曼哈顿最小生成树

#define _CRT_SECURE_NO_DEPRECATE#include <iostream>#include <cstdio>#include <algorithm>#define lowbit(x) (x&(-x))using namespace std;const int N = 100005;struct Point{int x, y, id;//点坐标bool operator<(const Point p)const{return x != p.x ? x<p.x : y<p.y;}}p[N];struct BIT{int min_val, pos;void init(){min_val = (1 << 30);pos = -1;}}bit[N];struct Edge{int u, v, d;//边上的点u,v，代价dbool operator<(const Edge e)const{return d<e.d;}}e[N << 2];int n, tot, pre[N];int find(int x){return pre[x] = (x == pre[x] ? x : find(pre[x]));}int dist(int i, int j){//曼哈顿距离return abs(p[i].x - p[j].x) + abs(p[i].y - p[j].y);}void addedge(int u, int v, int d){e[tot].u = u;e[tot].v = v;e[tot++].d = d;}void update(int x, int val, int pos){for (int i = x; i >= 1; i -= lowbit(i))if (val<bit[i].min_val)bit[i].min_val = val, bit[i].pos = pos;}int ask(int x, int m){int min_val = (1 << 30), pos = -1;for (int i = x; i <= m; i += lowbit(i))if (bit[i].min_val<min_val)min_val = bit[i].min_val, pos = bit[i].pos;return pos;}int Manhattan_minimum_spanning_tree(int n, Point *p){int a[N], b[N];for (int dir = 0; dir<4; dir++){//4种坐标变换if (dir == 1 || dir == 3){for (int i = 0; i<n; i++)swap(p[i].x, p[i].y);}else if (dir == 2){for (int i = 0; i<n; i++){p[i].x = -p[i].x;}}sort(p, p + n);for (int i = 0; i<n; i++){a[i] = b[i] = p[i].y - p[i].x;}sort(b, b + n);int m = unique(b, b + n) - b;for (int i = 1; i <= m; i++)bit[i].init();for (int i = n - 1; i >= 0; i--){int pos = lower_bound(b, b + m, a[i]) - b + 1;   //BIT中从1开始int ans = ask(pos, m);if (ans != -1)addedge(p[i].id, p[ans].id, dist(i, ans));update(pos, p[i].x + p[i].y, i);}}//计算最小生成树【Krusal算法】，返回花费int cost = 0;sort(e, e + tot);for (int i = 0; i<n; i++)pre[i] = i;for (int i = 0; i<tot; i++){int u = e[i].u, v = e[i].v;int fa = find(u), fb = find(v);if (fa != fb){//选中对应边u,v【非同一个连通分量】,权值dcost += e[i].d;pre[fa] = fb;}}return cost;}int main(){while (scanf("%d", &n) != EOF&&n){tot = 0;//初始化边数为0for (int i = 0; i<n; i++)//输入n个点的坐标{scanf("%d%d", &p[i].x, &p[i].y);p[i].id = i;}//求n各点对应曼哈顿最小生成树的代价printf("%d\n", Manhattan_minimum_spanning_tree(n, p));}return 0;}