[CSUOJ1804]有向无环图(树dp)

题目链接:http://acm.csu.edu.cn/OnlineJudge/problem.php?id=1804

题意:中文题面,那个式子也很清楚。

1e5这个点数量很大了,由于是个DAG,可以认为整张图是一个森林,关注点应该放在每一棵树上的每一个点对整题的贡献。

记每一个起点u,v是u的后继。v有多个,记作vi,u到vi的贡献是count(u,vi)*a(u)*b(vi),提出a(u),剩下count(u,vi)*b(vi),count(u,vi)可以后序遍历得到,整个结果存在dp(u)中,后序更新答案时dp(u)*a(u)即可。随后可以更新b(vi)部分,每次累加到dp(u)上,因为下一次的访问(u的父亲)必定包括了dp(u)的结果。

  1 /*
  2 ━━━━━┒ギリギリ♂ eye!
  3 ┓┏┓┏┓┃キリキリ♂ mind!
  4 ┛┗┛┗┛┃\○/
  5 ┓┏┓┏┓┃ /
  6 ┛┗┛┗┛┃ノ)
  7 ┓┏┓┏┓┃
  8 ┛┗┛┗┛┃
  9 ┓┏┓┏┓┃
 10 ┛┗┛┗┛┃
 11 ┓┏┓┏┓┃
 12 ┛┗┛┗┛┃
 13 ┓┏┓┏┓┃
 14 ┃┃┃┃┃┃
 15 ┻┻┻┻┻┻
 16 */
 17 #include <algorithm>
 18 #include <iostream>
 19 #include <iomanip>
 20 #include <cstring>
 21 #include <climits>
 22 #include <complex>
 23 #include <fstream>
 24 #include <cassert>
 25 #include <cstdio>
 26 #include <bitset>
 27 #include <vector>
 28 #include <deque>
 29 #include <queue>
 30 #include <stack>
 31 #include <ctime>
 32 #include <set>
 33 #include <map>
 34 #include <cmath>
 35 using namespace std;
 36 #define fr first
 37 #define sc second
 38 #define cl clear
 39 #define BUG puts("here!!!")
 40 #define W(a) while(a--)
 41 #define pb(a) push_back(a)
 42 #define Rint(a) scanf("%d", &a)
 43 #define Rll(a) scanf("%I64d", &a)
 44 #define Rs(a) scanf("%s", a)
 45 #define Cin(a) cin >> a
 46 #define FRead() freopen("in", "r", stdin)
 47 #define FWrite() freopen("out", "w", stdout)
 48 #define Rep(i, len) for(int i = 0; i < (len); i++)
 49 #define For(i, a, len) for(int i = (a); i < (len); i++)
 50 #define Cls(a) memset((a), 0, sizeof(a))
 51 #define Clr(a, x) memset((a), (x), sizeof(a))
 52 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))
 53 #define lrt rt << 1
 54 #define rrt rt << 1 | 1
 55 #define pi 3.14159265359
 56 #define RT return
 57 #define lowbit(x) x & (-x)
 58 #define onecnt(x) __builtin_popcount(x)
 59 typedef long long LL;
 60 typedef long double LD;
 61 typedef unsigned long long ULL;
 62 typedef pair<int, int> pii;
 63 typedef pair<string, int> psi;
 64 typedef pair<LL, LL> pll;
 65 typedef map<string, int> msi;
 66 typedef vector<int> vi;
 67 typedef vector<LL> vl;
 68 typedef vector<vl> vvl;
 69 typedef vector<bool> vb;
 70 
 71 const int maxn = 100100;
 72 const LL mod = 1e9+7;
 73 int n, m;
 74 int a[maxn], b[maxn];
 75 vi G[maxn];
 76 bool vis[maxn];
 77 LL dp[maxn];
 78 LL ret;
 79 
 80 void dfs(int u) {
 81     Rep(i, G[u].size()) {
 82         int v = G[u][i];
 83         if(!vis[v]) {
 84             vis[v] = 1;
 85             dfs(v);
 86         }
 87         dp[u] = (dp[u] + dp[v]) % mod;
 88     }
 89     ret = (ret + (dp[u] * a[u] % mod)) % mod;
 90     dp[u] = (dp[u] + b[u]) % mod;
 91 }
 92 
 93 int main() {
 94     // FRead();
 95     int u, v;
 96     while(~Rint(n)&&~Rint(m)) {
 97         ret = 0; Cls(vis); Cls(dp);
 98         For(i, 1, n+1) {
 99             Rint(a[i]), Rint(b[i]);
100             G[i].clear();
101         }
102         Rep(i, m) {
103             Rint(u); Rint(v);
104             G[u].pb(v);
105         }
106         For(i, 1, n+1) {
107             if(!vis[i]) dfs(i);
108         }
109         For(i, 1, n+1) cout << dp[i] << " ";
110         cout << endl;
111         cout << ret << endl;
112     }
113     RT 0;
114 }
原文地址:https://www.cnblogs.com/kirai/p/5842435.html