【HDOJ】5296 Annoying problem

LCA+RMQ。挺不错的一道题目。

思路是如何通过LCA维护费用。当加入新的点u是，费用增量为
dis[u]-dis[lca(u, lower_u)] - dis[lca(u, greater_u)] + dis[lca(lower_u, greater_u)]。
若beg[u]大于当前最大值或小于最小值，lower_u=min of current, greater_u = max of current。

/* 5296 */
#include <iostream>
#include <sstream>
#include <string>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <vector>
#include <deque>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <climits>
#include <cctype>
#include <cassert>
#include <functional>
#include <iterator>
#include <iomanip>
using namespace std;
//#pragma comment(linker,"/STACK:102400000,1024000")

#define sti                set<int>
#define stpii            set<pair<int, int> >
#define mpii            map<int,int>
#define vi                vector<int>
#define pii                pair<int,int>
#define vpii            vector<pair<int,int> >
#define rep(i, a, n)     for (int i=a;i<n;++i)
#define per(i, a, n)     for (int i=n-1;i>=a;--i)
#define clr                clear
#define pb                 push_back
#define mp                 make_pair
#define fir                first
#define sec                second
#define all(x)             (x).begin(),(x).end()
#define SZ(x)             ((int)(x).size())
#define lson            l, mid, rt<<1
#define rson            mid+1, r, rt<<1|1

typedef struct {
    int v, w, nxt;
} edge_t;

const int maxn = 1e5+5;
const int maxv = maxn;
const int maxe = maxv * 2;
int head[maxv];
edge_t E[maxe];
int dis[maxn], deep[maxn];
bool visit[maxn];
int beg[maxn];
int V[maxn<<1], D[maxn<<1];
int dp[18][maxn<<1];
int l, top;
sti st;
sti::iterator iter;

void init() {
    st.clr();
    memset(visit, false, sizeof(visit));
    memset(head, -1, sizeof(head));
    l = top = 0;
}

void addEdge(int u, int v, int w) {
    E[l].v = v;
    E[l].w = w;
    E[l].nxt = head[u];
    head[u] = l++;
    
    E[l].v = u;
    E[l].w = w;
    E[l].nxt = head[v];
    head[v] = l++;
}

void dfs(int u, int fa, int d, int w) {
    dis[u] = w;
    V[++top] = u;
    D[top] = d;
    beg[u] = top;
    
    int v, k;
    
    for (k=head[u]; k!=-1; k=E[k].nxt) {
        v = E[k].v;
        if (v == fa)
            continue;
        dfs(v, u, d+1, w+E[k].w);
        V[++top] = u;
        D[top] = d;
    }
}

void init_RMQ(int n) {
    int i, j;
    
    for (i=1; i<=n; ++i)
        dp[0][i] = i;
    for (j=1; (1<<j)<=n; ++j)
        for (i=1; i+(1<<j)-1<=n; ++i)
            if (D[dp[j-1][i]] < D[dp[j-1][i+(1<<(j-1))]])
                dp[j][i] = dp[j-1][i];
            else
                dp[j][i] = dp[j-1][i+(1<<(j-1))];
}

int RMQ(int l, int r) {
    if (l > r)
        swap(l, r);
    
    int k = 0;
    
    while (1<<(k+1) <= r-l+1)
        ++k;
    
    if (D[dp[k][l]] < D[dp[k][r-(1<<k)+1]])
        return V[dp[k][l]];
    else
        return V[dp[k][r-(1<<k)+1]];
}

int calc(int u) {
    if (st.empty())
        return 0;
    
    int x, y;
    
    iter = st.upper_bound(beg[u]);
    if (iter == st.end() || iter==st.begin()) {
        y = *st.rbegin();
        x = *st.begin();
    } else {
        y = *iter;
        --iter;
        x = *iter;
    }
    
    int ret = 0;
    
    ret = dis[u] - dis[RMQ(x, beg[u])] - dis[RMQ(beg[u], y)] + dis[RMQ(x, y)];
    return ret;
}

int main() {
    ios::sync_with_stdio(false);
    #ifndef ONLINE_JUDGE
        freopen("data.in", "r", stdin);
        freopen("data.out", "w", stdout);
    #endif
    
    int t;
    int n, q;
    int u, v, w;
    int op;
    int ans;
    
    scanf("%d", &t);
    rep(tt, 1, t+1) {
        scanf("%d %d", &n, &q);
        init();
        rep(i, 1, n) {
            scanf("%d %d %d", &u, &v, &w);
            addEdge(u, v, w);
        }
        dfs(1, 0, 0, 0);
        init_RMQ(top);
        printf("Case #%d:
", tt);
        ans = 0;
        while (q--) {
            scanf("%d %d", &op, &u);
            if (op == 1) {
                if (!visit[u]) {
                    visit[u] = true;
                    ans += calc(u);
                    st.insert(beg[u]);
                }
            } else {
                if (visit[u]) {
                    visit[u] = false;
                    st.erase(beg[u]);
                    ans -= calc(u);
                }
            }
            printf("%d
", ans);
        }
    }
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif
    
    return 0;
}

数据发生器。

from random import randint, shuffle
import shutil
import string


def GenDataIn():
    with open("data.in", "w") as fout:
        t = 10
        bound = 10**3
        fout.write("%d
" % (t))
        for tt in xrange(t):
            n = randint(20, 30)
            q = randint(20, 30)
            fout.write("%d %d
" % (n, q))
            ust = [1]
            vst = range(1, n+1)
            ust.append(1)
            vst.remove(1)
            un = 1
            vn = n - 1
            for i in xrange(1, n):
                uidx = randint(0, un-1)
                u = ust[uidx]
                vidx = randint(0, vn-1)
                v = vst[vidx]
                ust.append(v)
                vst.remove(v)
                un += 1
                vn -= 1
                w = randint(1, 100)
                fout.write("%d %d %d
" % (u, v, w))
            L = []
            for i in xrange(q):
                op = randint(1, 2)
                x = randint(1, n)
                fout.write("%d %d
" % (op, x))
            
                
                
def MovDataIn():
    desFileName = "F:eclipse_prjworkspacehdojdata.in"
    shutil.copyfile("data.in", desFileName)

    
if __name__ == "__main__":
    GenDataIn()
    MovDataIn()