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>sx and y such that the coordinates of point i are (x[i],y[i]). Return the number of subsets of the input set described byx and y that are n-squared for some n between nlow and nhigh, inclusive.

Definition

 Class:RangeSquaredSubsetsMethod:countSubsetsParameters:int, int, vector <int>, vector <int>Returns:long longMethod signature:long long countSubsets(int nlow, int nhigh, vector <int> x, vector <int> y)(be sure your method is public)

Limits

 Time limit (s):2.000Memory 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);    }};