【HDOJ】4322 Candy

状态DP显然可以解，发现T了，不知道优化后能不能过。
然后发现费用流可以解。trick是对need拆解成need/K, need%K两种情况讨论。

  1 /* 4312 */
  2 #include <iostream>
  3 #include <sstream>
  4 #include <string>
  5 #include <map>
  6 #include <queue>
  7 #include <set>
  8 #include <stack>
  9 #include <vector>
 10 #include <deque>
 11 #include <algorithm>
 12 #include <cstdio>
 13 #include <cmath>
 14 #include <ctime>
 15 #include <cstring>
 16 #include <climits>
 17 #include <cctype>
 18 #include <cassert>
 19 #include <functional>
 20 #include <iterator>
 21 #include <iomanip>
 22 using namespace std;
 23 //#pragma comment(linker,"/STACK:102400000,1024000")
 24 
 25 #define sti                set<int>
 26 #define stpii            set<pair<int, int> >
 27 #define mpii            map<int,int>
 28 #define vi                vector<int>
 29 #define pii                pair<int,int>
 30 #define vpii            vector<pair<int,int> >
 31 #define rep(i, a, n)     for (int i=a;i<n;++i)
 32 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 33 #define clr                clear
 34 #define pb                 push_back
 35 #define mp                 make_pair
 36 #define fir                first
 37 #define sec                second
 38 #define all(x)             (x).begin(),(x).end()
 39 #define SZ(x)             ((int)(x).size())
 40 #define lson            l, mid, rt<<1
 41 #define rson            mid+1, r, rt<<1|1
 42 
 43 typedef struct {
 44     int v, w, f, nxt;
 45 } edge_t;
 46 
 47 const int INF = 0x3f3f3f3f;
 48 const int maxv = 30;
 49 const int maxe = 1e5+5;
 50 int need[maxv];
 51 int a[15][15];
 52 int head[maxv], l;
 53 edge_t E[maxe];
 54 int dis[maxv];
 55 int pre[maxv], ID[maxv];
 56 bool visit[maxv];
 57 int cost, flow;
 58 int n, m, K;
 59 const int ed = maxv - 1;
 60 const int st = maxv - 2;
 61 
 62 void init() {
 63     l = 0;
 64     memset(head, -1, sizeof(head));
 65 }
 66 
 67 void addEdge(int u, int v, int w, int c) {
 68     E[l].v = v;
 69     E[l].w = w;
 70     E[l].f = c;
 71     E[l].nxt = head[u];
 72     head[u] = l++;
 73     
 74     E[l].v = u;
 75     E[l].w = -w;
 76     E[l].f = 0;
 77     E[l].nxt = head[v];
 78     head[v] = l++;
 79 }
 80 
 81 bool bfs() {
 82     queue<int> Q;
 83     int u, v, k;
 84     
 85     memset(dis, INF, sizeof(dis));
 86     memset(visit, false, sizeof(visit));
 87     Q.push(st);
 88     visit[st] = true;
 89     dis[st] = 0;
 90     
 91     while (!Q.empty()) {
 92         u = Q.front();
 93         Q.pop();
 94         visit[u] = false;
 95         for (k=head[u]; k!=-1; k=E[k].nxt) {
 96             v = E[k].v;
 97             if (E[k].f && dis[v]>dis[u]+E[k].w) {
 98                 dis[v] = dis[u] + E[k].w;
 99                 pre[v] = u;
100                 ID[v] = k;
101                 if (!visit[v]) {
102                     visit[v] = true;
103                     Q.push(v);
104                 }
105             }
106         }
107     }
108     
109     return dis[ed]==INF;
110 }
111 
112 void MCMF() {
113     int u, v, k;
114     int tmp;
115     
116     flow = 0, cost = 0;
117     
118     while (1) {
119         if (bfs())
120             break;
121         
122         tmp = INF;
123         for (v=ed, u=pre[v]; v!=st; v=u, u=pre[v]) {
124             k = ID[v];
125             tmp = min(tmp, E[k].f);
126         }
127         
128         for (v=ed, u=pre[v]; v!=st; v=u, u=pre[v]) {
129             k = ID[v];
130             E[k].f -= tmp;
131             E[k^1].f += tmp;
132         }
133         
134         flow += tmp;
135         cost += tmp * dis[ed];
136     }
137 }
138 
139 void solve() {
140     int tot = 0, tmp;
141     
142     init();
143     rep(i, 0, m)
144         addEdge(st, i+n, 0, 1);
145     
146     rep(i, 0, n) {
147         tot += need[i];
148         rep(j, 0, m) {
149             if (a[i][j])
150                 addEdge(j+n, i, 0, 1);
151         }
152         tmp = need[i] / K;
153         if (tmp) {
154             addEdge(i, ed, -K, tmp);
155         }
156         tmp = need[i] % K;
157         if (tmp > 1) {
158             addEdge(i, ed, -tmp, 1);
159         }
160     }
161     
162     MCMF();
163     
164     cost = -cost;
165     if (cost+m-flow < tot)
166         puts("NO");
167     else
168         puts("YES");
169 }
170 
171 int main() {
172     ios::sync_with_stdio(false);
173     #ifndef ONLINE_JUDGE
174         freopen("data.in", "r", stdin);
175         freopen("data.out", "w", stdout);
176     #endif
177     
178     int t;
179     
180     scanf("%d", &t);
181     rep(tt, 1, t+1) {
182         scanf("%d %d %d", &m, &n, &K);
183         rep(i, 0, n)
184             scanf("%d", &need[i]);
185         rep(i, 0, n)
186             rep(j, 0, m)
187                 scanf("%d", &a[i][j]);
188         printf("Case #%d: ", tt);
189         solve();
190     }
191     
192     #ifndef ONLINE_JUDGE
193         printf("time = %d.\n", (int)clock());
194     #endif
195     
196     return 0;
197 }

数据发生器。

 1 from copy import deepcopy
 2 from random import randint, shuffle
 3 import shutil
 4 import string
 5 
 6 
 7 def GenDataIn():
 8     with open("data.in", "w") as fout:
 9         t = 50
10         bound = 10**18
11         fout.write("%d\n" % (t))
12         for tt in xrange(t):
13             m = randint(1, 13)
14             n = randint(1, 13)
15             k = randint(2, 10)
16             fout.write("%d %d %d\n" % (m, n, k))
17             L = []
18             for i in xrange(n):
19                 x = randint(1, 20)
20                 L.append(x)
21             fout.write(" ".join(map(str, L)) + "\n")
22             for i in xrange(n):
23                 L = []
24                 for j in xrange(m):
25                     x = randint(0, 1)
26                     L.append(x)
27                 fout.write(" ".join(map(str, L)) + "\n")
28             
29                 
30 def MovDataIn():
31     desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
32     shutil.copyfile("data.in", desFileName)
33 
34     
35 if __name__ == "__main__":
36     GenDataIn()
37     MovDataIn()