洛谷P3128 [USACO15DEC]最大流Max Flow(树上差分)

题意

题目链接

sol

树上差分模板题

发现自己傻傻的分不清边差分和点差分

边差分就是对边进行操作，我们在$u, v$除加上$val$，同时在$lca$处减去$2 * val$

点差分是对点操作，我们在$u, v$处加上$val$，在$lca$和$fa[lca]$处减去$val$

就本题而言，属于点差分

#include<bits/stdc++.h>
const int maxn = 1e5 + 10;
using namespace std;
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * f;
}
int n, k, dep[maxn], fa[maxn][21], dfn[maxn], val[maxn], tot;
vector<int> v[maxn];
void dfs(int x, int _fa) {
    fa[x][0] = _fa; dep[x] = dep[fa[x][0]] + 1; dfn[++tot] = x;
    for(int i = 1; i <= 20; i++) fa[x][i] = fa[fa[x][i - 1]][i - 1];
    for(int i = 0, to; i < v[x].size(); i++) {
        if((to = v[x][i]) == _fa) continue;
        dfs(to, x);
    }
}
int lca(int x, int y) {
    if(dep[x] < dep[y]) swap(x, y);
    for(int i = 20; i >= 0; i--) if(dep[fa[x][i]] >= dep[y]) x = fa[x][i];
    if(x == y) return x;
    for(int i = 20; i >= 0; i--) if(fa[x][i] ^ fa[y][i]) x = fa[x][i], y = fa[y][i];
    return fa[x][0];
}
int main() {
    n = read(); k = read();
    for(int i = 1; i <= n - 1; i++) {
        int x = read(), y = read();
        v[x].push_back(y); v[y].push_back(x);
    }
    dfs(1, 0);
    for(int i = 1; i <= k; i++) {
        int x = read(), y = read();
        val[x]++; val[y]++;
        int lca = lca(x, y); 
        val[lca]--; val[fa[lca][0]]--;
    }
    int ans = 0;
    for(int i = n; i >= 1; i--) val[fa[dfn[i]][0]] += val[dfn[i]];
    for(int i = 1; i <= n; i++) ans = max(ans, val[i]);
    printf("%d", ans);
    return 0;
}