Tasks Details
medium
Given N rectangular buildings of width 1, find the minimum total area of two rectangular banners that cover all of the buildings.
Task Score
50%
Correctness
100%
Performance
0%
There are N rectangular buildings standing along the road next to each other. The K-th building is of size H[K] × 1.
Because a renovation of all of the buildings is planned, we want to cover them with rectangular banners until the renovations are finished. Of course, to cover a building, the banner has to be at least as high as the building. We can cover more than one building with a banner if it is wider than 1.
For example, to cover buildings of heights 3, 1, 4 we could use a banner of size 4×3 (i.e. of height 4 and width 3), marked here in blue:
We can order at most two banners and we want to cover all of the buildings. Also, we want to minimize the amount of material needed to produce the banners.
What is the minimum total area of at most two banners which cover all of the buildings?
Write a function:
def solution(H)
that, given an array H consisting of N integers, returns the minimum total area of at most two banners that we will have to order.
Examples:
1. Given H = [3, 1, 4], the function should return 10. The result can be achieved by covering the first two buildings with a banner of size 3×2 and the third building with a banner of size 4×1:
2. Given H = [5, 3, 2, 4], the function should return 17. The result can be achieved by covering the first building with a banner of size 5×1 and the other buildings with a banner of size 4×3:
3. Given H = [5, 3, 5, 2, 1], your function should return 19. The result can be achieved by covering the first three buildings with a banner of size 5×3 and the other two with a banner of size 2×2:
4. Given H = [7, 7, 3, 7, 7], your function should return 35. The result can be achieved by using one banner of size 7×5:
5. Given H = [1, 1, 7, 6, 6, 6], your function should return 30. The result can be achieved by using banners of size 1×2 and 7×4:
Write an efficient algorithm for the following assumptions:
- N is an integer within the range [1..100,000];
- each element of array H is an integer within the range [1..10,000].
Copyright 2009–2025 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.
Solution
Programming language used Python
Time spent on task 20 minutes
Notes
not defined yet
Code: 11:52:09 UTC,
java,
autosave
Code: 11:52:19 UTC,
cpp,
autosave
Code: 11:53:55 UTC,
java,
autosave
Code: 11:54:23 UTC,
java,
autosave
Code: 11:54:53 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
}
}
Code: 11:55:03 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax
}
}
Code: 11:59:10 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=i
}
}
Code: 11:59:38 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H)
}
}
Code: 11:59:49 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H>)
}
}
Code: 12:00:19 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H> {
if(lMax<H>)
}
}
}
Code: 12:00:37 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H> {
if(lMax<H> lMax=H[i];
}
}
}
Code: 12:00:54 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H> {
if(lMax<H> lMax=H[i];
if(rMax<H> rMax=H[i];
}
}
}
Code: 12:01:24 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H> {
if(lMax<H> lMax=H[i];
if(rMax<H> rMax=H[j];
var a=lMax*(i+1);
var b=rMax
}
}
}
Code: 12:01:54 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H> {
if(lMax<H> lMax=H[i];
if(rMax<H> rMax=H[j];
var a=lMax*(i+1);
var b=rMax*j;
var temp=a+b;
if(temp<minArea> {
minArea=
}
}
}
}
Code: 12:02:13 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H> {
if(lMax<H> lMax=H[i];
if(rMax<H> rMax=H[j];
var a=lMax*(i+1);
var b=rMax*j;
var temp=a+b;
if(temp<minArea> {
minArea=temp;
k=i+1;
}
j--;
}
}
}
Code: 12:03:36 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H> {
if(lMax<H> lMax=H[i];
if(rMax<H> rMax=H[j];
var a=lMax*(i+1);
var b=rMax*j;
var temp=a+b;
if(temp<minArea> {
minArea=temp;
k=i+1;
}
j--;
}
retu
}
}
Code: 12:03:42 UTC,
java,
verify,
result: Failed
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H> {
if(lMax<H> lMax=H[i];
if(rMax<H> rMax=H[j];
var a=lMax*(i+1);
var b=rMax*j;
var temp=a+b;
if(temp<minArea> {
minArea=temp;
k=i+1;
}
j--;
}
return minArea;
}
}
Analysis
Compile error
Solution.java:10: error: class expected
var minArea=int.MaxValue;
^
Solution.java:13: error: class expected
var lMax=int.Minvalue;
^
Solution.java:14: error: class expected
var rMax=int.MinValue;
^
Solution.java:15: error: illegal start of expression
for(var i=0;i<H> {
^
Solution.java:16: error: illegal start of expression
if(lMax<H> lMax=H[i];
^
Solution.java:16: error: ')' expected
if(lMax<H> lMax=H[i];
^
Solution.java:16: error: variable declaration not allowed here
if(lMax<H> lMax=H[i];
^
Solution.java:17: error: ')' expected
if(rMax<H> rMax=H[j];
^
Solution.java:22: error: illegal start of expression
if(temp<minArea> {
^
Solution.java:26: error: <identifier> expected
j--;
^
Solution.java:28: error: class, interface, or enum expected
return minArea;
^
Solution.java:29: error: class, interface, or enum expected
}
^
12 errors
Code: 12:04:25 UTC,
java,
autosave
Code: 12:04:35 UTC,
java,
autosave
// you can also use imports, for example:
// import java.util.*;
// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");
class Solution {
public int solution(int[] H) {
// write your code in Java SE 8
var minArea=int.MaxValue;
var k=0;
var j=H.Length-1;
var lMax=int.Minvalue;
var rMax=int.MinValue;
for(var i=0;i<H> {
if(lMax<H> lMax=H[i];
if(rMax<H> rMax=H[j];
var a=lMax*(i+1);
var b=rMax*j;
var temp=a+b;
if(temp<minArea> {
minArea=temp;
k=i+1;
}
j--;
}
return minArea;
}
}
Code: 12:08:33 UTC,
py,
autosave
Code: 12:08:51 UTC,
py,
autosave
Code: 12:09:01 UTC,
py,
autosave
Code: 12:09:12 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(h[0:1])* len(H[0:1]))+ (max(h[0:1])* len(H[0:1]))
Code: 12:09:42 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(h[0:1])* len(H[0:1]))+ (max(h[i:])* len(H[i:]))
if double_banner<smallest_area:
smallest
Code: 12:09:52 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(h[0:1])* len(H[0:1]))+ (max(h[i:])* len(H[i:]))
if double_banner<smallest_area:
smallest_area=double_banner
Code: 12:10:05 UTC,
py,
verify,
result: Failed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(h[0:1])* len(H[0:1]))+ (max(h[i:])* len(H[i:]))
if double_banner<smallest_area:
smallest_area=double_banner
return smallest_area
Analysis
expand all
Example tests
1.
0.040 s
RUNTIME ERROR,
tested program terminated with exit code 1
stderr:
Traceback (most recent call last):
File "exec.py", line 129, in <module>
main()
File "exec.py", line 91, in main
result = solution( H )
File "/tmp/solution.py", line 9, in solution
double_banner=(max(h[0:1])* len(H[0:1]))+ (max(h[i:])* len(H[i:]))
NameError: name 'h' is not defined
1.
0.040 s
RUNTIME ERROR,
tested program terminated with exit code 1
stderr:
Traceback (most recent call last):
File "exec.py", line 129, in <module>
main()
File "exec.py", line 91, in main
result = solution( H )
File "/tmp/solution.py", line 9, in solution
double_banner=(max(h[0:1])* len(H[0:1]))+ (max(h[i:])* len(H[i:]))
NameError: name 'h' is not defined
1.
0.036 s
RUNTIME ERROR,
tested program terminated with exit code 1
stderr:
Traceback (most recent call last):
File "exec.py", line 129, in <module>
main()
File "exec.py", line 91, in main
result = solution( H )
File "/tmp/solution.py", line 9, in solution
double_banner=(max(h[0:1])* len(H[0:1]))+ (max(h[i:])* len(H[i:]))
NameError: name 'h' is not defined
1.
0.040 s
RUNTIME ERROR,
tested program terminated with exit code 1
stderr:
Traceback (most recent call last):
File "exec.py", line 129, in <module>
main()
File "exec.py", line 91, in main
result = solution( H )
File "/tmp/solution.py", line 9, in solution
double_banner=(max(h[0:1])* len(H[0:1]))+ (max(h[i:])* len(H[i:]))
NameError: name 'h' is not defined
1.
0.040 s
RUNTIME ERROR,
tested program terminated with exit code 1
stderr:
Traceback (most recent call last):
File "exec.py", line 129, in <module>
main()
File "exec.py", line 91, in main
result = solution( H )
File "/tmp/solution.py", line 9, in solution
double_banner=(max(h[0:1])* len(H[0:1]))+ (max(h[i:])* len(H[i:]))
NameError: name 'h' is not defined
Code: 12:10:23 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(H[0:1])* len(H[0:1]))+ (max(H[i:])* len(H[i:]))
if double_banner<smallest_area:
smallest_area=double_banner
return smallest_area
Code: 12:10:23 UTC,
py,
verify,
result: Failed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(H[0:1])* len(H[0:1]))+ (max(H[i:])* len(H[i:]))
if double_banner<smallest_area:
smallest_area=double_banner
return smallest_area
Analysis
expand all
Example tests
1.
0.036 s
WRONG ANSWER,
got 7 expected 10
1.
0.036 s
WRONG ANSWER,
got 9 expected 17
1.
0.036 s
WRONG ANSWER,
got 6 expected 19
1.
0.036 s
WRONG ANSWER,
got 14 expected 35
1.
0.036 s
WRONG ANSWER,
got 7 expected 30
Code: 12:10:43 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(H[0:1])* len(H[0:1]))+ (max(H[i:])* len(H[i:]))
if double_banner < smallest_area:
smallest_area=double_banner
return smallest_area
Code: 12:10:53 UTC,
py,
autosave
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(H[0:i])* len(H[0:1]))+ (max(H[i:])* len(H[i:]))
if double_banner < smallest_area:
smallest_area=double_banner
return smallest_area
Code: 12:10:56 UTC,
py,
verify,
result: Passed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(H[0:i])* len(H[0:i]))+ (max(H[i:])* len(H[i:]))
if double_banner < smallest_area:
smallest_area=double_banner
return smallest_area
Code: 12:11:02 UTC,
py,
verify,
result: Passed
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(H[0:i])* len(H[0:i]))+ (max(H[i:])* len(H[i:]))
if double_banner < smallest_area:
smallest_area=double_banner
return smallest_area
Code: 12:11:06 UTC,
py,
final,
score:
50
# you can write to stdout for debugging purposes, e.g.
# print("this is a debug message")
def solution(H):
# write your code in Python 3.6
single_banner=max(H)* len(H)
smallest_area=single_banner
for i in range(1, len(H)):
double_banner=(max(H[0:i])* len(H[0:i]))+ (max(H[i:])* len(H[i:]))
if double_banner < smallest_area:
smallest_area=double_banner
return smallest_area
Analysis summary
The following issues have been detected: timeout errors.
Analysis
Detected time complexity:
O(N**2)
expand all
Correctness tests
1.
0.036 s
OK
2.
0.036 s
OK
3.
0.036 s
OK
4.
0.036 s
OK
5.
0.036 s
OK
6.
0.036 s
OK
1.
0.036 s
OK
2.
0.036 s
OK
3.
0.036 s
OK
4.
0.036 s
OK
5.
0.036 s
OK
1.
0.036 s
OK
2.
0.036 s
OK
1.
0.040 s
OK
2.
0.036 s
OK
3.
0.036 s
OK
4.
0.036 s
OK
5.
0.036 s
OK
1.
0.036 s
OK
2.
0.036 s
OK
3.
0.036 s
OK
4.
0.036 s
OK
5.
0.036 s
OK
6.
0.036 s
OK
1.
0.044 s
OK
2.
0.044 s
OK
3.
0.044 s
OK
4.
0.044 s
OK
expand all
Performance tests
distinct_large
Every value in the array is different. N=7,500.
Every value in the array is different. N=7,500.
✘
TIMEOUT ERROR
running time: 1.680 sec., time limit: 0.304 sec.
running time: 1.680 sec., time limit: 0.304 sec.
1.
1.680 s
TIMEOUT ERROR,
running time: 1.680 sec., time limit: 0.304 sec.
2.
1.676 s
TIMEOUT ERROR,
running time: 1.676 sec., time limit: 0.208 sec.
3.
1.672 s
TIMEOUT ERROR,
running time: 1.672 sec., time limit: 0.208 sec.
4.
1.676 s
TIMEOUT ERROR,
running time: 1.676 sec., time limit: 0.208 sec.
random_max
Random maximum tests. N=100,000.
Random maximum tests. N=100,000.
✘
TIMEOUT ERROR
Killed. Hard limit reached: 6.000 sec.
Killed. Hard limit reached: 6.000 sec.
1.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
2.
7.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 7.000 sec.
3.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
4.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
various_max
Various hard hand-created tests. N=100,000.
Various hard hand-created tests. N=100,000.
✘
TIMEOUT ERROR
Killed. Hard limit reached: 6.000 sec.
Killed. Hard limit reached: 6.000 sec.
1.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
2.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
3.
7.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 7.000 sec.
4.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
5.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
6.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
max_pyramid
Values in the tests are arranged into ascending or descending pyramids. N=100,000.
Values in the tests are arranged into ascending or descending pyramids. N=100,000.
✘
TIMEOUT ERROR
Killed. Hard limit reached: 6.000 sec.
Killed. Hard limit reached: 6.000 sec.
1.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
2.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
3.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
4.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
5.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
1.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
2.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
3.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
4.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
5.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
6.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.
7.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.