【BZOJ2599】[IOI2011]Race【点分治】

【题目链接】

点分治。

考虑经过点x的路径，对于x，用类似TreeDP的方法，记录no[d]，表示路径长度为d时经过边最少的点的编号。

对于已经走过的子树，更新no。对于当前子树，遍历到一个点v，用depth[no[k - dis[v]]] + depth[v]更新答案。

注意给no清零时，用dfs姿势清零，这样做是O(n)的。如果直接用for或者memset，这样做是O(k)的，会TLE。

/* Telekinetic Forest Guard */
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

const int maxn = 200005, maxk = 1000005, inf = 0x3f3f3f3f;

int n, k, head[maxn], cnt, dis[maxn], depth[maxn], no[maxk], mx[maxn], size[maxn];
int root, nsum, ans;
bool vis[maxn];

struct _edge {
int v, w, next;
} g[maxn << 1];

inline int iread() {
int f = 1, x = 0; char ch = getchar();
for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;
for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
return f * x;
}

inline void add(int u, int v, int w) {
g[cnt] = (_edge){v, w, head[u]};
head[u] = cnt++;
}

inline void getroot(int x, int f) {
size[x] = 1; mx[x] = 0;
for(int i = head[x]; ~i; i = g[i].next) if(!vis[g[i].v] && g[i].v ^ f) {
getroot(g[i].v, x);
size[x] += size[g[i].v];
mx[x] = max(mx[x], size[g[i].v]);
}
mx[x] = max(mx[x], nsum - size[x]);
if(mx[x] < mx[root]) root = x;
}

inline void calc(int x, int f) {
if(dis[x] > k) return;
if(~no[k - dis[x]]) ans = min(ans, depth[no[k - dis[x]]] + depth[x]);
for(int i = head[x]; ~i; i = g[i].next) if(!vis[g[i].v] && g[i].v ^ f) {
dis[g[i].v] = dis[x] + g[i].w;
depth[g[i].v] = depth[x] + 1;
calc(g[i].v, x);
}
}

inline void update(int x, int f) {
if(dis[x] > k) return;
if(!~no[dis[x]] || depth[no[dis[x]]] > depth[x]) no[dis[x]] = x;
for(int i = head[x]; ~i; i = g[i].next) if(!vis[g[i].v] && g[i].v ^ f)
update(g[i].v, x);
}

inline void clear(int x, int f) {
if(dis[x] > k) return;
no[dis[x]] = -1;
for(int i = head[x]; ~i; i = g[i].next) if(!vis[g[i].v] && g[i].v ^ f)
clear(g[i].v, x);
}

inline void work(int x) {
vis[x] = 1;
no[0] = x; dis[x] = depth[x] = 0;
for(int i = head[x]; ~i; i = g[i].next) if(!vis[g[i].v]) {
dis[g[i].v] = g[i].w; depth[g[i].v] = 1;
calc(g[i].v, x);
update(g[i].v, x);
}
clear(x, 0);
for(int i = head[x]; ~i; i = g[i].next) if(!vis[g[i].v]) {
root = 0; nsum = size[g[i].v];
getroot(g[i].v, 0);
work(root);
}
}

int main() {
n = iread(); k = iread();
for(int i = 1; i <= n; i++) head[i] = -1; cnt = 0;
for(int i = 1; i < n; i++) {
int u = iread(), v = iread(), w = iread(); u++; v++;
add(u, v, w); add(v, u, w);
}

for(int i = 0; i <= k; i++) no[i] = -1;
mx[0] = ans = inf;
root = 0; nsum = n;
getroot(1, 0);
work(root);

if(ans == inf) ans = -1;
printf("%d\n", ans);
return 0;
}