POJ 3162 - Walking Race(树形DP)

题目：

http://poj.org/problem?id=3162

题意：

树中节点的直径，最大值与最小值的差值不超过m的最大区间。

思路：

步骤1：求树的直径。

步骤2：求出区间，维护两个单调队列，一个递增一个递减。

AC.

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 1e6+5;
int n, m;

int tol, head[maxn];
struct Edge{
int to, w, next;
}edge[maxn*2];
void addedge(int u, int v, int w)
{
edge[tol].to = v;
edge[tol].w = w;
edge[tol].next = head[u];
head[u] = tol++;
}

int dis[maxn], dson[maxn], pre[maxn];
int d[maxn];
void dfs(int u, int fa)
{
int tmp = 0;
for(int i = head[u]; ~i; i = edge[i].next) {
int v = edge[i].to, w = edge[i].w;
if(v == fa) continue;
dfs(v, u);
dson[u] = max(dson[u], dson[v] + w);
}
}
void dfs1(int u, int fa)
{
int max1 = 0, max2 = 0, tmp;
int v1;

int v, w;
for(int i = head[u]; ~i; i = edge[i].next) {
v = edge[i].to; w = edge[i].w;
if(v == fa) continue;
tmp = dson[v] + w;
if(tmp > max1) {
max2 = max1; max1 = tmp;
v1 = v;
}
else if(tmp == max1 || tmp > max2) {
max2 = tmp;
}
}

if(u != 1) {
tmp = dis[u];
v = -1;
if(tmp > max1) {
max2 = max1; max1 = tmp;
v1 = v;
}
else if(max1 == tmp || tmp > max2) max2 = tmp;
}

for(int i = head[u]; ~i; i = edge[i].next) {
v = edge[i].to; w = edge[i].w;
if(v == fa) continue;

if(v == v1) dis[v] = max2+w; // printf("v= %d: %d\n", v, dis[v]);
else dis[v] = max1+w; // printf("**v= %d: %d\n", v, dis[v]);
dfs1(v, u);
}
}

int qmax[maxn], qmin[maxn];
void solve()
{
int ans = 1;
int s = 1,t = 1;
int t1=1, t2=1, i1=1, i2=1;
qmax[t1++] = d[1]; qmin[t2++] = d[1];
while(t < n) {
if(qmax[i1] - qmin[i2] <= m) {
t++;
int tmp = d[t];
while(i1 < t1 && qmax[t1-1] < tmp) t1--;
qmax[t1++] = tmp;

while(i2 < t2 && qmin[t2-1] > tmp) t2--;
qmin[t2++] = tmp;
}
else {
int tmp = d[s++];
if(qmax[i1] == tmp) i1++;
if(qmin[i2] == tmp) i2++;
}
if(qmax[i1] - qmin[i2] <= m) {
//printf("%d %d: ", qmax[i1], qmin[i2]);
//printf("(%d, %d)\n", s, t);
ans = max(ans, t-s+1);
}

}
printf("%d\n", ans);
}
void init()
{
tol = 0;
memset(head, -1, sizeof(head));

memset(dis, 0, sizeof(dis));
memset(d, 0, sizeof(d));
memset(dson, 0, sizeof(dson));
memset(qmax, 0, sizeof(qmax));
memset(qmin, 0, sizeof(qmin));
}
int main()
{
//freopen("inn", "r", stdin);
while(~scanf("%d%d", &n, &m)) {
init();
for(int u = 2; u <= n; ++u) {
int v, w;
scanf("%d%d", &v, &w);
addedge(u, v, w);
addedge(v, u, w);
}
dfs(1, -1);
dfs1(1, -1);

for(int i = 1; i <= n; ++i) {
//printf("%d %d: ", dson[i], dis[i]);
d[i] = max(dson[i], dis[i]);
// printf("%d\n", d[i]);
}
solve();
}
return 0;
}