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:
def 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.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
n = len(A)
summa = n*(n-1)/2
not_int = 0
for i in range(n):
for j in range(1,n):
if i!=j:
if i+k[i]<j-k[j]:
not_int+=1
return summa-not_int
print solution(1,5,2,1,4,0)
Traceback (most recent call last): File "exec.py", line 111, in <module> main() File "exec.py", line 69, in main sol = __import__('solution') File "/tmp/solution.py", line 16, in <module> print solution(1,5,2,1,4,0) TypeError: solution() takes exactly 1 argument (6 given)
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
n = len(A)
summa = n*(n-1)/2
not_int = 0
for i in range(n):
for j in range(1,n):
if i!=j:
if i+k[i]<j-k[j]:
not_int+=1
return summa-not_int
print solution([1,5,2,1,4,0])
Traceback (most recent call last): File "exec.py", line 111, in <module> main() File "exec.py", line 69, in main sol = __import__('solution') File "/tmp/solution.py", line 16, in <module> print solution([1,5,2,1,4,0]) File "/tmp/solution.py", line 12, in solution if i+k[i]<j-k[j]: NameError: global name 'k' is not defined
# you can write to stdout for debugging purposes, e.g.
# print "this is a debug message"
def solution(A):
# write your code in Python 2.7
n = len(A)
summa = n*(n-1)/2
not_int = 0
for i in range(n):
for j in range(1,n):
if i!=j:
if i+A[i]<j-A[j]:
not_int+=1
return summa-not_int
print solution([1,5,2,1,4,0])
The following issues have been detected: timeout errors.
10.000.000 intersections
running time: >6.00 sec., time limit: 0.36 sec.