Tasks Details
medium
1.
Flags
Find the maximum number of flags that can be set on mountain peaks.
Task Score
93%
Correctness
100%
Performance
85%
A non-empty array A consisting of N integers is given.
A peak is an array element which is larger than its neighbours. More precisely, it is an index P such that 0 < P < N − 1 and A[P − 1] < A[P] > A[P + 1].
For example, the following array A:
A[0] = 1 A[1] = 5 A[2] = 3 A[3] = 4 A[4] = 3 A[5] = 4 A[6] = 1 A[7] = 2 A[8] = 3 A[9] = 4 A[10] = 6 A[11] = 2has exactly four peaks: elements 1, 3, 5 and 10.
You are going on a trip to a range of mountains whose relative heights are represented by array A, as shown in a figure below. You have to choose how many flags you should take with you. The goal is to set the maximum number of flags on the peaks, according to certain rules.
Flags can only be set on peaks. What's more, if you take K flags, then the distance between any two flags should be greater than or equal to K. The distance between indices P and Q is the absolute value |P − Q|.
For example, given the mountain range represented by array A, above, with N = 12, if you take:
- two flags, you can set them on peaks 1 and 5;
- three flags, you can set them on peaks 1, 5 and 10;
- four flags, you can set only three flags, on peaks 1, 5 and 10.
You can therefore set a maximum of three flags in this case.
Write a function:
class Solution { public int solution(int[] A); }
that, given a non-empty array A of N integers, returns the maximum number of flags that can be set on the peaks of the array.
For example, the following array A:
A[0] = 1 A[1] = 5 A[2] = 3 A[3] = 4 A[4] = 3 A[5] = 4 A[6] = 1 A[7] = 2 A[8] = 3 A[9] = 4 A[10] = 6 A[11] = 2the function should return 3, as explained above.
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [1..400,000];
- each element of array A is an integer within the range [0..1,000,000,000].
Copyright 2009–2025 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.
Solution
Programming language used C#
Time spent on task 1 minutes
Notes
not defined yet
Code: 02:49:47 UTC,
java,
autosave
Code: 02:49:49 UTC,
cs,
autosave
using System;
// you can also use other imports, for example:
// using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution {
public int solution(int[] A) {
// write your code in C# 6.0 with .NET 4.5 (Mono)
}
}
Code: 02:49:55 UTC,
cs,
autosave
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980
using System;
// you can also use other imports, for example:
// using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution2
{
public int solution(int[] A)
{
// write your code in C# 6.0 with .NET 4.5 (Mono)
List<int> peaks = new List<int>();
int minDistance = int.MaxValue;
int lastIndexOfPeek = -1;
for (int i = 1; i < A.Length - 1; i++)
{
if (A[i] > A[i - 1] && A[i] > A[i + 1])
{
peaks.Add(i); // 1 based
if (lastIndexOfPeek != -1)
{
int distance = i - lastIndexOfPeek;
minDistance = Math.Min(distance, minDistance);
lastIndexOfPeek = i;
}
else
{
lastIndexOfPeek = i;
}
}
}
int numberOfPeaks = peaks.Count;
if (minDistance >= numberOfPeaks)
{
return numberOfPeaks;
}
numberOfPeaks = Math.Min(Convert.ToInt32(Math.Floor(Math.Sqrt(A.Length))), numberOfPeaks);
int maxPlacedFlags = 0;
for (
int attemptedNumberOfFlagsInThisRun = numberOfPeaks;
0 < attemptedNumberOfFlagsInThisRun;
attemptedNumberOfFlagsInThisRun--
)
{
if (maxPlacedFlags >= attemptedNumberOfFlagsInThisRun)
{
break;
}
int calculatedPeaks = 1;
int numberOfPeaksPassed = 0;
for (int i = 1; i < peaks.Count; i++)
{
if (peaks[i] - peaks[i - 1 - numberOfPeaksPassed] >= attemptedNumberOfFlagsInThisRun)
{
calculatedPeaks++;
numberOfPeaksPassed = 0;
}
else
{
numberOfPeaksPassed++;
continue;
}
}
maxPlacedFlags = Math.Max(maxPlacedFlags, calculatedPeaks);
}
return maxPlacedFlags;
}
}
Code: 02:50:01 UTC,
cs,
verify,
result: Failed
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182
using System;
using System.Collections.Generic;
using System.Linq;
// you can also use other imports, for example:
// using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution2
{
public int solution(int[] A)
{
// write your code in C# 6.0 with .NET 4.5 (Mono)
List<int> peaks = new List<int>();
int minDistance = int.MaxValue;
int lastIndexOfPeek = -1;
for (int i = 1; i < A.Length - 1; i++)
{
if (A[i] > A[i - 1] && A[i] > A[i + 1])
{
peaks.Add(i); // 1 based
if (lastIndexOfPeek != -1)
{
int distance = i - lastIndexOfPeek;
minDistance = Math.Min(distance, minDistance);
lastIndexOfPeek = i;
}
else
{
lastIndexOfPeek = i;
}
}
}
int numberOfPeaks = peaks.Count;
if (minDistance >= numberOfPeaks)
{
return numberOfPeaks;
}
numberOfPeaks = Math.Min(Convert.ToInt32(Math.Floor(Math.Sqrt(A.Length))), numberOfPeaks);
int maxPlacedFlags = 0;
for (
int attemptedNumberOfFlagsInThisRun = numberOfPeaks;
0 < attemptedNumberOfFlagsInThisRun;
attemptedNumberOfFlagsInThisRun--
)
{
if (maxPlacedFlags >= attemptedNumberOfFlagsInThisRun)
{
break;
}
int calculatedPeaks = 1;
int numberOfPeaksPassed = 0;
for (int i = 1; i < peaks.Count; i++)
{
if (peaks[i] - peaks[i - 1 - numberOfPeaksPassed] >= attemptedNumberOfFlagsInThisRun)
{
calculatedPeaks++;
numberOfPeaksPassed = 0;
}
else
{
numberOfPeaksPassed++;
continue;
}
}
maxPlacedFlags = Math.Max(maxPlacedFlags, calculatedPeaks);
}
return maxPlacedFlags;
}
}
Analysis
Compile error
Compilation failed: 1 error(s), 0 warnings exec.cs(16,5): error CS0246: The type or namespace name `Solution' could not be found. Are you missing an assembly reference?
Code: 02:50:07 UTC,
cs,
verify,
result: Passed
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182
using System;
using System.Collections.Generic;
using System.Linq;
// you can also use other imports, for example:
// using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution
{
public int solution(int[] A)
{
// write your code in C# 6.0 with .NET 4.5 (Mono)
List<int> peaks = new List<int>();
int minDistance = int.MaxValue;
int lastIndexOfPeek = -1;
for (int i = 1; i < A.Length - 1; i++)
{
if (A[i] > A[i - 1] && A[i] > A[i + 1])
{
peaks.Add(i); // 1 based
if (lastIndexOfPeek != -1)
{
int distance = i - lastIndexOfPeek;
minDistance = Math.Min(distance, minDistance);
lastIndexOfPeek = i;
}
else
{
lastIndexOfPeek = i;
}
}
}
int numberOfPeaks = peaks.Count;
if (minDistance >= numberOfPeaks)
{
return numberOfPeaks;
}
numberOfPeaks = Math.Min(Convert.ToInt32(Math.Floor(Math.Sqrt(A.Length))), numberOfPeaks);
int maxPlacedFlags = 0;
for (
int attemptedNumberOfFlagsInThisRun = numberOfPeaks;
0 < attemptedNumberOfFlagsInThisRun;
attemptedNumberOfFlagsInThisRun--
)
{
if (maxPlacedFlags >= attemptedNumberOfFlagsInThisRun)
{
break;
}
int calculatedPeaks = 1;
int numberOfPeaksPassed = 0;
for (int i = 1; i < peaks.Count; i++)
{
if (peaks[i] - peaks[i - 1 - numberOfPeaksPassed] >= attemptedNumberOfFlagsInThisRun)
{
calculatedPeaks++;
numberOfPeaksPassed = 0;
}
else
{
numberOfPeaksPassed++;
continue;
}
}
maxPlacedFlags = Math.Max(maxPlacedFlags, calculatedPeaks);
}
return maxPlacedFlags;
}
}
Analysis
Code: 02:50:11 UTC,
cs,
verify,
result: Passed
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182
using System;
using System.Collections.Generic;
using System.Linq;
// you can also use other imports, for example:
// using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution
{
public int solution(int[] A)
{
// write your code in C# 6.0 with .NET 4.5 (Mono)
List<int> peaks = new List<int>();
int minDistance = int.MaxValue;
int lastIndexOfPeek = -1;
for (int i = 1; i < A.Length - 1; i++)
{
if (A[i] > A[i - 1] && A[i] > A[i + 1])
{
peaks.Add(i); // 1 based
if (lastIndexOfPeek != -1)
{
int distance = i - lastIndexOfPeek;
minDistance = Math.Min(distance, minDistance);
lastIndexOfPeek = i;
}
else
{
lastIndexOfPeek = i;
}
}
}
int numberOfPeaks = peaks.Count;
if (minDistance >= numberOfPeaks)
{
return numberOfPeaks;
}
numberOfPeaks = Math.Min(Convert.ToInt32(Math.Floor(Math.Sqrt(A.Length))), numberOfPeaks);
int maxPlacedFlags = 0;
for (
int attemptedNumberOfFlagsInThisRun = numberOfPeaks;
0 < attemptedNumberOfFlagsInThisRun;
attemptedNumberOfFlagsInThisRun--
)
{
if (maxPlacedFlags >= attemptedNumberOfFlagsInThisRun)
{
break;
}
int calculatedPeaks = 1;
int numberOfPeaksPassed = 0;
for (int i = 1; i < peaks.Count; i++)
{
if (peaks[i] - peaks[i - 1 - numberOfPeaksPassed] >= attemptedNumberOfFlagsInThisRun)
{
calculatedPeaks++;
numberOfPeaksPassed = 0;
}
else
{
numberOfPeaksPassed++;
continue;
}
}
maxPlacedFlags = Math.Max(maxPlacedFlags, calculatedPeaks);
}
return maxPlacedFlags;
}
}
Analysis
Code: 02:50:13 UTC,
cs,
final,
score:
93
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182
using System;
using System.Collections.Generic;
using System.Linq;
// you can also use other imports, for example:
// using System.Collections.Generic;
// you can write to stdout for debugging purposes, e.g.
// Console.WriteLine("this is a debug message");
class Solution
{
public int solution(int[] A)
{
// write your code in C# 6.0 with .NET 4.5 (Mono)
List<int> peaks = new List<int>();
int minDistance = int.MaxValue;
int lastIndexOfPeek = -1;
for (int i = 1; i < A.Length - 1; i++)
{
if (A[i] > A[i - 1] && A[i] > A[i + 1])
{
peaks.Add(i); // 1 based
if (lastIndexOfPeek != -1)
{
int distance = i - lastIndexOfPeek;
minDistance = Math.Min(distance, minDistance);
lastIndexOfPeek = i;
}
else
{
lastIndexOfPeek = i;
}
}
}
int numberOfPeaks = peaks.Count;
if (minDistance >= numberOfPeaks)
{
return numberOfPeaks;
}
numberOfPeaks = Math.Min(Convert.ToInt32(Math.Floor(Math.Sqrt(A.Length))), numberOfPeaks);
int maxPlacedFlags = 0;
for (
int attemptedNumberOfFlagsInThisRun = numberOfPeaks;
0 < attemptedNumberOfFlagsInThisRun;
attemptedNumberOfFlagsInThisRun--
)
{
if (maxPlacedFlags >= attemptedNumberOfFlagsInThisRun)
{
break;
}
int calculatedPeaks = 1;
int numberOfPeaksPassed = 0;
for (int i = 1; i < peaks.Count; i++)
{
if (peaks[i] - peaks[i - 1 - numberOfPeaksPassed] >= attemptedNumberOfFlagsInThisRun)
{
calculatedPeaks++;
numberOfPeaksPassed = 0;
}
else
{
numberOfPeaksPassed++;
continue;
}
}
maxPlacedFlags = Math.Max(maxPlacedFlags, calculatedPeaks);
}
return maxPlacedFlags;
}
}Analysis summary
The following issues have been detected: wrong answers.
Analysis
Detected time complexity:
O(N)
expand all
Correctness tests
1.
0.016 s
OK
2.
0.016 s
OK
3.
0.016 s
OK
1.
0.016 s
OK
2.
0.016 s
OK
3.
0.016 s
OK
4.
0.016 s
OK
5.
0.020 s
OK
1.
0.020 s
OK
2.
0.020 s
OK
1.
0.020 s
OK
1.
0.020 s
OK
1.
0.020 s
OK
1.
0.024 s
OK
2.
0.020 s
OK
1.
0.020 s
OK
2.
0.020 s
OK
expand all
Performance tests
1.
0.048 s
OK
2.
0.036 s
OK
1.
0.044 s
OK
2.
0.116 s
OK
1.
0.044 s
OK
2.
0.048 s
OK
1.
0.144 s
OK
2.
0.036 s
WRONG ANSWER,
got 317 expected 316
1.
0.052 s
OK
2.
0.052 s
OK
1.
0.080 s
OK
2.
0.080 s
OK
1.
0.112 s
OK
2.
0.112 s
OK