UVALive 6900Road Repair（点分治）

题意:

给定N≤2×104的一棵树,给定描述这棵树的四元组,(u,v,cost,profit),cost,profit≤103
对于树的所有简单路,找到一条简单路满足∑cost≤C≤2×107,且∑profit最大
求这个最大的∑profit

分析:

首先O(n2)暴力肯定要挂,dp背包的话显然C太大不行
我们需要一个带log的算法,考虑点分治
这题与POJ 1741 Tree很像,对于我们枚举的一条到重心的路径,假设这条路径的信息为(c,p)
此时我们需要知道当前子问题中其它到重心的路径(c′,p′)的max{p′},c′≤C−c,如何快速知道这个,可以考虑线段树或者BIT来维护最大值
那么ans=max{p+p′}
−−memset初始化BIT会T,正常回溯即可

代码:

////  Created by TaoSama on 2015-12-18//  Copyright (c) 2015 TaoSama. All rights reserved.////#pragma comment(linker, "/STACK:1024000000,1024000000")#include <algorithm>#include <cctype>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iomanip>#include <iostream>#include <map>#include <queue>#include <string>#include <set>#include <vector>using namespace std;#define pr(x) cout << #x << " = " << x << "  "#define prln(x) cout << #x << " = " << x << endlconst int N = 2e4 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;const int M = 2e7 + 10;int n, C, ans;void getMax(int &x, int y) {x = max(x, y);}struct BIT {    int mx[M];    void del(int i) {        for(; i < M; i += i & -i) mx[i] = 0;    }    void update(int i, int v) {        for(; i < M; i += i & -i) getMax(mx[i], v);    }    int query(int i) {        int ret = 0;        for(; i; i -= i & -i) getMax(ret, mx[i]);        return ret;    }} bit;struct Edge {    int v, nxt, c, b;} edge[N << 1];int head[N], cnt;void addEdge(int u, int v, int c, int b) {    edge[cnt] = (Edge) {v, head[u], c, b};    head[u] = cnt++;    edge[cnt] = (Edge) {u, head[v], c, b};    head[v] = cnt++;}bool vis[N];int sz[N], mx[N], centroid;int getAll(int u, int f) {    int ret = 1;    for(int i = head[u]; ~i; i = edge[i].nxt) {        int v = edge[i].v;        if(v == f || vis[v]) continue;        ret += getAll(v, u);    }    return ret;}void getCentroid(int u, int f, int all) {    sz[u] = 1; mx[u] = 0;    for(int i = head[u]; ~i; i = edge[i].nxt) {        int v = edge[i].v;        if(v == f || vis[v]) continue;        getCentroid(v, u, all);        sz[u] += sz[v];        getMax(mx[u], sz[v]);    }    getMax(mx[u], all - sz[u]);    if(!centroid || mx[u] < mx[centroid]) centroid = u;}typedef pair<int, int> P;void getPath(int u, int f, int cost, int profit, vector<P>& path) {    if(cost > C) return;    path.push_back(P(cost, profit));    for(int i = head[u]; ~i; i = edge[i].nxt) {        int v = edge[i].v;        if(v == f || vis[v]) continue;        getPath(v, u, cost + edge[i].c, profit + edge[i].b, path);    }}void solve(int u) {    centroid = 0;    getCentroid(u, -1, getAll(u, -1));    int s = centroid;    vis[s] = true;    for(int i = head[s]; ~i; i = edge[i].nxt) {        int v = edge[i].v;        if(vis[v]) continue;        solve(v);    }    vector<P> dummy;    for(int i = head[s]; ~i; i = edge[i].nxt) {        int v = edge[i].v;        if(vis[v]) continue;        vector<P> path;        getPath(v, s, edge[i].c, edge[i].b, path);        for(P &p : path) getMax(ans, p.second + bit.query(C - p.first));        for(P &p : path) bit.update(p.first, p.second);        dummy.insert(dummy.end(), path.begin(), path.end());    }    for(P &p : dummy) bit.del(p.first);    vis[s] = false;}int main() {#ifdef LOCAL    freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);//  freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);#endif    ios_base::sync_with_stdio(0);    int t; scanf("%d", &t);    while(t--) {        cnt = 0; memset(head, -1, sizeof head);        scanf("%d", &n);        for(int i = 1; i < n; ++i) {            int u, v, c, b; scanf("%d%d%d%d", &u, &v, &c, &b);            addEdge(u, v, c, b);        }        scanf("%d", &C);        ans = 0;        solve(1);        printf("%d\n", ans);    }    return 0;}