxv, sumr+rhs.suml);        return c;    }} p[MAXN<<1];vector<int> G[MAXN];int num[MAXN], top[MAXN], dep[MAXN];int dfn[MAXN], b[MAXN], fa[MAXN], dfs_clock;int que[MAXN], iii[MAXN], a[MAXN];int n, q, ql, qr, _v;void gao(){    int ft = 0, rear = 0;    que[rear++] = 1;    fa[1] = 0;    dep[1] = 1;    while(ft < rear)    {        int u = que[ft++];        for(int i = 0; i < G[u].size(); i++)        {            int v = G[u][i];            if(v == fa[u]) continue;            fa[v] = u;            que[rear++] = v;            dep[v] = dep[u]+1;        }    }    memset(num, 0, sizeof num);    for(int i = n-1; i >= 0; i--)    {        int u = que[i];        num[u]++;        num[fa[u]] += num[u];    }    for(int i = 1; i <= n; i++)    {        for(int j = 1; j < G[i].size(); j++) if(G[i][j] != fa[i])                if(G[i][0] == fa[i] || num[G[i][j]] > num[G[i][0]])                    swap(G[i][0], G[i][j]);    }    top[1] = 1;    for(int i = 1; i < n; i++)    {        int u = que[i];        if(G[fa[u]][0] == u) top[u] = top[fa[u]];        else top[u] = u;    }    memset(iii, 0, sizeof iii);    ft = 0;    dfs_clock = 0;    que[++ft] = 1;    dfn[1] = ++dfs_clock;    b[1] = a[1];    while(ft)    {        int u = que[ft];        if(iii[u] >= G[u].size()) ft--;        else if(G[u][iii[u]] == fa[u]) iii[u]++;        else        {            int v = G[u][iii[u]];            que[++ft] = v;            dfn[v] = ++dfs_clock;            b[dfn[v]] = a[v];            iii[u]++;        }    }}void print(int a[]){    for(int i = 1; i <= n; i++)        printf("%d ", a[i]);    puts("");}void test(){    print(fa);    print(top);    print(dep);    print(dfn);    print(b);    print(num);}void build(int l, int r){    int idx=getidx(l,r),mid=MID(l,r);    p[idx].sett=INF;    if(l==r)    {        p[idx].setv(b[l], 1);        return;    }    build(lson);    build(rson);    p[idx]=p[ls]+p[rs];}void push_down(int l, int r){    int idx=getidx(l,r),mid=MID(l,r);    if(p[idx].sett!=INF)    {        p[ls].setv(p[idx].sett,mid-l+1);        p[rs].setv(p[idx].sett,r-mid);        p[idx].sett=INF;    }}void update(int l,int r,int L,int R){    int idx=getidx(l,r),mid=MID(l,r);    if(L<=l && r<=R)    {        p[idx].setv(_v, r-l+1);        return;    }    push_down(l,r);    if(L<=mid) update(lson,L,R);    if(R>mid) update(rson,L,R);    p[idx]=p[ls]+p[rs];}Node query(int l, int r,int L,int R){    int idx=getidx(l,r),mid=MID(l,r);    if(L==l && r==R)        return p[idx];    push_down(l,r);    if(R<=mid) return query(lson,L,R);    if(L>mid)  return query(rson,L,R);    return query(lson,L,mid)+query(rson,mid+1,R);}int lca(int u, int v){    while(top[u] != top[v])    {        if(dep[top[u]] < dep[top[v]]) swap(u, v);        u=fa[top[u]];    }    return dep[u] > dep[v] ? v : u;}void change(int u, int v, int c){    int t=lca(u, v);    _v=c;    while(top[u] != top[t])    {        update(1,n,dfn[top[u]],dfn[u]);        u=fa[top[u]];    }    update(1,n,dfn[t],dfn[u]);    while(top[v] != top[t])    {        update(1,n,dfn[top[v]],dfn[v]);        v=fa[top[v]];    }    if(v != t)        update(1,n,dfn[t]+1,dfn[v]);}ll outputquery(int u, int v){    if(dfn[u] > dfn[v]) swap(u, v);    int t=lca(u, v);    if(t==u) swap(u, v);    Node L,R;    while(top[u] != top[t])    {        L=query(1,n,dfn[top[u]],dfn[u])+L;        u=fa[top[u]];    }    L=query(1,n,dfn[t],dfn[u])+L;    while(top[v] != top[t])    {        R=query(1,n,dfn[top[v]],dfn[v])+R;        v=fa[top[v]];    }    if(v!=t)        R=R+query(1,n,dfn[t]+1,dfn[v]);    return max(max(L.maxv, R.maxv), L.suml+R.suml);}int main(){    //freopen("data.txt","r",stdin);    int op, u, v, c;    while(~scanf("%d %d",&n,&q))    {        for(int i=1; i<=n; i++)        {            read(a[i]);            G[i].clear();        }        for(int i=1; i < n; i++)        {            read(u),read(v);            G[u].push_back(v);            G[v].push_back(u);        }        gao();        build(1,n);        while(q--)        {            read(op),read(u),read(v),read(c);            if(op==1)                change(u,v,c);            else                write(outputquery(u,v)),putchar('\n');        }    }    return 0;}

不要求LCA的方法。

#include <bits/stdc++.h>#define MAXN 300500#define lson getidx(l, mid)#define rson getidx(mid + 1, r)using namespace std;typedef long long LL;const LL inf = 0x3f3f3f3f3f3f;struct edge{    int to,next;} E[MAXN*2];int head[MAXN],si,sz[MAXN],top[MAXN],son[MAXN],fa[MAXN],w[MAXN],dep[MAXN], add[MAXN<<1], isupdate[MAXN<<1], N, Q, A[MAXN], idx, mp[MAXN], que[MAXN];struct node{    LL sum,ls,rs,ans;    node(LL _ans = 0, LL _sum = 0, LL _ls = 0, LL _rs = 0 )    {        ans = _ans;        sum = _sum;        ls = _ls;        rs = _rs;    }} tree[MAXN<<1];void add_edge(int u,int v){    E[si].to = v;    E[si].next = head[u];    head[u] = si ++;}void bfs(int v){//printf("fa[%d]=%d\n",v,fa[v]);    int l = 0, r = 0;    for(que[r ++] = v; l < r; l ++)    {        int now = que[l];        for(int i =head[now]; ~i; i = E[i].next)        {            int u =E[i].to;            if( u == fa[now] )continue;            fa[u] = now;            dep[u] = dep[now] + 1;            que[r ++] = u;        }    }    for(; r; r --)    {        int now = que[r - 1];        sz[now] = 1;        son[now] = 0;        for(int i =head[now]; ~i; i = E[i].next)        {            int u =E[i].to;            if( u == fa[now] )continue;            sz[now] += sz[u];            if( sz[son[now]] < sz[u] )            {                son[now] = u;            }        }    }}void rdfs(int v,int root){    w[v] = ++ idx;    mp[idx] = v;    top[v] = root;    if( son[v] ) rdfs(son[v], root);    for(int i =head[v]; ~i; i = E[i].next)    {        int u = E[i].to;        if( u == fa[v] || u == son[v] )continue;        rdfs(u,u);    }}int getidx(int l,int r){    return l + r | l != r;}void updatenode(node &p, int x, int l, int r){    p = node( x, x * (r - l + 1), x, x );    if( x >= 0)    {        p = node(x * (r - l + 1), x * (r - l + 1), x * (r - l + 1), x * (r - l + 1));    }}void push_down(int l, int r){    int p =getidx(l, r), mid = l + r >> 1;    if( l == r || !isupdate[p] )return;    updatenode(tree[lson], add[p], l, mid);    updatenode(tree[rson], add[p], mid + 1, r);    isupdate[p] = false;    isupdate[lson] = true;    isupdate[rson] = true;    add[lson] = add[rson] = add[p];}node unite(node a, node b){    node p;    p.ans = max(a.ans, b.ans);    p.ans = max(p.ans, a.rs + b.ls);    p.sum = a.sum + b.sum;    p.ls = max(a.ls, a.sum + b.ls);    p.rs = max(b.rs, b.sum + a.rs);    return p;}void put_up(int l, int r){    int p =getidx(l, r), mid = l + r >> 1;    if( l == r ) return;    tree[p] = unite(tree[lson], tree[rson]);}void build(int l,int r){    int p =getidx(l, r);    isupdate[p] = false;    add[p] = 0;    if( l == r )    {        updatenode(tree[p], A[mp[l]], l, r);        //  printf("[%d,%d]:%lld, %lld ,%lld, %lld\n",l, r,tree[p].ans, tree[p].sum, tree[p].ls, tree[p].rs);        return;    }    int mid = l + r >> 1;    build(l, mid);    build(mid + 1, r);    put_up(l, r);    //printf("[%d,%d]:%lld, %lld ,%lld, %lld\n",l, r,tree[p].ans, tree[p].sum, tree[p].ls, tree[p].rs);}void update(int l, int r, int _l, int _r, int x){    if( l > _r || r < _l )return;    if( _l <= l && r <= _r )    {        int p = getidx(l, r);        updatenode(tree[p], x, l, r);        add[p] = x;        isupdate[p] = true;        return;    }    int mid = l + r >> 1;    push_down(l, r);    update(l, mid, _l, _r, x);    update(mid + 1, r, _l, _r, x);    put_up(l, r);}void update(int u,int v,int x){    int a = top[u], b = top[v];    while(a != b)    {        if( dep[a] < dep[b] )        {            swap(a, b);            swap(u, v);        }        update(1, N, w[a], w[u], x);        u = fa[a];        a = top[u];    }    if( dep[u] < dep[v] )    {        swap(u, v);    }    update(1, N, w[v], w[u], x);}node query(int l, int r, int _l, int _r){    if( _l <= l && r <= _r )    {        return tree[getidx(l, r)];    }    int mid = l + r >> 1;    push_down(l, r);    if( _r <= mid ) return query(l, mid, _l, _r);    else if( _l > mid ) return  query(mid + 1, r, _l, _r);    else    {        return unite(query(l, mid, _l, _r), query(mid + 1, r, _l, _r));    }}LL query(int u, int v){    int a = top[u], b = top[v];    node lpath = node(-inf , 0, -inf, -inf), rpath = node(-inf, 0, -inf, -inf);    while(a != b)    {        if( dep[a] > dep[b])        {            node res = query(1, N, w[a], w[u]);            swap(res.ls, res.rs);            lpath = unite(lpath, res);            //  printf("lpath:%d->%d: %lld %lld %lld %lld\n", a, u, lpath.ans,lpath.sum, lpath.ls, lpath.rs);            u = fa[a];            a = top[u];        }        else        {            node res = query(1, N, w[b], w[v]);            rpath = unite(res, rpath);            //printf("rpath:%d->%d: %lld %lld %lld %lld\n", b, v, rpath.ans,rpath.sum, rpath.ls, rpath.rs);            v = fa[b];            b = top[v];        }    }    node ans;    if( dep[u] < dep[v] )    {        ans = query(1, N, w[u], w[v]);    }    else    {        ans = query(1, N, w[v], w[u]);        swap(ans.ls,ans.rs);    }    // printf("%d->%d: %lld %lld %lld %lld\n", v, u, ans.ans,ans.sum, ans.ls, ans.rs);    ans = unite(lpath, ans);    //  printf(": %lld %lld %lld %lld\n",  ans.ans,ans.sum, ans.ls, ans.rs);    ans = unite(ans, rpath);    return ans.ans;}int main(){    //  freopen("in", "r", stdin);    scanf("%d %d", &N, &Q);    for(int i = 1; i <= N; i ++)    {        scanf("%d", &A[i]);    }    memset(head, -1, sizeof head);    si = 0;    idx = 0;    for(int i = 1, u, v; i < N; i ++)    {        scanf("%d%d", &u, &v);        add_edge(u, v);        add_edge(v, u);    }    fa[1] = dep[1] = 0;    bfs(1);    rdfs(1, 1);    build(1, N);    for(int i = 1, t, u, v, x; i <= Q; i ++)    {        scanf("%d%d%d%d", &t, &u, &v, &x);        if( t == 1 )        {            update(u, v, x);        }        else        {            long long ans = query(u, v);            printf("%lld\n", ans);        }    }    return 0;}