【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 = 30;
const int maxe = 1e5+5;
int need[maxv];
int a[15][15];
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 - 1;
const int st = maxv - 2;

void init() {
    l = 0;
    memset(head, -1, 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 = 0;
    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] = 0;
    
    while (!Q.empty()) {
        u = Q.front();
        Q.pop();
        visit[u] = false;
        for (k=head[u]; k!=-1; 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 = 0, cost = 0;
    
    while (1) {
        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^1].f += tmp;
        }
        
        flow += tmp;
        cost += tmp * dis[ed];
    }
}

void solve() {
    int tot = 0, tmp;
    
    init();
    rep(i, 0, m)
        addEdge(st, i+n, 0, 1);
    
    rep(i, 0, n) {
        tot += need[i];
        rep(j, 0, m) {
            if (a[i][j])
                addEdge(j+n, i, 0, 1);
        }
        tmp = need[i] / K;
        if (tmp) {
            addEdge(i, ed, -K, tmp);
        }
        tmp = need[i] % K;
        if (tmp > 1) {
            addEdge(i, ed, -tmp, 1);
        }
    }
    
    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, 1, t+1) {
        scanf("%d %d %d", &m, &n, &K);
        rep(i, 0, n)
            scanf("%d", &need[i]);
        rep(i, 0, n)
            rep(j, 0, m)
                scanf("%d", &a[i][j]);
        printf("Case #%d: ", tt);
        solve();
    }
    
    #ifndef ONLINE_JUDGE
        printf("time = %d.
", (int)clock());
    #endif
    
    return 0;
}

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
" % (t))
        for tt in xrange(t):
            m = randint(1, 13)
            n = randint(1, 13)
            k = randint(2, 10)
            fout.write("%d %d %d
" % (m, n, k))
            L = []
            for i in xrange(n):
                x = randint(1, 20)
                L.append(x)
            fout.write(" ".join(map(str, L)) + "
")
            for i in xrange(n):
                L = []
                for j in xrange(m):
                    x = randint(0, 1)
                    L.append(x)
                fout.write(" ".join(map(str, L)) + "
")
            
                
def MovDataIn():
    desFileName = "F:eclipse_prjworkspacehdojdata.in"
    shutil.copyfile("data.in", desFileName)

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