hdu 4123 Bob’s Race(树形dp+RMQ)

题目链接：hdu 4123 Bob’s Race

题目大意：一个城镇有N个住户，N-1条路连接两个住户，保证N个住户联通，M次询问，给定N条边的信息，包括连

接的住户序号以及路的长度。然后是M次询问，每次询问Q，要求找到最长的连续序号，使得Max(dis[i]) - Min(dis[i]) ≤ 

Q(l≤i≤r)，输出最大的r-l+1。dis[i]为从第i个住户出发，不重复走过路能移动的最远距离。

解题思路：树形dp，通过两次dfs，第1次处理出每个节点中孩子节点移动的最长距离和第二长距离，第2次考虑从父

亲节点过来的路径，维护每个节点的最长距离即可。

然后用RMQ与处理加快询问速度，枚举右边界确定左边界，单次复杂度为o(n).

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 50005;

int N, M, E, Q, first[maxn], jump[maxn * 2], dpMax[maxn][20], dpMin[maxn][20];
struct Edge {
int u, v, w;
void set(int u, int v, int w) {
this->u = u;
this->v = v;
this->w = w;
}
}ed[maxn * 2];

inline void add_Edge (int u, int v, int w) {
ed[E].set(u, v, w);
jump[E] = first[u];
first[u] = E++;
}

int fmax[maxn], fidx[maxn], smax[maxn], sidx[maxn];

inline void maintain(int u, int w, int v) {
if (w > smax[u]) {
smax[u] = w;
sidx[u] = v;
}

if (smax[u] > fmax[u]) {
swap(smax[u], fmax[u]);
swap(sidx[u], fidx[u]);
}
}

void dfs(int u, int pre) {
fmax[u] = fidx[u] = smax[u] = sidx[u] = 0;
for (int i = first[u]; i + 1; i = jump[i]) {
int v = ed[i].v;
if (v == pre)
continue;
dfs(v, u);
maintain(u, fmax[v] + ed[i].w, v);
}
}

void dfs(int u, int pre, int d) {
maintain(u, d, pre);
for (int i = first[u]; i + 1; i = jump[i]) {
int v = ed[i].v;
if (v == pre)
continue;
dfs(v, u, (v == fidx[u] ? smax[u] : fmax[u]) + ed[i].w);
}
}

void rmq_init() {
for (int i = 1; i <= N; i++)
dpMax[i][0] = dpMin[i][0] = fmax[i];

for (int k = 1; (1<<k) <= N; k++) {
for (int i = 1; i + (1<<k) - 1 <= N; i++) {
dpMax[i][k] = max(dpMax[i][k-1], dpMax[i+(1<<(k-1))][k-1]);
dpMin[i][k] = min(dpMin[i][k-1], dpMin[i+(1<<(k-1))][k-1]);
}
}
}

int rmq_query(int l, int r) {
int k = 0;
while ((1<<(k+1)) <= r - l + 1) k++;
return max(dpMax[l][k], dpMax[r-(1<<k)+1][k]) - min(dpMin[l][k], dpMin[r-(1<<k)+1][k]);
}

int main () {
while (scanf("%d%d", &N, &M) == 2 && N + M) {
int u, v, w;
E = 0;
memset(first, -1, sizeof(first));
for (int i = 1; i < N; i++) {
scanf("%d%d%d", &u, &v, &w);
add_Edge(u, v, w);
add_Edge(v, u, w);
}

dfs(1, 0);
dfs(1, 0, 0);

rmq_init();
while (M--) {
int ans = 0, mv = 1;
scanf("%d", &Q);
for (int i = 1; i <= N; i++) {
while (mv <= i && rmq_query(mv , i) > Q) mv++;
ans = max(ans, i - mv + 1);
}
printf("%d\n", ans);
}
}
return 0;
}