We draw N discs on a plane. The discs are numbered from 0 to N − 1. An array A of N non-negative integers, specifying the radiuses of the discs, is given. The J-th disc is drawn with its center at (J, 0) and radius A[J].
We say that the J-th disc and K-th disc intersect if J ≠ K and the J-th and K-th discs have at least one common point (assuming that the discs contain their borders).
The figure below shows discs drawn for N = 6 and A as follows:
A[0] = 1 A[1] = 5 A[2] = 2 A[3] = 1 A[4] = 4 A[5] = 0There are eleven (unordered) pairs of discs that intersect, namely:
- discs 1 and 4 intersect, and both intersect with all the other discs;
- disc 2 also intersects with discs 0 and 3.
Write a function:
int solution(vector<int> &A);
that, given an array A describing N discs as explained above, returns the number of (unordered) pairs of intersecting discs. The function should return −1 if the number of intersecting pairs exceeds 10,000,000.
Given array A shown above, the function should return 11, as explained above.
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [0..100,000];
- each element of array A is an integer within the range [0..2,147,483,647].
// you can also use includes, for example:
#include <algorithm>
#include <map>
inline bool mySortFunction(pair<int,int> p1, pair<int,int> p2)
{
return ( p1.first < p2.first );
}
int solution ( const vector<int> &A ) {
int i, size = A.size();
if ( size <= 1 ) return 0;
// Compute lower boundary of all discs and sort them in ascending order
vector< pair<int,int> > lowBounds(size);
for(i=0; i<size; i++) lowBounds[i] = pair<int,int>(i-A[i],i+A[i]);
sort(lowBounds.begin(), lowBounds.end(), mySortFunction);
// Browse discs
long nbIntersect = 0;
for(i=0; i<size; i++)
{
int curBound = lowBounds[i].second;
for(int j=i+1; j<size && lowBounds[j].first<=curBound; j++)
{
nbIntersect++;
// Maximal number of intersections
if ( nbIntersect > 10000000 ) return -1;
}
}
return nbIntersect;
}
// you can also use includes, for example:
#include <algorithm>
#include <map>
inline bool mySortFunction(pair<int,int> p1, pair<int,int> p2)
{
return ( p1.first < p2.first );
}
int solution ( const vector<int> &A ) {
int i, size = A.size();
if ( size <= 1 ) return 0;
// Compute lower boundary of all discs and sort them in ascending order
vector< pair<int,int> > lowBounds(size);
for(i=0; i<size; i++) lowBounds[i] = pair<int,int>(i-A[i],i+A[i]);
sort(lowBounds.begin(), lowBounds.end(), mySortFunction);
// Browse discs
long nbIntersect = 0;
for(i=0; i<size; i++)
{
int curBound = lowBounds[i].second;
for(int j=i+1; j<size && lowBounds[j].first<=curBound; j++)
{
nbIntersect++;
// Maximal number of intersections
if ( nbIntersect > 10000000 ) return -1;
}
}
return nbIntersect;
}
// you can also use includes, for example:
#include <algorithm>
#include <map>
inline bool mySortFunction(pair<int,int> p1, pair<int,int> p2)
{
return ( p1.first < p2.first );
}
int solution ( const vector<int> &A ) {
int i, size = A.size();
if ( size <= 1 ) return 0;
// Compute lower boundary of all discs and sort them in ascending order
vector< pair<int,int> > lowBounds(size);
for(i=0; i<size; i++) lowBounds[i] = pair<int,int>(i-A[i],i+A[i]);
sort(lowBounds.begin(), lowBounds.end(), mySortFunction);
// Browse discs
long nbIntersect = 0;
for(i=0; i<size; i++)
{
int curBound = lowBounds[i].second;
for(int j=i+1; j<size && lowBounds[j].first<=curBound; j++)
{
nbIntersect++;
// Maximal number of intersections
if ( nbIntersect > 10000000 ) return -1;
}
}
return nbIntersect;
}
// you can also use includes, for example:
#include <algorithm>
#include <map>
inline bool mySortFunction(pair<int,int> p1, pair<int,int> p2)
{
return ( p1.first < p2.first );
}
int solution ( const vector<int> &A ) {
int i, size = A.size();
if ( size <= 1 ) return 0;
// Compute lower boundary of all discs and sort them in ascending order
vector< pair<int,int> > lowBounds(size);
for(i=0; i<size; i++) lowBounds[i] = pair<int,int>(i-A[i],i+A[i]);
sort(lowBounds.begin(), lowBounds.end(), mySortFunction);
// Browse discs
long nbIntersect = 0;
for(i=0; i<size; i++)
{
int curBound = lowBounds[i].second;
for(int j=i+1; j<size && lowBounds[j].first<=curBound; j++)
{
nbIntersect++;
// Maximal number of intersections
if ( nbIntersect > 10000000 ) return -1;
}
}
return nbIntersect;
}
The following issues have been detected: wrong answers.