kuangbin专题五：并查集

不想写实验，不想改paper，写点代码吧（；´д｀）ゞ

思路：简单并查集。

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int INF = 0x3f3f3f3f;
const int maxn = 1e3 + 5;
int N, D;
int p[maxn];
bool vis[maxn];

struct Pos{
    int x, y;
}pos[maxn];

int findP(int x){
    return x == p[x] ? x : p[x] = findP(p[x]);
}

void Union(int x, int y){
    int px = findP(x), py = findP(y);
    if(px != py)
        p[px] = py;
}

bool in_dis(int x, int y){
    int dx = pos[x].x - pos[y].x;
    int dy = pos[x].y - pos[y].y;
    return dx*dx + dy*dy <= D*D;
}

void repair(int x){
    for(int i = 1; i <= N; i++)
        if(vis[i] && in_dis(i, x))
            Union(i, x);
    vis[x] = true;
}

int main(){
    cin >> N >> D;

    for(int i = 1; i <= N; i++) p[i] = i;

    for(int i = 1; i <= N; i++)
        cin >> pos[i].x >> pos[i].y;

    char op;
    int u, v;
    while(cin >> op){
        if(op == 'O'){
            cin >> u;
            repair(u);
        }
        else{
            cin >> u >> v;
            int pu = findP(u), pv = findP(v);
            cout << (pu == pv ? "SUCCESS" : "FAIL") << endl;
        }
    }
    return 0;
}

View Code

POJ1611 The Suspects

思路：简单并查集。

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int INF = 0x3f3f3f3f;
const int maxn = 3e4 + 5;
const int maxm = 505;
int p[maxn];

inline int findP(int x){
    return x == p[x] ? x : p[x] = findP(p[x]);
}

inline void Union(int x, int y){
    int px = findP(x), py = findP(y);
    if(px != py)
        p[px] = py;
}

int main(){
    int n, m;
    while(cin >> n >> m && (n + m > 0)){
        for(int i = 0; i < n; i++) p[i] = i;

        int k, s1, s2;
        for(int i = 1; i <= m; i++){
            cin >> k;
            if(k) cin >> s1;
            for(int j = 1; j < k; j++){
                cin >> s2;
                Union(s1, s2);
            }
        }
        int res = 0;
        for(int i = 0; i < n; i++)
            if(findP(0) == findP(i))
                res++;
        cout << res << endl;
    }
    return 0;
}

View Code

HDU1213 How Many Tables

思路：简单并查集。

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int INF = 0x3f3f3f3f;
const int maxn = 1e3 + 5;
const int maxm = 1e3 + 5;
int p[maxn];
bool vis[maxn];

inline int findP(int x){
    return x == p[x] ? x : p[x] = findP(p[x]);
}

inline void Union(int x, int y){
    int px = findP(x), py = findP(y);
    if(px != py)
        p[px] = py;
}

int main(){
    int T;
    cin >> T;
    while(T--){
        int n, m;
        cin >> n >> m;

        for(int i = 1; i <= n; i++) p[i] = i;
        memset(vis, 0, sizeof(vis));

        for(int i = 1; i <= m; i++){
            int x, y;
            cin >> x >> y;
            Union(x, y);
        }

        int res = 0;
        for(int i = 1; i <= n; i++){
            int pi = findP(i);
            if(!vis[pi]){
                vis[pi] = true;
                res++;
            }
        }
        cout << res << endl;
    }
    return 0;
}

View Code

HDU3038 How Many Answers Are Wrong

思路：带权并查集。这题个人觉得模型比较难想到，我第一次接触到的时候被提醒了才想起来带权并查集。

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn = 2e5 + 5;
int p[maxn], w[maxn];

int findP(int x){
    if(x != p[x]){
        int px = p[x];
        p[x] = findP(p[x]);
        w[x] += w[px];
    }
    return p[x];
}

int main(){
    int n, m;
    while(scanf("%d%d", &n, &m) != EOF){
        for(int i = 0; i <= n; i++) p[i] = i, w[i] = 0;

        int res = 0;
        while(m--){
            int a, b, s;
            scanf("%d%d%d", &a, &b, &s);
            a--;
            int pa = findP(a), pb = findP(b);
            if(pa == pb){
                if((w[a] - w[b]) != s) res++;
            }
            else{
                p[pa] = pb;
                w[pa] = w[b] - w[a] + s;
            }
        }
        cout << res << endl;
    }
    return 0;
}

View Code

POJ1182 食物链

思路：经典带权并查集问题了。

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
const int maxn = 5e4 + 5;
int p[maxn], w[maxn];

int findP(int x){
    if(x != p[x]){
        int px = p[x];
        p[x] = findP(p[x]);
        w[x] = (w[x] + w[px]) % 3;
    }
    return p[x];
}

int main(){
    int n, m;
    scanf("%d%d", &n, &m);
    for(int i = 1; i <= n; i++) p[i] = i, w[i] = 0;

    int res = 0;
    while(m--){
        int d, x, y;
        scanf("%d%d%d", &d, &x, &y);

        if (x > n || y > n) {
            res++;
            continue;
        }
        if (d == 2 && x == y) {
            res++;
            continue;
        }
        d--;

        int px = findP(x), py = findP(y);
        if (px == py && (w[y] - w[x] + 3) % 3 != d){
            res++;
        }
        else {
            p[py] = px;
            w[py] = (w[x] + d - w[y] + 3) % 3;
        }
    }
    cout << res << endl;
    return 0;
}

View Code

POJ1417 True Liars

思路：这题的DP好烦，不想写了。

POJ1456 Supermarket

思路：贪心。从后向前，找最贵的物品卖。感觉和并查集关系不大。

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<queue>
using namespace std;
const int maxn = 10005;
int p[maxn], w[maxn];

struct Item{
    int p, d;
} item[maxn];

bool d_cmp(const Item& a, const Item& b) {
    return a.d < b.d;
}

struct p_cmp{
    bool operator()(const Item &a, const Item &b){
        return a.p < b.p;
    }
};

int findP(int x){
    if(x != p[x]){
        int px = p[x];
        p[x] = findP(p[x]);
        w[x] = (w[x] + w[px]) % 2;
    }
    return p[x];
}

int main(){
    int n;
    while(cin >> n){
        for(int i = 0; i < n; i++)
            cin >> item[i].p >> item[i].d;
        sort(item, item + n, d_cmp);

        int res = 0;
        int last = item[n-1].d, ind = n-1;
        priority_queue<Item, vector<Item>, p_cmp> q;
        for(int i = last; i > 0; i--){
            while(ind >= 0 && item[ind].d >= i){
                q.push(item[ind]);
                ind--;
            }
            if(q.size()){
                Item itm = q.top(); q.pop();
                res += itm.p;
            }
        }
        cout << res << endl;
    }
    return 0;
}

View Code

POJ1733 Parity game

思路：带权并查集。用以前的代码了。

#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<queue>
using namespace std;
const int maxn = 10005;
int p[maxn], w[maxn], f[maxn];

struct Node{
    int l, r;
    char s[5];
} q[maxn];

int findP(int x){
    if(x != p[x]){
        int px = p[x];
        p[x] = findP(p[x]);
        w[x] ^= w[px];
    }
    return p[x];
}

int main(){
    int n, m, k = 0;
    cin >> n >> m;
    for(int i = 1; i <= m; i++){
        cin >> q[i].l >> q[i].r >> q[i].s;
        q[i].l--;
        f[++k] = q[i].l, f[++k] = q[i].r;
    }
    sort(f + 1, f + 1 + k);
    for(int i = 1; i <= k; i++) p[i] = i, w[i] = 0;
    int i = 0;
    for(i = 1; i <= m; i++){
        int l = lower_bound(f+1, f+1+k, q[i].l) - f;
        int r = lower_bound(f+1, f+1+k, q[i].r) - f;
        int u = findP(l), v = findP(r);
        int d = 0;
        if(q[i].s[0] == 'o') d = 1;
        if(u == v && w[l]^d != w[r]) break;
        else if(u < v) p[u] = v, w[u] = w[l] ^ w[r] ^ d;
        else if(v < u) p[v] = u, w[v] = w[l] ^ w[r] ^ d;
    }
    cout << i - 1 << endl;
    return 0;
}

View Code

POJ1984 Navigation Nightmare

思路：带权并查集。需要两个权重，分别对应两个点的x坐标相对位置和y坐标相对位置。代码一直有bug，以后再把代码贴上来吧。

POJ2492 A Bug's Life

思路：简单并查集。

#include <iostream>
#include <algorithm>
#include <stdio.h>
using namespace std;
const int maxn = 2e3+10;
int T, N, M;
int p[maxn], w[maxn];

int findP(int x){
    if(x != p[x]){
        int px = p[x];
        p[x] = findP(p[x]);
        w[x] ^= w[px];
    }
    return p[x];
}

void Union(int x,int y){
    int px = findP(x), py = findP(y);
    if(px != py){
        p[px] = py;
        w[px] = 1 ^ w[y] ^ w[x];
    }
}
int main(){
    cin >> T;
    for(int t = 1; t <= T; t++){
        cin >> N >> M;

        for(int i = 1; i <= N; i++) p[i] = i, w[i] = 0;

        bool flag = false;
        while(M--){
            int x, y;
            scanf("%d%d",&x,&y);

            int px = findP(x), py = findP(y);
            if(px != py){
                Union(x,y);
            }else if(w[x] == w[y]){
                flag = true;
            }
        }
        printf("Scenario #%d:\n",t);
        if(flag) puts("Suspicious bugs found!");
        else puts("No suspicious bugs found!");
        puts("");
    }
    return 0;
}

View Code

POJ2912 Rochambeau

思路：枚举所有孩子情况，略。

ZOJ3261 Connections in Galaxy War

HDU1272 小希的迷宫

思路：注意输入只有0，和图不联通的情况。

#include <iostream>
#include <algorithm>
#include <stdio.h>
using namespace std;
const int maxn = 1e5 + 5;
int p[maxn];
bool vis[maxn];

int findP(int x){
    return x == p[x] ? p[x] : p[x] = findP(p[x]);
}

int main(){
    int a, b;
    while(cin >> a >> b && (a != -1 && b != -1)){
        if(a == 0 && b == 0){
            cout << "Yes" << endl;
            continue;
        }

        for(int i = 0; i < maxn; i++) p[i] = i, vis[i] = 0;
        bool flag = true;
        int cnt = 0;
        do {
            vis[a] = vis[b] = true;
            int pa = findP(a), pb = findP(b);
            if(pa != pb) p[pa] = pb, cnt++;
            else flag = false;
            cin >> a >> b;
        } while(a != 0 && b != 0);

        int tot = 0;
        for(int i = 1; i < maxn; i++)
            if(vis[i])
                tot++;
        if(flag && cnt+1 == tot)
            cout << "Yes" << endl;
        else
            cout << "No" << endl;
    }
    return 0;
}

View Code

POJ1308 Is It A Tree?

思路：同上一题

#include <iostream>
#include <algorithm>
#include <stdio.h>
using namespace std;
const int maxn = 1e5 + 5;
int p[maxn];
bool vis[maxn];

int findP(int x){
    return x == p[x] ? p[x] : p[x] = findP(p[x]);
}

int main(){
    int a, b, t = 0;
    while(cin >> a >> b && (a != -1 && b != -1)){
        t++;
        if(a == 0 && b == 0){
            printf("Case %d is a tree.\n", t);
            continue;
        }

        for(int i = 0; i < maxn; i++) p[i] = i, vis[i] = 0;
        bool flag = true;
        int cnt = 0;
        do {
            vis[a] = vis[b] = true;
            int pa = findP(a), pb = findP(b);
            if(pa != pb) p[pa] = pb, cnt++;
            else flag = false;
            cin >> a >> b;
        } while(a != 0 && b != 0);

        int tot = 0;
        for(int i = 1; i < maxn; i++)
            if(vis[i])
                tot++;
        if(flag && cnt+1 == tot)
            printf("Case %d is a tree.\n", t);
        else
            printf("Case %d is not a tree.\n", t);
    }
    return 0;
}

View Code

posted @ 2021-02-01 11:57 Nanachi 阅读(54) 评论(0) 收藏举报

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