树的重心

今天想起来学树上点分治，其实我还是不明白为啥，大概就学了一手树的重心吧2333
定义是去掉重心之后能使剩下的每个子树尽量平衡。那么先处理出每个点子树的size，然后枚举去掉每个点后最大子树最小的就是重心。最大子树包括两部分，由于dfs求size的时候是自己设定根为1的，而求重心判断的时候是以当前点为根的，所以除了正常的这个点的子树外，他的父亲所在的也作为他的一课子树

模版题
poj 1655

让你求树的重心以及这个重心最大的子树，注意相同情况下取序号小的为答案

#include<iostream>#include<cstring>#include<algorithm>#include<cstdio>using namespace std;//thanks to pyf ...//thanks to qhl ...#define INF 0x3f3f3f3fconst int N = 2e5 + 7;struct Edge{    int u, v, next;} edge[N * 2];int sz[N], Min, Mx[N];int head[N];int tot = 0;int ans;void init(){    tot = 0;    Min = INF;    memset(head, -1, sizeof(head));    memset(sz, 0, sizeof(sz));}void add_edge(int u, int v){    edge[tot].u = u, edge[tot].v = v;    edge[tot].next = head[u];    head[u] = tot ++;}void get_sz(int u, int fa){    sz[u] = 1;    Mx[u] = 0;    for (int i = head[u]; ~i; i = edge[i].next)    {        int v = edge[i].v;        if (v == fa)            continue;        get_sz(v, u);        sz[u] += sz[v];        Mx[u] = max(Mx[u], sz[v]);    }}void get_root(int r, int u, int fa){    Mx[u] = max(Mx[u], sz[r] - sz[u]);    if (Min > Mx[u] || (Min == Mx[u] && u < ans))        ans = u, Min = Mx[u];    for (int i = head[u]; ~i; i = edge[i].next)    {        int v = edge[i].v;        if (v == fa)            continue;        get_root(r, v, u);    }}int main(){    int T;    scanf("%d", &T);    while (T--)    {        init();        int n;        scanf("%d", &n);        for (int i = 1; i < n; i++)        {            int u, v;            scanf("%d%d", &u, &v);            add_edge(u, v);            add_edge(v, u);        }        get_sz(1, 0);        get_root(1, 1, 0);        printf("%d %d\n", ans, Mx[ans]);    }}

poj3107

求这棵树的所有重心

#include<iostream>#include<cstring>#include<algorithm>#include<cstdio>#include<vector>using namespace std;//thanks to pyf ...//thanks to qhl ...#define INF 0x3f3f3f3fconst int N = 2e5 + 7;struct Edge{    int u, v, next;} edge[N * 2];int sz[N], Min, Mx[N];int head[N];int tot = 0;int ans;void init(){    tot = 0;    Min = INF;    memset(head, -1, sizeof(head));    memset(sz, 0, sizeof(sz));}void add_edge(int u, int v){    edge[tot].u = u, edge[tot].v = v;    edge[tot].next = head[u];    head[u] = tot ++;}void get_sz(int u, int fa){    sz[u] = 1;    Mx[u] = 0;    for (int i = head[u]; ~i; i = edge[i].next)    {        int v = edge[i].v;        if (v == fa)            continue;        get_sz(v, u);        sz[u] += sz[v];        Mx[u] = max(Mx[u], sz[v]);    }}void get_root(int r, int u, int fa){    Mx[u] = max(Mx[u], sz[r] - sz[u]);    if (Min > Mx[u] || (Min == Mx[u] && u < ans))        ans = u, Min = Mx[u];    for (int i = head[u]; ~i; i = edge[i].next)    {        int v = edge[i].v;        if (v == fa)            continue;        get_root(r, v, u);    }}vector<int>tar;int main(){    int n;    while (scanf("%d", &n) == 1)    {        init();        for (int i = 1; i < n; i++)        {            int u, v;            scanf("%d%d", &u, &v);            add_edge(u, v);            add_edge(v, u);        }        get_sz(1, 0);        get_root(1, 1, 0);        tar.clear();        for (int i = 1; i <= n; i++)            if (Mx[i] == Mx[ans])                tar.push_back(i);        for (int i = 0; i < tar.size(); i++)        {            if (i)                printf("%s", " ");            printf("%d", tar[i]);        }        printf("\n");    }}

poj1741

男人八题楼教主的树上点分治。感觉比较精髓的是加减答案的部分，可惜。。。不是很懂

#include<iostream>#include<algorithm>#include<cstring>#include<vector>#include<cstdio>using namespace std;//thanks to pyf ...//thanks to qhl ...#define INF 0x3f3f3f3fconst int N = 2e5 + 7;struct Edge{    int u, v, d, next;} edge[N * 2];int Mx[N], sz[N], vis[N];int head[N];int root, Min;int n, k;vector<int>dis;int tot = 0, ans = 0;void init(){    memset(head, -1, sizeof(head));    memset(vis, 0, sizeof(vis));    tot = ans = 0;}void add_edge(int u, int v, int d){    edge[tot].u = u, edge[tot].v = v, edge[tot].d = d;    edge[tot].next = head[u];    head[u] = tot ++;}void dfs_sz(int u, int fa){    sz[u] = 1;    Mx[u] = 0;    for (int i = head[u]; ~i; i = edge[i].next)    {        int v = edge[i].v;        if (v == fa || vis[v])            continue;        dfs_sz(v, u);        sz[u] += sz[v];        Mx[u] = max(Mx[u], sz[v]);    }}void dfs_root(int r, int u, int fa){    Mx[u] = max(Mx[u] , sz[r] - sz[u]);    if (Mx[u] < Min)        root = u, Min = Mx[u];    for (int i = head[u]; ~i; i = edge[i].next)    {        int v = edge[i].v;        if (v == fa || vis[v])            continue;        dfs_root(r, v, u);    }}void get_dis(int u, int fa, int d){    dis.push_back(d);    for (int i = head[u]; ~i; i = edge[i].next)    {        int v = edge[i].v;        int w = edge[i].d;        if (v == fa || vis[v])            continue;        get_dis(v, u, d + w);    }}int get_ans(int u, int d){    dis.clear();    get_dis(u, 0, d);    sort(dis.begin(), dis.end());    int i = 0, j = dis.size() - 1;    int res = 0;    while (i < j)    {        while (dis[i] + dis[j] > k && i < j)            j--;        res += j - i;        i ++;    }    return res;}void dfs(int u){    Min = n;    dfs_sz(u, 0);    dfs_root(u, u, 0);    ans += get_ans(root, 0);    vis[root] = 1;    for (int i = head[root]; ~i; i = edge[i].next)    {        int v = edge[i].v;        if (vis[v])            continue;        ans -= get_ans(v, edge[i].d);        dfs(v);    }}int main(){    while (scanf("%d%d", &n, &k) == 2)    {        if (n == 0 && k == 0)            break;        init();        for (int i = 1; i < n; i++)        {            int u, v, d;            scanf("%d%d%d", &u, &v, &d);            add_edge(u, v, d);            add_edge(v, u, d);        }        dfs(1);        printf("%d\n", ans);    }}