输入输出样例
输入 #1复制
11 12 1 2 1 3 1 4 2 5 3 6 4 7 5 8 6 9 7 10 8 11 9 11 10 11
输出 #1复制
1 4 7 10 11 2 5 8 3 6 9 3
说明/提示
1\leq n\leq 150,1\leq m\leq 60001≤n≤150,1≤m≤6000
由@FlierKing提供SPJ
思路
既然是网络流24中的题目，就从网络流的方法下手吧。
对于样例来说
其实不难看出这题是和流的路径有关的。
为了保证每个点只能用一次，
可以考虑把每个点拆成出入两个点，
它们之间的通道容量为1.
由于起点终点的不确定，
对整张图建立源点和汇点即可。
CODE
1 #include <bits/stdc++.h>
2 #define dbg(x) cout << #x << "=" << x << endl
3 #define eps 1e-8
4 #define pi acos(-1.0)
5
6 using namespace std;
7 typedef long long LL;
8
9 const int inf = 0x3f3f3f3f;
10
11 template<class T>inline void read(T &res)
12 {
13 char c;T flag=1;
14 while((c=getchar())<‘0‘||c>‘9‘)if(c==‘-‘)flag=-1;res=c-‘0‘;
15 while((c=getchar())>=‘0‘&&c<=‘9‘)res=res*10+c-‘0‘;res*=flag;
16 }
17
18 namespace _buff {
19 const size_t BUFF = 1 << 19;
20 char ibuf[BUFF], *ib = ibuf, *ie = ibuf;
21 char getc() {
22 if (ib == ie) {
23 ib = ibuf;
24 ie = ibuf + fread(ibuf, 1, BUFF, stdin);
25 }
26 return ib == ie ? -1 : *ib++;
27 }
28 }
29
30 int qread() {
31 using namespace _buff;
32 int ret = 0;
33 bool pos = true;
34 char c = getc();
35 for (; (c < ‘0‘ || c > ‘9‘) && c != ‘-‘; c = getc()) {
36 assert(~c);
37 }
38 if (c == ‘-‘) {
39 pos = false;
40 c = getc();
41 }
42 for (; c >= ‘0‘ && c <= ‘9‘; c = getc()) {
43 ret = (ret << 3) + (ret << 1) + (c ^ 48);
44 }
45 return pos ? ret : -ret;
46 }
47
48 const int maxn = 2e4 + 7;
49
50 int s, t, cnt;
51 int head[maxn << 1], edge[maxn << 1], nxt[maxn << 1], vis[maxn << 1];
52 int w[maxn << 1];//残量网络
53 int rev[maxn << 1];
54 int depth[maxn << 1];//图层
55 int n, m;
56
57 void BuildGraph(int u, int v, int cap) {
58 ++cnt;
59 edge[cnt] = v;
60 nxt[cnt] = head[u];
61 rev[cnt] = cnt + 1;
62 w[cnt] = cap;
63 head[u] = cnt;
64
65 ++cnt;
66 edge[cnt] = u;
67 nxt[cnt] = head[v];
68 w[cnt] = 0;
69 rev[cnt] = cnt - 1;
70 head[v] = cnt;
71 }
72
73 bool bfs(int x) {
74 queue<int> q;
75 while(!q.empty()) {
76 q.pop();
77 }
78 memset(depth, 63, sizeof(depth));
79 depth[s] = 0;
80 q.push(s);
81 do {
82 int u = q.front();
83 q.pop();
84 for ( int i = head[u]; i; i = nxt[i] ) {
85 int v = edge[i];
86 if(w[i] > 0 && depth[u] + 1 < depth[v]) {
87 depth[v] = depth[u] + 1;
88 q.push(v);
89 if(v == t) {
90 return true;
91 }
92 }
93 }
94 } while (!q.empty());
95 return false;
96 }
97
98 int dfs(int u, int dist) {
99 if(u == t) {
100 return dist;
101 }
102 for ( int i = head[u]; i; i = nxt[i] ) {
103 int v = edge[i];
104 if(depth[v] == depth[u] + 1 && w[i] > 0) {
105 int di = dfs(v, min(dist, w[i]));
106 if(di > 0) {
107 w[i] -= di;
108 w[rev[i]] += di;
109 vis[u] = v;
110 //printf("vis[%d]:%d\n",u, v);
111 return di;
112 }
113 }
114 }
115 return 0;
116 }
117
118 int main()
119 {
120 //freopen("data.txt", "r", stdin);
121 memset(vis, 0, sizeof(vis));
122 read(n); read(m);
123 s = 0, t = 2 * n + 1;
124 for ( int i = 1; i <= m; ++i ) {
125 int u, v;
126 read(u); read(v);
127 BuildGraph(u, v + n, 1);
128 }
129 for ( int i = 1; i <= n; ++i ) {
130 BuildGraph(s, i, 1);
131 BuildGraph(n + i, t, 1);
132 }
133 int ans = 0;
134 while(bfs(s)) {
135 //cout << "!" << endl;
136 int res = dfs(0, 0x7f7f7f7f);
137 ans += res;
138 }
139 for ( int i = 1; i <= n; ++i ) {
140 if(vis[i]) {
141 int temp = i;
142 do {
143 if(temp > n) {
144 temp -= n;
145 }
146 printf("%d ",temp);
147 int x = vis[temp];
148 vis[temp] = 0;
149 temp = x;
150 } while (temp != 0);
151 puts("");
152 }
153 }
154 printf("%d\n",n - ans);
155 return 0;
156 }
#include <bitsst#define dbg(x) cout << #x << "=" << x << endl#define eps 1e-8#define pi acos(-1.0)usingnamespacestd; typedeflonglong LL; constint inf = 0x3f3f3f3f; template<class T>inline void read(T &res) {char c;T flag=1; while((c=getchar())<‘0‘||c>‘9‘)if(c==‘-‘)flag=-1;res=c-‘0‘; while((c=getchar())>=‘0‘&&c<=‘9‘)res=res*10+c-‘0‘;res*=flag; } namespace _buff { constsize_t BUFF = 1 << 19; char ibuf[BUFF], *ib = ibuf, *ie = ibuf; char getc() { if (ib == ie) { ib = ibuf; ie = ibuf + fread(ibuf, 1, BUFF, stdin); } return ib == ie ? -1 : *ib++; } } int qread() { usingnamespace _buff; int ret = 0; bool pos = true; char c = getc(); for (; (c < ‘0‘ || c > ‘9‘) && c != ‘-‘; c = getc()) { assert(~c); } if (c == ‘-‘) { pos = false; c = getc(); } for (; c >= ‘0‘ && c <= ‘9‘; c = getc()) { ret = (ret << 3) + (ret << 1) + (c ^ 48); } return pos ? ret : -ret; } constint maxn = 2e4 + 7; int s, t, cnt; int head[maxn << 1], edge[maxn << 1], nxt[maxn << 1], vis[maxn << 1]; int w[maxn << 1];//残量网络int rev[maxn << 1]; int depth[maxn << 1];//图层int n, m; void BuildGraph(int u, int v, int cap) { ++cnt; edge[cnt] = v; nxt[cnt] = head[u]; rev[cnt] = cnt + 1; w[cnt] = cap; head[u] = cnt; ++cnt; edge[cnt] = u; nxt[cnt] = head[v]; w[cnt] = 0; rev[cnt] = cnt - 1; head[v] = cnt; } bool bfs(int x) { queue<int> q; while(!q.empty()) { q.pop(); } memset(depth, 63, sizeof(depth)); depth[s] = 0; q.push(s); do { int u = q.front(); q.pop(); for ( int i = head[u]; i; i = nxt[i] ) { int v = edge[i]; if(w[i] > 0 && depth[u] + 1 < depth[v]) { depth[v] = depth[u] + 1; q.push(v); if(v == t) { returntrue; } } } } while (!q.empty()); returnfalse; } int dfs(int u, int dist) { if(u == t) { return dist; } for ( int i = head[u]; i; i = nxt[i] ) { int v = edge[i]; if(depth[v] == depth[u] + 1 && w[i] > 0) { int di = dfs(v, min(dist, w[i])); if(di > 0) { w[i] -= di; w[rev[i]] += di; vis[u] = v; //printf("vis[%d]:%d\n",u, v);return di; } } } return0; } int main() { //freopen("data.txt", "r", stdin);memset(vis, 0, sizeof(vis)); read(n); read(m); s = 0, t = 2 * n + 1; for ( int i = 1; i <= m; ++i ) { int u, v; read(u); read(v); BuildGraph(u, v + n, 1); } for ( int i = 1; i <= n; ++i ) { BuildGraph(s, i, 1); BuildGraph(n + i, t, 1); } int ans = 0; while(bfs(s)) { //cout << "!" << endl;int res = dfs(0, 0x7f7f7f7f); ans += res; } for ( int i = 1; i <= n; ++i ) { if(vis[i]) { int temp = i; do { if(temp > n) { temp -= n; } printf("%d ",temp); int x = vis[temp]; vis[temp] = 0; temp = x; } while (temp != 0); puts(""); } } printf("%d\n",n - ans); return0; }
原文地址：https://www.cnblogs.com/orangeko/p/12639171.html