BZOJ 1570: [JSOI2008]Blue Mary的旅行( 二分答案 + 最大流 )

二分答案, 然后对于答案m, 把地点分成m层, 对于边(u, v), 第x层的u -> 第x+1层的v 连边. 然后第x层的u -> 第x+1层的u连边(+oo), S->第一层的1(PEOPLE_NUMBER), 每一层N -> T(+oo), 假如最大流是等于人数，就是可行答案.

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#include<cstdio>

#include<cstring>

#include<algorithm>

 

using namespace std;

 

#define Id(a, b) ((a) + (b) * N)

 

const int maxn = 59;

const int maxV = 5009;

 

int V, S, T, cnt[maxV], h[maxV];

int d[maxn][maxn], NUM, N;

 

struct edge {

int t, c;

edge *n, *r;

} E[100000], *pt, *e, *H[maxV], *p[maxV], *cur[maxV];

 

inline void Add(int u, int v, int c) {

pt->t = v, pt->c = c, pt->n = H[u], H[u] = pt++;

}

inline void AddEdge(int u, int v, int c) {

Add(u, v, c), Add(v, u, 0);

H[u]->r = H[v], H[v]->r = H[u];

}

 

int maxFlow() {

for(int i = 0; i < V; i++)

cur[i] = H[i], cnt[i] = h[i] = 0;

cnt[0] = V;

int ret = 0;

for(int x = S, A = maxV; h[S] < V; ) {

for(e = cur[x]; e; e = e->n)

if(e->c && h[e->t] + 1 == h[x]) break;

if(e) {

A = min(e->c, A);

p[e->t] = cur[x] = e;

if((x = e->t) == T) {

for(; x != S; x = p[x]->r->t)

p[x]->c -= A, p[x]->r->c += A;

ret += A;

A = maxV;

}

} else {

if(!--cnt[h[x]]) break;

h[x] = V;

for(e = H[x]; e; e = e->n) if(h[e->t] + 1 < h[x] && e->c) {

h[x] = h[e->t] + 1;

cur[x] = e;

}

++cnt[h[x]];

if(x != S) x = p[x]->r->t;

}

}

return ret;

}

 

void Build(int x) {

pt = E;

memset(H, 0, sizeof H);

V = N * x, S = V++, T = V++;

AddEdge(S, 0, NUM);

for(int i = 0; i < x; i++)

AddEdge(Id(N - 1, i), T, maxV);

for(int i = 1; i < x; i++)

for(int j = 0; j < N; j++) {

for(int k = 0; k < N; k++)

if(d[j][k]) AddEdge(Id(j, i - 1), Id(k, i), d[j][k]);

AddEdge(Id(j, i - 1), Id(j, i), maxV);

}

}

 

void Init() {

int m;

scanf("%d%d%d", &N, &m, &NUM);

memset(d, 0, sizeof d);

while(m--) {

int u, v;

scanf("%d%d", &u, &v);

scanf("%d", &d[--u][--v]);

}

}

 

void Work() {

int l = 1, r = 100, ans;

while(l <= r) {

int m = (l + r) >> 1;

Build(m);

if(maxFlow() == NUM) {

ans = m, r = m - 1;

} else

l = m + 1;

}

printf("%d\n", --ans);

}

 

int main() {

Init();

Work();

return 0;

}

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