关键词:
题目链接:http://poj.org/problem?id=1703
题意:有n个人分别属于两个团伙,接下来m组形如 ch, x, y的数据,ch为“D"表示 x, y属于不同的团伙,ch为"A"表示询问x,y书否属于同一个团伙;
解法1:我们可以用jion(x, y)属于同一个团伙,jion(x+n, y)表示x属于第二个团伙,y属于第一个团伙,jion(x, y+n)表示x属于第一个团伙,y属于第二个团伙;
那么对于每组不同团伙的x, y我们只需要jion(x+n, y) ,jion(x, y+n)即可;查询时判断x,y或者x+n, y+n根节点是否相同即可,因为集合关系jion表示属于同一团伙,根节点相同则属于相同团伙,若x, y+n,或者x+n, y根节点相同则属于不同团伙,其余情况即为不能确定;
代码:
1 #include <iostream>
2 #include <cstdio>
3 #include <cstring>
4 #define MAXN (100000+10) //***MAXN后面做下标时MAXN*2,要加括号,不然会越界!!run time error!!!
5 using namespace std;
6
7 int pre[MAXN*2], rank[MAXN*2]; //***rank用来区分树的高度,但其不存储树的具体高度
8
9 int find(int x){
10 int r = x;
11 while(pre[r]!=r){
12 r = pre[r];
13 }
14 int i = x; //****路径压缩
15 while(pre[i]!=r){
16 int gg = pre[i];
17 pre[i] = r;
18 i = gg;
19 }
20 return r;
21 }
22
23 void jion(int x, int y){
24 int xx = find(x);
25 int yy = find(y);
26 if(rank[xx]>rank[yy]){ //***启发式合并,就是把矮的树合并到高的树地下,把合并时间从0(n)降到o(logn)
27 pre[yy] = xx;
28 }else{
29 pre[xx] = yy;
30 if(rank[xx] == rank[yy]){ //**若树的标记高度一样,那么给合并后作为父亲的树rank+1,以区分树的高度
31 rank[xx]++;
32 }
33 }
34 }
35
36 int main(void){
37 int t;
38 scanf("%d", &t);
39 while(t--){
40 int n, m;
41 scanf("%d%d", &n, &m);
42 for(int i=1; i<=2*n; i++){
43 pre[i] = i;
44 rank[i] = 0;
45 }
46 while(m--){
47 char ch[2];
48 int x, y;
49 scanf("%s%d%d", ch, &x, &y);
50 if(ch[0]==‘D‘){
51 jion(x, y+n);
52 jion(x+n, y);
53 }else{
54 if(find(y+n)==find(x)||find(x+n)==find(y)){
55 printf("In different gangs.
");
56 }else if(find(x)==find(y)||find(x+n)==find(y+n)){
57 printf("In the same gang.
");
58 }else{
59 printf("Not sure yet.
");
60 }
61 }
62 }
63 }
64 return 0;
65 }
方法2:用vis数组标记不同的集合,如:vis[x]=y,表示与x不同集合的点y;
用并查集合并属于同一类的点集;
代码:
1 #include <iostream>
2 #include <stdio.h>
3 #define MAXN 100010
4 using namespace std;
5
6 int pre[MAXN], vis[MAXN], rank[MAXN]; //***vis标记不同集合的编号,rank区分树高
7 //***vis[x]=y,表示记录x与y不同集合,相当于无向图,所以需双向标记
8
9 /*int find(int x){ //**400+ms
10 int r = x;
11 while(pre[r]!=r){
12 r = pre[r];
13 }
14 int i = x;
15 while(i!=r){
16 int gg = pre[i];
17 pre[i] = r;
18 i = gg;
19 }
20 return r;
21 }*/
22
23 int find(int x){ //**306ms (再加启发式合并=282ms)
24 return pre[x]==x ? x : pre[x] = find(pre[x]);
25 }
26
27 void jion(int x, int y){
28 int xx = find(x);
29 int yy = find(y);
30 if(rank[xx] > rank[yy]){
31 pre[yy] = xx;
32 }else{
33 pre[xx] = yy;
34 if(rank[xx] == rank[yy]){
35 rank[yy]++;
36 }
37 }
38 }
39
40 int main(void){
41 int t;
42 scanf("%d", &t);
43 while(t--){
44 int n, m;
45 scanf("%d%d", &n, &m);
46 for(int i=1; i<=n; i++){
47 pre[i] = i;
48 vis[i] = 0;
49 rank[i] = 0;
50 }
51 while(m--){
52 char ch[2];
53 int x, y;
54 scanf("%s%d%d", ch, &x, &y);
55 if(ch[0]==‘D‘){
56 if(vis[x]==0 && vis[y]==0){ //**x, y都没出现过
57 vis[x] = y;
58 vis[y] = x;
59 }else if(vis[x]==0){ //**x没出现过
60 vis[x] = y;
61 jion(x, vis[y]);
62 }else if(vis[y]==0){ //**y没出现过
63 vis[y] = x;
64 jion(y, vis[x]);
65 }else{ //**都出现过
66 jion(x, vis[y]);
67 jion(y, vis[x]);
68 }
69 }else{
70 if(find(x)==find(y)){
71 printf("In the same gang.
");
72 }else if(find(x)==find(vis[y])){
73 printf("In different gangs.
");
74 }else{
75 printf("Not sure yet.
");
76 }
77 }
78 }
79 }
80 return 0;
81 }
方法3:
种类并查集,先区分能不能辨别的情况,然后只要考虑同和不同两种情况,可以用rank数组记录当前节点x与其根节点是否相同的信息,1表相同,0表不同;
代码:
1 #include <iostream>
2 #include <stdio.h>
3 #define MAXN 100010
4 using namespace std;
5
6 int pre[MAXN], rank[MAXN]; //**rank储存x与x的根节点是否相同的信息,1表相同,0表不同
7
8 int find(int x){
9 if(x==pre[x]){
10 return pre[x];
11 }
12 int xx = pre[x];
13 pre[x] = find(pre[x]);
14 rank[x] = (rank[x] + rank[xx])&1; //**压缩路径,x的根节点改变了,rank[x]也要改变
15 return pre[x];
16 }
17
18 void jion(int x, int y){
19 int xx = find(x);
20 int yy = find(y);
21 if(xx!=yy){
22 pre[yy] = xx;
23 rank[yy] = (rank[x] + rank[y] + 1)&1; //**合并只需改变yy之前的rank值
24 }
25 }
26
27 int main(void){
28 int t;
29 scanf("%d", &t);
30 while(t--){
31 int n, m;
32 scanf("%d%d", &n, &m);
33 for(int i=1; i<=n; i++){
34 pre[i] = i;
35 rank[i] = 0;
36 }
37 while(m--){
38 char ch[2];
39 int x, y;
40 scanf("%s%d%d", ch, &x, &y);
41 if(ch[0]==‘D‘){
42 jion(x, y);
43 }else{
44 if(find(x)==find(y)){
45 if(rank[x]==rank[y]){
46 printf("In the same gang.
");
47 }else{
48 printf("In different gangs.
");
49 }
50 }else{
51 printf("Not sure yet.
");
52 }
53 }
54 }
55 }
56 return 0;
57 }
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