Queries on count of points lie inside a circle | Computing the x ^ 2 + y ^ 2 for each given points and sorting them . ; Return count of points lie inside or on circumference of circle using binary search on p [ 0. . n - 1 ] ; Driver program to test above function ; Compute distances of all points and keep the distances sorted so that query can work in O ( logn ) using Binary Search . ; Print number of points in a circle of radius 3. ; Print number of points in a circle of radius 32.
function preprocess ( p , x , y , n ) { for ( let i = 0 ; i < n ; i ++ ) p [ i ] = x [ i ] * x [ i ] + y [ i ] * y [ i ] ; p . sort ( function ( a , b ) { return a - b ; } ) ; } function query ( p , n , rad ) { let start = 0 , end = n - 1 ; while ( ( end - start ) > 1 ) { let mid = Math . floor ( ( start + end ) / 2 ) ; let tp = Math . sqrt ( p [ mid ] ) ; if ( tp > ( rad * 1.0 ) ) end = mid - 1 ; else start = mid ; } let tp1 = Math . sqrt ( p [ start ] ) ; let tp2 = Math . sqrt ( p [ end ] ) ; if ( tp1 > ( rad * 1.0 ) ) return 0 ; else if ( tp2 <= ( rad * 1.0 ) ) return end + 1 ; else return start + 1 ; } let x = [ 1 , 2 , 3 , - 1 , 4 ] ; let y = [ 1 , 2 , 3 , - 1 , 4 ] ; let n = x . length ; let p = new Array ( n ) ; for ( let i = 0 ; i < n ; i ++ ) { p [ i ] = 0 ; } preprocess ( p , x , y , n ) ; document . write ( query ( p , n , 3 ) + " " ) ; document . write ( query ( p , n , 32 ) + " " ) ;