quick_fond算法, quick_union算法, weighted_quick_union算法, weighted_quick_union_with_path_comperession算法, 森林,并查集,朋友圈问题
题目描述
所谓一个朋友圈子,不一定其中的人都互相直接认识。
例如:小张的朋友是小李,小李的朋友是小王,那么他们三个人属于一个朋友圈。
现在给出一些人的朋友关系,人按照从 1到 n编号在这中间会进行询问某两个人是否属于一个朋友圈,请你编写程序,实现这个过程。
输 入
第一行输入两个整数 n,m(1≤n≤10000,3≤m≤100000),分别代表人数和操作数。
接下来 m行,每行三个整 a,b,c(a∈[1,2], 1≤b,c≤n)当 a=1时,代表新增一条已知信息,b,c是朋友当 a=2
时,代表根据以上信息,询问 b,c是否是朋友
输 出
对于每个 a=2 的操作,输出『Yes』或『No』
代表询问的两个人是否是朋友关系。
样例输入
6 5
1 1 2
2 1 3
1 2 4
1 4 3
2 1 3
样例输出
No
Yes
quick_find算法
#include <stdio.h>
#include <stdlib.h>
typedef struct unionSet {
int *color, n;
}UnionSet;
UnionSet *init(int n) {
UnionSet *u = (UnionSet *)malloc(sizeof(UnionSet));
u->color = (int *)malloc(sizeof(int) * n);
u->n = n;
for (int i = 0; i < n; i++) u->color[i] = i;
return u;
}
int fine(UnionSet *u, int n) {
if (!u) return -1;
return u->color[n];
}
int merge(UnionSet *u, int j1, int j2) {
if (!u) return -1;
int temp = u->color[j1];
for (int i = 0; i < u->n; i++) u->color[i] - temp || (u->color[i] = u->color[j2]);
return 1;
}
void clear(UnionSet *u) {
if (!u) return ;
free(u->color);
free(u);
return ;
}
int main() {
int n, m, a, b, c;
scanf("%d%d", &n, &m);
UnionSet *u = init(n);
for (int i = 0; i < m; i++) {
scanf("%d%d%d", &a, &b, &c);
--b, --c;
a ^ 1 && printf("%s\n", fine(u, b) ^ fine(u, c) ? "No" : "Yes") || merge(u, b, c);
}
clear(u);
return 0;
}
quick_union算法
#include <stdio.h>
#include <stdlib.h>
typedef struct unionSet {
int *father, n;
}UnionSet;
UnionSet *init(int n) {
UnionSet *u = (UnionSet *)malloc(sizeof(UnionSet));
u->father = (int *)malloc(sizeof(int) * n);
u->n = n;
for (int i = 0; i < n; i++) u->father[i] = i;
return u;
}
int find(UnionSet *u, int n) {
if (u->father[n] - n) return find(u, u->father[n]);
return n;
}
int merge(UnionSet *u, int j1, int j2) {
if (!u) return -1;
int temp1 = find(u, j1), temp2 = find(u, j2);
temp1 - temp2 && (u->father[temp1] = u->father[temp2]);
return 1;
}
void clear(UnionSet *u) {
if (!u) return ;
free(u->father);
free(u);
return ;
}
int main() {
int n, m, a, b, c;
scanf("%d%d", &n, &m);
UnionSet *u = init(n);
for (int i = 0; i < m; i++) {
scanf("%d%d%d", &a, &b, &c);
--b, --c;
a ^ 1 && printf("%s\n", find(u, b) ^ find(u, c) ? "No" : "Yes") || merge(u, b, c);
}
clear(u);
return 0;
}
weighted_quick_union算法
#include <stdio.h>
#include <stdlib.h>
#define swap(a, b) ({\
__typeof(a) __temp = a;\
a = b, b = __temp;\
})
typedef struct unionSet {
int *father, *size, n;
}UnionSet;
UnionSet *init(int n) {
UnionSet *u = (UnionSet *)malloc(sizeof(UnionSet));
u->father = (int *)malloc(sizeof(int) * n);
u->size = (int *)malloc(sizeof(int) * n);
u->n = n;
for (int i = 0; i < n; i++) u->father[i] = i, u->size[i] = 1;
return u;
}
int find(UnionSet *u, int n) {
if (u->father[n] - n) return find(u, u->father[n]);
return n;
}
int merge(UnionSet *u, int j1, int j2) {
if (!u) return -1;
int temp1 = find(u, j1), temp2 = find(u, j2);
temp1 - temp2 && u->size[temp1] > u->size[temp2] && swap(temp1, temp2);
temp1 - temp2 && (u->father[temp1] = temp2, u->size[temp2] += u->size[temp1]);
return 1;
}
void clear(UnionSet *u) {
if (!u) return ;
free(u->father);
free(u);
return ;
}
int main() {
int n, m, a, b, c;
scanf("%d%d", &n, &m);
UnionSet *u = init(n);
for (int i = 0; i < m; i++) {
scanf("%d%d%d", &a, &b, &c);
--b, --c;
a ^ 1 && printf("%s\n", find(u, b) ^ find(u, c) ? "No" : "Yes") || merge(u, b, c);
}
clear(u);
return 0;
}
weighted_quick_union_with_path_comperession算法
#include <stdio.h>
#include <stdlib.h>
#define swap(a, b) ({\
__typeof(a) __temp = a;\
a = b, b = __temp;\
})
typedef struct unionSet {
int *father, *size, n;
}UnionSet;
UnionSet *init(int n) {
UnionSet *u = (UnionSet *)malloc(sizeof(UnionSet));
u->father = (int *)malloc(sizeof(int) * n);
u->size = (int *)malloc(sizeof(int) * n);
u->n = n;
for (int i = 0; i < n; i++) u->father[i] = i, u->size[i] = 1;
return u;
}
int find(UnionSet *u, int n) {
return u->father[n] - n ? (u->father[n] = find(u, u->father[n])) : n;
}
int merge(UnionSet *u, int j1, int j2) {
if (!u) return -1;
int temp1 = find(u, j1), temp2 = find(u, j2);
temp1 - temp2 && u->size[temp1] > u->size[temp2] && swap(temp1, temp2);
temp1 - temp2 && (u->father[temp1] = temp2, u->size[temp2] += u->size[temp1]);
return 1;
}
void clear(UnionSet *u) {
if (!u) return ;
free(u->father);
free(u);
return ;
}
int main() {
int n, m, a, b, c;
scanf("%d%d", &n, &m);
UnionSet *u = init(n);
for (int i = 0; i < m; i++) {
scanf("%d%d%d", &a, &b, &c);
--b, --c;
a ^ 1 && printf("%s\n", find(u, b) ^ find(u, c) ? "No" : "Yes") || merge(u, b, c);
}
clear(u);
return 0;
}