题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=5413
题意:给定一张有向图,对于边e<u,v>,如果去掉它的话,u仍然可以到达v的话,那么这条边就是多余边。
解法:显然的一个思路是倒着做。先topo一遍,然后倒着来,这里需要用到bitset维护每个点可以和哪些点直接相连,利用bitset是为了不超内存,然后用bitset处理出关系之后就可以遍历寻找答案了。
#include <bits/stdc++.h>
using namespace std;
struct FastIO
{
static const int S = 1310720;
int wpos;
char wbuf[S];
FastIO() : wpos(0) {}
inline int xchar()
{
static char buf[S];
static int len = 0, pos = 0;
if (pos == len)
pos = 0, len = fread(buf, 1, S, stdin);
if (pos == len) return -1;
return buf[pos ++];
}
inline int xuint()
{
int c = xchar(), x = 0;
while (c <= 32) c = xchar();
for (; '0' <= c && c <= '9'; c = xchar()) x = x * 10 + c - '0';
return x;
}
inline int xint()
{
int s = 1, c = xchar(), x = 0;
while (c <= 32) c = xchar();
if (c == '-') s = -1, c = xchar();
for (; '0' <= c && c <= '9'; c = xchar()) x = x * 10 + c - '0';
return x * s;
}
inline void xstring(char *s)
{
int c = xchar();
while (c <= 32) c = xchar();
for (; c > 32; c = xchar()) * s++ = c;
*s = 0;
}
inline void wchar(int x)
{
if (wpos == S) fwrite(wbuf, 1, S, stdout), wpos = 0;
wbuf[wpos ++] = x;
}
inline void wint(int x)
{
if (x < 0) wchar('-'), x = -x;
char s[24];
int n = 0;
while (x || !n) s[n ++] = '0' + x % 10, x /= 10;
while (n--) wchar(s[n]);
wchar('\n');
}
inline void wstring(const char *s)
{
while (*s) wchar(*s++);
}
~FastIO()
{
if (wpos) fwrite(wbuf, 1, wpos, stdout), wpos = 0;
}
} io;
const int maxn = 2e4+2;
int n, m, top, in[maxn], rec[maxn];
bitset <maxn> dp[maxn];
int head[maxn], edgecnt;
struct edge{
int u, v, next;
}E[100002];
struct node{
int u, v;
}q[100002];
void add(int u, int v){
E[edgecnt].u = u ,E[edgecnt].v = v, E[edgecnt].next = head[u], head[u] = edgecnt++;
}
void Toposort()
{
top = 0;
for(int i=1; i<=n; i++) if(in[i]==0) rec[top++]=i;
for(int i=0; i<top; i++){
int u = rec[i];
for(int j=head[u]; ~j; j=E[j].next){
int v = E[j].v;
if(--in[v]==0) rec[top++] = v;
}
}
}
int main()
{
int T;
T = io.xint();
while(T--)
{
n = io.xint();
m = io.xint();
edgecnt=0;
for(int i=1; i<=n; i++){
head[i]=-1;
in[i]=0;
}
for(int i=1; i<=m; i++){
int u, v;
u = io.xint();
v = io.xint();
q[i].u = u, q[i].v = v;
add(u, v);
in[v]++;
}
Toposort();
for(int i=0; i<=n; i++){
dp[i].reset();
dp[i].set(i);
}
int ans = 0;
for(int i=top-1; i>=0; i--){
int u = rec[i];
for(int j=head[u]; ~j; j=E[j].next){
int v = E[j].v;
dp[u][v] = 1;
dp[u]|=dp[v];
}
}
for(int i=1; i<=m; i++){
int u = q[i].u;
int v = q[i].v;
for(int j=head[u]; ~j; j=E[j].next){
if(E[j].v!=v&&dp[E[j].v][v]){
ans++;
break;
}
}
}
io.wint(ans);
}
return 0;
}