UVALive 6902Three Squares（二分 + 搜索）

题意:

给定N≤105个点,找到边长最小的三个正方形使得可以包住所有的点,求最小边长

分析:

显然的二分边长
考虑check,对于当前点的集合,我们找到一个所有的点的x,y的范围,然后从这个矩形的四个顶点开始搜就好了,搜三层
因为所有的点都是要包括的,所以从顶点开始扩展

代码:

////  Created by TaoSama on 2015-12-14//  Copyright (c) 2015 TaoSama. All rights reserved.////#pragma comment(linker, "/STACK:1024000000,1024000000")#include <algorithm>#include <cctype>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <iomanip>#include <iostream>#include <map>#include <queue>#include <string>#include <set>#include <vector>using namespace std;#define pr(x) cout << #x << " = " << x << "  "#define prln(x) cout << #x << " = " << x << endlconst int N = 1e5 + 10, INF = 0x3f3f3f3f, MOD = 1e9 + 7;int n, x[N], y[N], vis[N];inline void getMin(int &x, int y) {x = min(x, y);}inline void getMax(int &x, int y) {x = max(x, y);}inline bool inBound(int i, int l, int r, int d, int u) {    return x[i] >= l && x[i] <= r && y[i] >= d && y[i] <= u;}inline void update(int l, int r, int d, int u, bool v) {    for(int i = 1; i <= n; ++i)        if(inBound(i, l, r, d, u)) vis[i] = v;}bool dfs(int d, int l) {    if(d > 3) {        int cnt = 0;        for(int i = 1; i <= n; ++i) cnt += vis[i];        return cnt == n;    }    int minX = INF, maxX = -INF, minY = INF, maxY = -INF;    for(int i = 1; i <= n; ++i) {        if(vis[i]) continue;        getMin(minX, x[i]);        getMax(maxX, x[i]);        getMin(minY, y[i]);        getMax(maxY, y[i]);    }    //top left    update(minX, minX + l, maxY - l, maxY, true);    if(dfs(d + 1, l)) return true;    update(minX, minX + l, maxY - l, maxY, false);    //top right    update(maxX - l, maxX, maxY - l, maxY, true);    if(dfs(d + 1, l)) return true;    update(maxX - l, maxX, maxY - l, maxY, false);    //bottom right    update(maxX - l, maxX, minY, minY + l, true);    if(dfs(d + 1, l)) return true;    update(maxX - l, maxX, minY, minY + l, false);    //bottom left    update(minX, minX + l, minY, minY + l, true);    if(dfs(d + 1, l)) return true;    update(minX, minX + l, minY, minY + l, false);    return false;}int main() {#ifdef LOCAL    freopen("C:\\Users\\TaoSama\\Desktop\\in.txt", "r", stdin);//  freopen("C:\\Users\\TaoSama\\Desktop\\out.txt","w",stdout);#endif    ios_base::sync_with_stdio(0);    int t; scanf("%d", &t);    while(t--) {        scanf("%d", &n);        for(int i = 1; i <= n; ++i) scanf("%d%d", x + i, y + i);        int l = 0, r = 2e9 + 10;        while(l <= r) {            int m = l + r >> 1;            memset(vis, false, sizeof vis);            if(dfs(1, m)) r = m - 1;            else l = m + 1;        }        printf("%d\n", l);    }    return 0;}