题目背景
缩点+DP
题目描述
给定一个n个点m条边有向图,每个点有一个权值,求一条路径,使路径经过的点权值之和最大。你只需要求出这个权值和。
允许多次经过一条边或者一个点,但是,重复经过的点,权值只计算一次。
输入输出格式
输入格式:
第一行,n,m
第二行,n个整数,依次代表点权
第三至m+2行,每行两个整数u,v,表示u->v有一条有向边
输出格式:
共一行,最大的点权之和。
输入输出样例
输入样例#1:
复制
2 2 1 1 1 2 2 1
输出样例#1: 复制
2
说明
n<=10^4,m<=10^5,点权<=1000
算法:Tarjan缩点+DAGdp
Tarjan+记忆化搜索;
缩点以后,重新建图,然后dp;
#include<iostream> #include<cstdio> #include<algorithm> #include<cstdlib> #include<cstring> #include<string> #include<cmath> #include<map> #include<set> #include<vector> #include<queue> #include<bitset> #include<ctime> #include<deque> #include<stack> #include<functional> #include<sstream> //#include<cctype> //#pragma GCC optimize(2) using namespace std; #define maxn 400005 #define inf 0x7fffffff //#define INF 1e18 #define rdint(x) scanf("%d",&x) #define rdllt(x) scanf("%lld",&x) #define rdult(x) scanf("%lu",&x) #define rdlf(x) scanf("%lf",&x) #define rdstr(x) scanf("%s",x) typedef long long ll; typedef unsigned long long ull; typedef unsigned int U; #define ms(x) memset((x),0,sizeof(x)) const long long int mod = 1e9 + 7; #define Mod 1000000000 #define sq(x) (x)*(x) #define eps 1e-3 typedef pair<int, int> pii; #define pi acos(-1.0) const int N = 1005; #define REP(i,n) for(int i=0;i<(n);i++) typedef pair<int, int> pii; inline ll rd() { ll x = 0; char c = getchar(); bool f = false; while (!isdigit(c)) { if (c == ‘-‘) f = true; c = getchar(); } while (isdigit(c)) { x = (x << 1) + (x << 3) + (c ^ 48); c = getchar(); } return f ? -x : x; } ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a%b); } ll sqr(ll x) { return x * x; } /*ll ans; ll exgcd(ll a, ll b, ll &x, ll &y) { if (!b) { x = 1; y = 0; return a; } ans = exgcd(b, a%b, x, y); ll t = x; x = y; y = t - a / b * y; return ans; } */ int n, m; int idx; int col[maxn], dp[maxn], sum[maxn]; int head[maxn]; int sk[maxn], top; int dfn[maxn], low[maxn]; int tot; int vis[maxn]; int val[maxn]; struct node { int u, v, nxt; }edge[maxn]; int cnt; void addedge(int x, int y) { edge[++cnt].v = y; edge[cnt].nxt = head[x]; head[x] = cnt; } void tarjan(int x) { sk[++top] = x; vis[x] = 1; low[x] = dfn[x] = ++idx; for (int i = head[x]; i; i = edge[i].nxt) { int v = edge[i].v; if (!dfn[v]) { tarjan(v); low[x] = min(low[x], low[v]); } else if (vis[v]) { low[x] = min(low[x], dfn[v]); } } if (dfn[x] == low[x]) { tot++; while (sk[top + 1] != x) { col[sk[top]] = tot; sum[tot] += val[sk[top]]; vis[sk[top--]] = 0; } } } void DP(int x) { int maxx = 0; if (dp[x])return; dp[x] = sum[x]; for (int i = head[x]; i; i = edge[i].nxt) { int v = edge[i].v; if (!dp[v])DP(v); maxx = max(maxx, dp[v]); } dp[x] += maxx; } int x[maxn], y[maxn]; int main() { //ios::sync_with_stdio(0); rdint(n); rdint(m); for (int i = 1; i <= n; i++)rdint(val[i]); for (int i = 1; i <= m; i++) { rdint(x[i]); rdint(y[i]); addedge(x[i], y[i]); } for (int i = 1; i <= n; i++)if (!dfn[i])tarjan(i); ms(edge); cnt = 0; ms(head); for (int i = 1; i <= m; i++) { if (col[x[i]] != col[y[i]]) { addedge(col[x[i]], col[y[i]]); } } int ans = 0; for (int i = 1; i <= tot; i++) { if (!dp[i]) { DP(i); ans = max(ans, dp[i]); } } cout << ans << endl; return 0; }
原文地址:https://www.cnblogs.com/zxyqzy/p/10165401.html
时间: 2024-10-14 21:46:08