HDU - 1272 小希的迷宫 【并查集】

题目链接

http://acm.hdu.edu.cn/showproblem.php?pid=1272

思路

只需要判断 这张图 无环 并且只有一个连通块 就可以了

要注意 如果 只输入 0 0 那给的是空图 要给出 Yes

判断 无环 有两个方法

0.在并查集的合并操作中 如果 find(x) == find(y) 就说明 x 和 y 已经有一条边了 再加 就是成环了 直接 flag = 0

1.我们可以对边的个数 计数 只有 边数== 结点个数-1 才是满足条件的

AC代码

#include <cstdio>
#include <cstring>
#include <ctype.h>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <deque>
#include <vector>
#include <queue>
#include <string>
#include <map>
#include <stack>
#include <set>
#include <numeric>
#include <sstream>
#include <iomanip>
#include <limits>

#define CLR(a, b) memset(a, (b), sizeof(a))
#define pb push_back

using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
typedef pair<string, int> psi;
typedef pair<string, string> pss;

const double PI = acos(-1.0);
const double E = exp(1.0);
const double eps = 1e-30;

const int INF = 0x3f3f3f3f;
const int maxn = 1e5 + 10;
const int MOD = 1e9 + 7;

int pre[maxn];

int find(int x)
{
    int r = x;
    while (pre[r] != r)
        r = pre[r];
    int i = x, j;
    while (i != r)
    {
        j = pre[i];
        pre[i] = r;
        i = j;
    }
    return r;
}

void join(int x, int y)
{
    int fx = find(x), fy = find(y);
    if (x != fy)
        pre[fx] = fy;
}

void init()
{
    for (int i = 0; i < maxn; i++)
        pre[i] = i;
}

int main()
{
    int x, y;
    set <int> s;
    s.clear();
    int edge = 0;
    init();
    while (scanf("%d%d", &x, &y))
    {
        if (x == -1 && y == -1)
            break;
        else if ((x || y))
        {
            edge++;
            s.insert(x);
            s.insert(y);
            join(x, y);
        }
        else
        {
            if (edge == 0)
            {
                printf("Yes\n");
                continue;
            }
            map <int, int> m;
            int len = s.size();
            while (!s.empty())
            {
                int num = find(*s.begin());
                s.erase(s.begin());
                m[num]++;
            }
            int flag = 1;
            if (edge != len - 1 || m.size() != 1)
                flag = 0;
            if (flag)
                printf("Yes\n");
            else
                printf("No\n");
            s.clear();
            edge = 0;
            init();
        }
    }
}

AC代码

#include <cstdio>
#include <cstring>
#include <ctype.h>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <deque>
#include <vector>
#include <queue>
#include <string>
#include <map>
#include <stack>
#include <set>
#include <numeric>
#include <sstream>
#include <iomanip>
#include <limits>

#define CLR(a, b) memset(a, (b), sizeof(a))
#define pb push_back

using namespace std;
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
typedef pair<string, int> psi;
typedef pair<string, string> pss;

const double PI = acos(-1.0);
const double E = exp(1.0);
const double eps = 1e-30;

const int INF = 0x3f3f3f3f;
const int maxn = 1e5 + 10;
const int MOD = 1e9 + 7;

int pre[maxn];

int flag;

int find(int x)      //路径压缩
{
    int r = x;
    while (pre[r] != r)
        r = pre[r];
    int i = x, j;
    while (i != r)
    {
        j = pre[i];
        pre[i] = r;
        i = j;
    }
    return r;
}

//int find(int x)
//{
//  while (x != pre[x])
//      x = pre[x];
//  return x;
//}

void join(int x, int y)
{
    int fx = find(x), fy = find(y);
    if (fx != fy)
        pre[fx] = fy;
    else
        flag = 0;
}

void init()
{
    for (int i = 0; i < maxn; i++)
        pre[i] = i;
}

int main()
{
    int x, y;
    set <int> s;
    s.clear();
    init();
    flag = 1;
    while (scanf("%d%d", &x, &y))
    {
        if (x == -1 && y == -1)
            break;
        else if ((x || y))
        {
            s.insert(x);
            s.insert(y);
            join(x, y);
        }
        else
        {
            if (s.size() == 0)
            {
                printf("Yes\n");
                continue;
            }
            map <int, int> m;
            int len = s.size();
            while (!s.empty())
            {
                int num = find(*s.begin());
                s.erase(s.begin());
                m[num]++;
            }
            if (m.size() != 1)
                flag = 0;
            if (flag)
                printf("Yes\n");
            else
                printf("No\n");
            s.clear();
            init();
            flag = 1;
        }
    }
}