Suppose we have a number n and an array called rounds. We have a circular track which consists of n different sectors labeled from 1 to n. Now consider a race will be held on this track, the race consists of m different rounds. The ith round starts at sector rounds[i - 1] and ends at sector rounds[i]. For example, if the round 1 starts at sector rounds[0] and ends at sector rounds[1]. So we have to find the most visited sectors sorted in ascending order. (The track numbers are in ascending order of sector numbers in the counter-clockwise direction)
So, if the input is like n = 4 rounds = [1,3,1,2], then the output will be [1, 2]
because the race starts from sector 1. The order of the visited sectors is as follows: [1,2,3 (end of first round),4,1 (end of second round), 2 (end of 3rd round)]. Here both of the sectors 1 and 2 are visited twice and they are the most visited sectors. And sectors 3 and 4 are visited only once.
To solve this, we will follow these steps −
d := a new map
for j in range 1 to n, do
d[j] := 0
d[rounds[0]] := 1
for i in range 1 to size of rounds - 1, do
if rounds[i] > rounds[i-1], then
for j in range rounds[i-1]+1 to rounds[i]+1, do
d[j] := d[j] + 1
otherwise,
for j in range rounds[i-1]+1 to n, do
d[j] := d[j] + 1
for j in range 1 to rounds[i], do
d[j] := d[j] + 1
curr := d[rounds[0]]
out := [rounds[0]]
for i in range 1 to n, do
if i is not same as rounds[0], then
if d[i] > curr, then
curr := d[i]
out := [i]
otherwise when d[i] is same as curr, then
append i with out
return out after sorting
Example (Python)
Let us see the following implementation to get better understanding −
def solve(n, rounds):
d = {}
for j in range(1,n+1):
d[j] = 0
d[rounds[0]] = 1
for i in range(1, len(rounds)):
if rounds[i] > rounds[i-1]:
for j in range(rounds[i-1]+1, rounds[i]+1):
d[j] += 1
else:
for j in range(rounds[i-1]+1,n+1):
d[j] += 1
for j in range(1,rounds[i]+1):
d[j] += 1
curr = d[rounds[0]]
out = [rounds[0]]
for i in range(1,n+1):
if i != rounds[0]:
if d[i] > curr:
curr = d[i]
out = [i]
elif d[i] == curr:
out = out + [i]
return(sorted(out))
n = 4
rounds = [1,3,1,2]
print(solve(n, rounds))Input
4, [1,3,1,2]
Output
[1, 2]