思路
比赛的时候读了下感觉是网络流，还口胡了正解
然而打歪了？？？
一直以为只能用一周做完任务，还在想只有7天枚举不就好了还写啥Dinic，真是图样啊
一开始做的是动态建图跑最大流枚举悔边（毕竟一开始以为只能用一周来做任务
建立源点，连接周几，容量为e，然后对每个可以在这一天上开展的任务连边，容量为inf，最后把任务连汇点，容量为 c [ i ]，对于天数动态加边建立一张图跑最大流
其实这样做反而复杂化了。
如果不是在一周内做完的话，实际上就是一个求能满足整张图的跑满时边的容量的最大值最小的问题
那么很容易想到二分法
因为容量实际上是和天数相关的，而我们最终也是在求这个天数
所以考虑二分天数
天数和流量的关系是什么呢？
不难想到，从 0 周开始算，例如周一的容量就是 本周是第 i 周 * e + 这周是否已经过了周一 * e
以此类推，可以以此表示出不同天数的从 S 到周几的容量
然后跑DINIC，如果当前容量可以跑满的话，说明当前天数一定是 >= 最少天数的
以此作为 check 来更新 mid 和 ans 来求最少天数即可
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 LL inf = 1e14; 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 = 200007; 49 50 int n, m; 51 int s, t; 52 53 struct edge{ 54 int from,to; 55 LL cap,flow; 56 }; 57 58 map<int, int> vis; 59 60 struct DINIC { 61 int head[maxn << 1], nxt[maxn << 1]; 62 int edge[maxn << 1], cnt; 63 LL cap[maxn << 1], depth[maxn << 1]; 64 65 void init() { 66 cnt = 1; 67 memset(head, 0, sizeof(head)); 68 memset(depth, 0, sizeof(depth)); 69 memset(cap, 0, sizeof(cap)); 70 } 71 72 void BuildGraph(int u, int v, LL w) { 73 ++cnt; 74 edge[cnt] = v; 75 nxt[cnt] = head[u]; 76 cap[cnt] = w; 77 head[u] = cnt; 78 79 ++cnt; 80 edge[cnt] = u; 81 nxt[cnt] = head[v]; 82 cap[cnt] = 0; 83 head[v] = cnt; 84 } 85 86 queue<int> q; 87 88 bool bfs() { 89 memset(depth, 0, sizeof(depth)); 90 depth[s] = 1; 91 q.push(s); 92 while(!q.empty()) { 93 int u = q.front(); 94 q.pop(); 95 for ( int i = head[u]; i; i = nxt[i] ) { 96 int v = edge[i]; 97 if(depth[v]) { 98 continue; 99 } 100 if(cap[i]) { 101 depth[v] = depth[u] + 1; 102 q.push(v); 103 } 104 } 105 } 106 return depth[t]; 107 } 108 109 LL dfs(int u, LL dist) { 110 if(u == t) { 111 return dist; 112 } 113 LL flow = 0; 114 for ( int i = head[u]; i && dist; i = nxt[i] ) { 115 if(cap[i] == 0) 116 continue; 117 int v = edge[i]; 118 if(depth[v] != depth[u] + 1) { 119 continue; 120 } 121 LL res = dfs(v, min(cap[i], dist)); 122 cap[i] -= res; 123 cap[i ^ 1] += res; 124 //printf("cap[%d]:%d ",t, cap[t]); 125 dist -= res; 126 flow += res; 127 } 128 return flow; 129 } 130 131 LL maxflow() { 132 LL ans = 0; 133 while(bfs()) { 134 ans += dfs(s, inf); 135 } 136 return ans; 137 } 138 } dinic; 139 140 int e; 141 LL c[maxn], mi[maxn]; 142 int a[maxn][10]; 143 LL tot = 0; 144 145 void BuildGraph(LL limit) { 146 dinic.init(); 147 s = 0, t = n + 8; 148 for ( int i = 1; i <= 7; ++i ) { 149 LL day = limit / 7; 150 if(limit % 7 >= i) { 151 day++; 152 } 153 dinic.BuildGraph(s, i, day * e); 154 } 155 for ( int i = 1; i <= n; ++i ) { 156 for ( int j = 1; j <= mi[i]; ++j ) { 157 dinic.BuildGraph(a[i][j], i + 7, inf); 158 } 159 dinic.BuildGraph(i + 7, t, c[i]); 160 } 161 } 162 163 bool check(LL mid) { 164 if(e * mid < tot) { 165 return false; 166 } 167 BuildGraph(mid); 168 LL temp = dinic.maxflow(); 169 //if(temp < 100) dbg(temp); 170 return temp >= tot; 171 } 172 173 int main() 174 { 175 //freopen("data.txt", "r", stdin); 176 dinic.init(); 177 read(n); read(e); 178 s = 0, t = n + 8; 179 for ( int i = 1; i <= n; ++i ) { 180 read(c[i]); read(mi[i]); 181 tot += c[i]; 182 for ( int j = 1; j <= mi[i]; ++j ) { 183 read(a[i][j]); 184 } 185 } 186 LL l = 1, r = tot / e, mid, ans = 0; 187 while(l <= r) { 188 mid = (l + r) >> 1; 189 if(check(mid)) { 190 r = mid - 1; 191 ans = mid; 192 } 193 else { 194 l = mid + 1; 195 } 196 } 197 cout << ans << endl; 198 return 0; 199 }
#include <bits/stdc++.h>
#define dbg(x) cout << #x << "=" << x << endl
#define eps 1e-8
#define pi acos(-1.0)
using namespace std;
typedef long long LL;
const LL inf = 1e14;
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 {
const size_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() {
using namespace _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;
}
const int maxn = 200007;
int n, m;
int s, t;
struct edge{
int from,to;
LL cap,flow;
};
map<int, int> vis;
struct DINIC {
int head[maxn << 1], nxt[maxn << 1];
int edge[maxn << 1], cnt;
LL cap[maxn << 1], depth[maxn << 1];
void init() {
cnt = 1;
memset(head, 0, sizeof(head));
memset(depth, 0, sizeof(depth));
memset(cap, 0, sizeof(cap));
}
void BuildGraph(int u, int v, LL w) {
++cnt;
edge[cnt] = v;
nxt[cnt] = head[u];
cap[cnt] = w;
head[u] = cnt;
++cnt;
edge[cnt] = u;
nxt[cnt] = head[v];
cap[cnt] = 0;
head[v] = cnt;
}
queue<int> q;
bool bfs() {
memset(depth, 0, sizeof(depth));
depth[s] = 1;
q.push(s);
while(!q.empty()) {
int u = q.front();
q.pop();
for ( int i = head[u]; i; i = nxt[i] ) {
int v = edge[i];
if(depth[v]) {
continue;
}
if(cap[i]) {
depth[v] = depth[u] + 1;
q.push(v);
}
}
}
return depth[t];
}
LL dfs(int u, LL dist) {
if(u == t) {
return dist;
}
LL flow = 0;
for ( int i = head[u]; i && dist; i = nxt[i] ) {
if(cap[i] == 0)
continue;
int v = edge[i];
if(depth[v] != depth[u] + 1) {
continue;
}
LL res = dfs(v, min(cap[i], dist));
cap[i] -= res;
cap[i ^ 1] += res;
//printf("cap[%d]:%d
",t, cap[t]);
dist -= res;
flow += res;
}
return flow;
}
LL maxflow() {
LL ans = 0;
while(bfs()) {
ans += dfs(s, inf);
}
return ans;
}
} dinic;
int e;
LL c[maxn], mi[maxn];
int a[maxn][10];
LL tot = 0;
void BuildGraph(LL limit) {
dinic.init();
s = 0, t = n + 8;
for ( int i = 1; i <= 7; ++i ) {
LL day = limit / 7;
if(limit % 7 >= i) {
day++;
}
dinic.BuildGraph(s, i, day * e);
}
for ( int i = 1; i <= n; ++i ) {
for ( int j = 1; j <= mi[i]; ++j ) {
dinic.BuildGraph(a[i][j], i + 7, inf);
}
dinic.BuildGraph(i + 7, t, c[i]);
}
}
bool check(LL mid) {
if(e * mid < tot) {
return false;
}
BuildGraph(mid);
LL temp = dinic.maxflow();
//if(temp < 100) dbg(temp);
return temp >= tot;
}
int main()
{
//freopen("data.txt", "r", stdin);
dinic.init();
read(n); read(e);
s = 0, t = n + 8;
for ( int i = 1; i <= n; ++i ) {
read(c[i]); read(mi[i]);
tot += c[i];
for ( int j = 1; j <= mi[i]; ++j ) {
read(a[i][j]);
}
}
LL l = 1, r = tot / e, mid, ans = 0;
while(l <= r) {
mid = (l + r) >> 1;
if(check(mid)) {
r = mid - 1;
ans = mid;
}
else {
l = mid + 1;
}
}
cout << ans << endl;
return 0;
}