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] = 0
There 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:
function solution(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 write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(A) {
// write your code in JavaScript (Node.js 8.9.4)
const N = A.length;
let array = new Array();
let intersect = 0;
for(let i=0; i<N; i++){
let circle = {
left: i - A[i],
right: i + A[i]
}
array.push(circle);
}
array.sort((a, b) => a.left - b.left );
for(let i=0; i<N-1; i++){
for(let j=i+1; j<N; j++){
if(intersect > 10000000){
return -1;
}
if(array[j].left > array[i].right){
break;
}
if(array[j].left >= array[i].left && array[j].left <= array[i].right){
intersect++;
}
}
}
return intersect;
}// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(A) {
// write your code in JavaScript (Node.js 8.9.4)
const N = A.length;
let array = new Array();
let intersect = 0;
for(let i=0; i<N; i++){
let circle = {
left: i - A[i],
right: i + A[i]
}
array.push(circle);
}
array.sort((a, b) => a.left - b.left );
for(let i=0; i<N-1; i++){
for(let j=i+1; j<N; j++){
if(intersect > 10000000){
return -1;
}
if(array[j].left > array[i].right){
break;
}
if(array[j].left >= array[i].left && array[j].left <= array[i].right){
intersect++;
}
}
}
return intersect;
}// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(A) {
// write your code in JavaScript (Node.js 8.9.4)
const N = A.length;
let array = new Array();
let intersect = 0;
for(let i=0; i<N; i++){
let circle = {
left: i - A[i],
right: i + A[i]
}
array.push(circle);
}
array.sort((a, b) => a.left - b.left );
for(let i=0; i<N-1; i++){
for(let j=i+1; j<N; j++){
if(intersect > 10000000){
return -1;
}
if(array[j].left > array[i].right){
break;
}
if(array[j].left >= array[i].left && array[j].left <= array[i].right){
intersect++;
}
}
}
return intersect;
}The solution obtained perfect score.