【codeforces】 461B Appleman and Tree

CF上的官方题解：

Fill a DP table such as the following bottom-up:

• DP[v][0] = the number of ways that the subtree rooted at vertex v has no black vertex.
• DP[v][1] = the number of ways that the subtree rooted at vertex v has one black vertex.

The recursion pseudo code is folloing:

DFS(v): DP[v][0] = 1 DP[v][1] = 0 foreach u : the children of vertex v  DFS(u)  DP[v][1] *= DP[u][0]  DP[v][1] += DP[v][0]*DP[u][1]  DP[v][0] *= DP[u][0] if x[v] == 1:  DP[v][1] = DP[v][0] else:  DP[v][0] += DP[v][1]

The answer is DP[root][1].

UPD:
The above code calculate the DP table while regarding that the vertex v is white (x[v]==0) in the foreach loop.

After that the code thinks about the color of vertex v and whether we cut the edge connecting vertex v and its parent or not in "if x[v] == 1: DP[v][1] = DP[v][0] else: DP[v][0] += DP[v][1]".

#include <iostream>  #include <queue>  #include <stack>  #include <map>  #include <set>  #include <bitset>  #include <cstdio>  #include <algorithm>  #include <cstring>  #include <climits>  #include <cstdlib>#include <cmath>#include <time.h>#define maxn 100005#define maxm 200005#define eps 1e-10#define mod 1000000007#define INF 999999999#define lowbit(x) (x&(-x))#define mp mark_pair#define ls o<<1#define rs o<<1 | 1#define lson o<<1, L, mid  #define rson o<<1 | 1, mid+1, R  //typedef vector<int>::iterator IT;typedef long long LL;//typedef int LL;using namespace std;LL qpow(LL a, LL b){LL res=1,base=a;while(b){if(b%2)res=res*base;base=base*base;b/=2;}return res;}LL powmod(LL a, LL b){LL res=1,base=a;while(b){if(b%2)res=res*base%mod;base=base*base%mod;b/=2;}return res;}void scanf(int &__x){__x=0;char __ch=getchar();while(__ch==' '||__ch=='\n')__ch=getchar();while(__ch>='0'&&__ch<='9')__x=__x*10+__ch-'0',__ch = getchar();}LL gcd(LL _a, LL _b){if(!_b) return _a;else return gcd(_b, _a%_b);}// headint h[maxn], next[maxm], v[maxm];int color[maxn], vis[maxn];LL dp[maxn][2];int cnt, n;void addedges(int a, int b){next[cnt] = h[a], h[a] = cnt, v[cnt] = b, cnt++;}void init(void){cnt = 0;memset(h, -1, sizeof h);memset(vis, 0, sizeof vis);}void read(void){scanf("%d", &n);for(int i = 1, j; i < n; i++) {scanf("%d", &j);addedges(i, j);addedges(j, i);}for(int i = 0; i < n; i++) scanf("%d", &color[i]);}void dfs(int u){dp[u][0] = 1;dp[u][1] = 0;for(int e = h[u]; ~e; e = next[e]) if(!vis[v[e]]) {vis[v[e]] = true;dfs(v[e]);dp[u][1] = (dp[u][1] * dp[v[e]][0]) % mod;dp[u][1] = (dp[u][1] + dp[u][0] * dp[v[e]][1]) % mod;dp[u][0] = (dp[u][0] * dp[v[e]][0]) % mod;}if(color[u]) dp[u][1] = dp[u][0];else dp[u][0] = (dp[u][0] + dp[u][1]) % mod;}void work(void){vis[0] = true;dfs(0);printf("%I64d\n", dp[0][1]);}int main(void){init();read();work();return 0;}