题意:给你一个01矩阵,然后求是否存在选择一些行,使得每一列的1的个数都为1。
思路:貌似朴素的DFS也可以,加点剪枝就可以过。这里贴个DLX的模版。
推荐博客:http://www.cppblog.com/notonlysuccess/archive/2009/07/10/89701.html
这里讲的很详细。
#include <set>
#include <map>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <string>
#include <vector>
#include <iomanip>
#include <cstring>
#include <iostream>
#include <algorithm>
#define Max 2505
#define FI first
#define SE second
#define ll long long
#define PI acos(-1.0)
#define inf 0x3fffffff
#define LL(x) ( x << 1 )
#define bug puts("here")
#define PII pair<int,int>
#define RR(x) ( x << 1 | 1 )
#define mp(a,b) make_pair(a,b)
#define mem(a,b) memset(a,b,sizeof(a))
#define REP(i,s,t) for( int i = ( s ) ; i <= ( t ) ; ++ i ) using namespace std; #define N 5555 ///DLX
int L[N] , R[N] , D[N] , U[N] ,S[N] , C[N] ,st[N] ;//S[] 表示这一列的点数。C[] 表示这个点位于那一列。
int n , m , num , head ; void insert(int col , int pos){//在这一列插入序号为pos的点
int now = col ;
while(D[now] != col) now = D[now] ;
D[now] = pos ;
D[pos] = col ;
U[pos] = now ;
U[col] = pos ;
} void init(){
head = 0 ;
R[head] = 1 ;L[head] = m ;
for (int i = 1 ; i <= m ; i ++ ){//每一行的头指针
if(i == 1)L[i] = head ;
else L[i] = i - 1 ;
if(i == m)R[i] = head ;
else R[i] = i + 1 ;
U[i] = i ;
D[i] = i ;
S[i] = 0 ;
C[i] = i ;
}
num = m ;//已经插入m个节点
int k ;
for (int i = 1 ; i <= n ; i ++ ){
mem(st ,0) ;
for (int j = 1 ; j <= m ; j ++ ){
scanf("%d",&k) ;
if(!k)continue ;
num ++ ;
insert(j , num) ;
if(st[0] == 0){//每行的第一个
L[num] = num ; R[num] = num ;
}else{
L[num] = st[st[0]] ;
R[num] = st[1] ;
R[st[st[0]]] = num ;
L[st[1]] = num ;
}
st[++st[0]] = num ;
C[num] = j ;
S[j] ++ ;
}
}
} void remove(const int &c){//删除
L[R[c]] = L[c] ;R[L[c]] = R[c] ;
for (int i = D[c] ; i != c ; i = D[i]){
for (int j = R[i] ; j != i ; j = R[j]){
U[D[j]] = U[j] ;
D[U[j]] = D[j] ;
-- S[C[j]] ;
}
}
} void resume(const int &c){//恢复
for (int i = U[c] ; i != c ; i = U[i]){
for (int j = L[i] ; j != i ; j = L[j]){
++ S[C[j]] ;
U[D[j]] = j ;
D[U[j]] = j ;
}
}
L[R[c]] = c ;
R[L[c]] = c ;
} int dfs(const int &k){
if(R[head] == head)return 1 ;
int MX = inf ,c ;
for (int t = R[head] ; t != head ; t = R[t]){//找出点最少的一列
if(S[t] < MX){
MX = S[t] ;
c = t ;
}
}
remove(c) ;
for (int i = D[c] ; i != c ; i = D[i]){
for (int j = R[i] ; j != i ; j = R[j]){
remove(C[j]) ;
}
if(dfs(k + 1))return 1 ;
for (int j = L[i] ; j != i ; j = L[j]){
resume(C[j]) ;
}
}
resume(c) ;
return 0 ;
}
int main() {
while(cin >> n >> m){
init() ;
if(dfs(0))puts("Yes, I found it") ;
else puts("It is impossible") ;
}
return 0 ;
}