【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。

 /* 4312 */
 #include <iostream>
 #include <sstream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 #include <functional>
 #include <iterator>
 #include <iomanip>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,1024000")

 #define sti                set<int>
 #define stpii            set<pair<int, int> >
 #define mpii            map<int,int>
 #define vi                vector<int>
 #define pii                pair<int,int>
 #define vpii            vector<pair<int,int> >
 #define rep(i, a, n)     for (int i=a;i<n;++i)
 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 #define clr                clear
 #define pb                 push_back
 #define mp                 make_pair
 #define fir                first
 #define sec                second
 #define all(x)             (x).begin(),(x).end()
 #define SZ(x)             ((int)(x).size())
 #define lson            l, mid, rt<<1
 #define rson            mid+1, r, rt<<1|1

 typedef struct {
     int v, w, f, nxt;
 } edge_t;

 const int INF = 0x3f3f3f3f;
 const int maxv = ;
 const int maxe = 1e5+;
 int need[maxv];
 int a[][];
 int head[maxv], l;
 edge_t E[maxe];
 int dis[maxv];
 int pre[maxv], ID[maxv];
 bool visit[maxv];
 int cost, flow;
 int n, m, K;
 const int ed = maxv - ;
 const int st = maxv - ;

 void init() {
     l = ;
     memset(head, -, sizeof(head));
 }

 void addEdge(int u, int v, int w, int c) {
     E[l].v = v;
     E[l].w = w;
     E[l].f = c;
     E[l].nxt = head[u];
     head[u] = l++;

     E[l].v = u;
     E[l].w = -w;
     E[l].f = ;
     E[l].nxt = head[v];
     head[v] = l++;
 }

 bool bfs() {
     queue<int> Q;
     int u, v, k;

     memset(dis, INF, sizeof(dis));
     memset(visit, false, sizeof(visit));
     Q.push(st);
     visit[st] = true;
     dis[st] = ;

     while (!Q.empty()) {
         u = Q.front();
         Q.pop();
         visit[u] = false;
         for (k=head[u]; k!=-; k=E[k].nxt) {
             v = E[k].v;
             if (E[k].f && dis[v]>dis[u]+E[k].w) {
                 dis[v] = dis[u] + E[k].w;
                 pre[v] = u;
                 ID[v] = k;
                 if (!visit[v]) {
                     visit[v] = true;
                     Q.push(v);
                 }
             }
         }
     }

     return dis[ed]==INF;
 }

 void MCMF() {
     int u, v, k;
     int tmp;

     flow = , cost = ;

     while () {
         if (bfs())
             break;

         tmp = INF;
         for (v=ed, u=pre[v]; v!=st; v=u, u=pre[v]) {
             k = ID[v];
             tmp = min(tmp, E[k].f);
         }

         for (v=ed, u=pre[v]; v!=st; v=u, u=pre[v]) {
             k = ID[v];
             E[k].f -= tmp;
             E[k^].f += tmp;
         }

         flow += tmp;
         cost += tmp * dis[ed];
     }
 }

 void solve() {
     int tot = , tmp;

     init();
     rep(i, , m)
         addEdge(st, i+n, , );

     rep(i, , n) {
         tot += need[i];
         rep(j, , m) {
             if (a[i][j])
                 addEdge(j+n, i, , );
         }
         tmp = need[i] / K;
         if (tmp) {
             addEdge(i, ed, -K, tmp);
         }
         tmp = need[i] % K;
         if (tmp > ) {
             addEdge(i, ed, -tmp, );
         }
     }

     MCMF();

     cost = -cost;
     if (cost+m-flow < tot)
         puts("NO");
     else
         puts("YES");
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     int t;

     scanf("%d", &t);
     rep(tt, , t+) {
         scanf("%d %d %d", &m, &n, &K);
         rep(i, , n)
             scanf("%d", &need[i]);
         rep(i, , n)
             rep(j, , m)
                 scanf("%d", &a[i][j]);
         printf("Case #%d: ", tt);
         solve();
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }

数据发生器。

 from copy import deepcopy
 from random import randint, shuffle
 import shutil
 import string

 def GenDataIn():
     with open("data.in", "w") as fout:
         t = 50
         bound = 10**18
         fout.write("%d\n" % (t))
         for tt in xrange(t):
             m = randint(1, 13)
             n = randint(1, 13)
             k = randint(2, 10)
             fout.write("%d %d %d\n" % (m, n, k))
             L = []
             for i in xrange(n):
                 x = randint(1, 20)
                 L.append(x)
             fout.write(" ".join(map(str, L)) + "\n")
             for i in xrange(n):
                 L = []
                 for j in xrange(m):
                     x = randint(0, 1)
                     L.append(x)
                 fout.write(" ".join(map(str, L)) + "\n")

 def MovDataIn():
     desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
     shutil.copyfile("data.in", desFileName)

 if __name__ == "__main__":
     GenDataIn()
     MovDataIn()