TopCoder - SRM521 div1 500 RangeSquaredSubsets

Problem Statement
	Given a real number n, a set of points P in the XY plane is called n-squared if it is not empty and there exists a square of side n in the XY plane with its sides parallel to the axes such that a point from the given set of points is in P if and only if it is contained within the square. A point lying on a side or a vertex of the square is considered to be contained in it. You will be given two ints nlow and nhigh. You will also be given two vector <int>s x and y such that the coordinates of point i are (x[i],y[i]). Return the number of subsets of the input set described by x and y that are n-squared for some n between nlow and nhigh, inclusive.
Definition
	Class: RangeSquaredSubsets Method: countSubsets Parameters: int, int, vector <int>, vector <int> Returns: long long Method signature: long long countSubsets(int nlow, int nhigh, vector <int> x, vector <int> y) (be sure your method is public)
Limits
	Time limit (s): 2.000 Memory limit (MB): 64
Constraints
-	nlow will be between 1 and 100000000 (10^8), inclusive.
-	nhigh will be between nlow and 100000000 (10^8), inclusive.
-	x and y will contain between 1 and 40 elements, inclusive.
-	x and y will contain the same number of elements.
-	Each element of x and y will be between -100000000 (-10^8) and 100000000 (10^8), inclusive.
-	All described points will be different.
Examples
0)
	5 5 {-5,0,5} {0,0,0} Returns: 5 The following subsets are 5-squared: {(-5,0)}, {(0,0)}, {(5,0)}, {(-5,0),(0,0)}, {(0,0),(5,0)}.
1)
	10 10 {-5,0,5} {0,0,0} Returns: 5 The following subsets are 10-squared: {(-5,0)}, {(5,0)}, {(0,0),(5,0)}, {(-5,0),(0,0)}, {(-5,0),(0,0),(5,0)}.
2)
	1 100 {-5,0,5} {0,0,0} Returns: 6 {(-5,0),(5,0)} is not x-squared for any x. From the previous 2 examples you can infer that all other non-empty subsets are 5-squared or 10-squared.
3)
	3 100000000 {-1,-1,-1,0,1,1,1} {-1,0,1,1,-1,0,1} Returns: 21
4)
	64 108 {-56,-234,12,324,-12,53,0,234,1,12,72} {6,34,2,235,234,234,342,324,234,234,234} Returns: 26

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离散化枚举， 注意细节

#include <iostream>
#include <vector>
#include <set>
#include <algorithm>
#include "limits.h"
using namespace std;

class RangeSquaredSubsets{
public:

struct point{
int x, y;
point(int X, int Y) : x(X), y(Y) {}
};

int INF = 1e9;

long long countSubsets(int nlow, int nhigh, vector <int> x, vector <int> y){
int n = x.size();
set<long long> ans;
vector<point> points;
for(int i = 0; i < n; ++i){
points.push_back(point(x[i], y[i]));
}
x.push_back(INF); x.push_back(-INF);
y.push_back(INF); y.push_back(-INF);
sort(x.begin(), x.end());
sort(y.begin(), y.end());
x.erase(unique(x.begin(), x.end()), x.end());
y.erase(unique(y.begin(), y.end()), y.end());
int nx = x.size();
int ny = y.size();
for(int i = 1; i < nx - 1; ++i) for(int j = i; j < nx - 1; ++j)
for(int k = 1; k < ny - 1; ++k) for(int l = k; l < ny - 1; ++l){
if(fit(nlow, nhigh, x[j] - x[i], y[l] - y[k], x[j + 1] - x[i - 1], y[l + 1] - y[k - 1])){
long long mask = 0;
for(int a = 0; a < n; ++a){
if(inSquare(points[a], x[i], x[j], y[k], y[l])){
mask |= 1ll << a;
}
}
if(mask) ans.insert(mask);
}
}
return ans.size();
}

bool fit(int nlow, int nhigh, int sx, int sy, int lx, int ly){
int w = max(nlow, max(sx, sy));
return (w <= nhigh) && (lx > w) && (ly > w);
}

bool inSquare(point p, int left, int right, int down, int up){
return (p.x >= left) && (p.x <= right) && (p.y >= down) && (p.y <= up);
}

};