LA 3662 Another Minimum Spanning Tree (曼哈顿距离最小生成树 模板)

题目大意：

曼哈顿最小距离生成树

算法讨论：

同上。

这回的模板真的准了。

#include <iostream>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <cstdio>
using namespace std;
const int N = 100000 + 5;
const int M = N * 8;
typedef long long ll;
const ll oo = 100000000000000LL;

int n, etot;
ll W = 0, c[N];
int fa[N], id[N];
int A[N], B[N];

struct Point{
    int x, y, id;
    bool operator < (const Point &a)const {
        if(a.x == x) return y < a.y;
        return x < a.x;
    }
}p[N];

struct Edge{
    int from, to;
    ll dis;
    bool operator < (const Edge &a)const {
        return dis < a.dis;
    }
}e[M];

int find(int x){return fa[x] == x ? x : fa[x] = find(fa[x]);}
void update(int x, ll val, int pos){
    for(int i = x; i > 0; i -= (i&(-i))){
        if(val < c[i]){
            c[i] = val;
            id[i] = pos;
        }
    }
}
int query(int pos, int up){
    int res = -1;
    ll val = oo;
    for(int i = pos; i <= up; i += (i&(-i))){
        if(c[i] < val){
            val = c[i];
            res = id[i];
        }
    }
    return res;
}
void MST(){
    int up;
    for(int dir = 1; dir <= 4; ++ dir){
        if(dir % 2 == 0)
            for(int i = 1; i <= n; ++ i)
                swap(p[i].x, p[i].y);
        else if(dir == 3)
            for(int i = 1; i <= n; ++ i)
                p[i].x = -p[i].x;
        sort(p + 1, p + n + 1);
        for(int i = 1; i <= n; ++ i) A[i] = B[i] = (int) p[i].y - p[i].x;
        sort(B + 1, B + n + 1);
        up = unique(B + 1, B + n + 1) - B - 1;
        
        for(int i = 1; i <= up; ++ i){
            c[i] = oo; id[i] = -1;
        }
                
        for(int i = n; i >= 1; -- i){
            A[i] = lower_bound(B + 1, B + up + 1, A[i]) - B;
            int np = query(A[i], up);
            if(np != -1){
                ++ etot;
                e[etot].from = p[i].id;
                e[etot].to = p[np].id;
                e[etot].dis = abs(p[i].x - p[np].x) + abs(p[i].y - p[np].y);
            }
            update(A[i], p[i].x + p[i].y, i);
        }
    }
    
    int have = 0;
    sort(e + 1, e + etot + 1);
    for(int i = 1; i <= n; ++ i) fa[i] = i;
    for(int i = 1; i <= etot; ++ i){
        int fx = find(e[i].from), fy = find(e[i].to);
        if(fx != fy){
            fa[fx] = fy;
            ++ have;
            W += e[i].dis;
            if(have == n-1) break;
        }
    }
}

int main(){
    int cnt = 0;
    while(scanf("%d", &n) && n){
        ++ cnt; etot = 0;
        for(int i = 1; i <= n; ++ i){
            scanf("%d%d", &p[i].x, &p[i].y);
            p[i].id = i;
        }
        W = 0;
        MST();
        printf("Case %d: Total Weight = %lld
", cnt, W);
    }    
    return 0;
}