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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%
Task description
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:
class Solution { public int solution(int[] 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 Java 21
Time spent on task 27 minutes
Notes
not defined yet
Task timeline
Code: 08:43:54 UTC,
java,
autosave
Code: 08:44:18 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
int max = 0;
int minSize = 0;
for(int i=0; i<nums.length;i++) {
int currentSize = 0;
if(max < nums[i]) {
max = nums[i];
}
int j=0;int width = 1;
for(; j<=i; j++) {
if(j==i) {
currentSize = width * max;
} else {
width++;
}
}
width = 0;
int maxInTheRemainingPosition = 0;
for(int k=j; k < nums.length; k++) {
if(maxInTheRemainingPosition < nums[k]) {
maxInTheRemainingPosition = nums[k];
}
width++;
}
currentSize += (width * maxInTheRemainingPosition);
if(minSize == 0) {
minSize = currentSize;
}
else if(currentSize < minSize) {
minSize = currentSize;
}
}
return minSize;
}
}
Code: 08:44:22 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
int max = 0;
int minSize = 0;
for(int i=0; i<nums.length;i++) {
int currentSize = 0;
if(max < nums[i]) {
max = nums[i];
}
int j=0;int width = 1;
for(; j<=i; j++) {
if(j==i) {
currentSize = width * max;
} else {
width++;
}
}
width = 0;
int maxInTheRemainingPosition = 0;
for(int k=j; k < nums.length; k++) {
if(maxInTheRemainingPosition < nums[k]) {
maxInTheRemainingPosition = nums[k];
}
width++;
}
currentSize += (width * maxInTheRemainingPosition);
if(minSize == 0) {
minSize = currentSize;
}
else if(currentSize < minSize) {
minSize = currentSize;
}
}
return minSize;
}
}
Analysis
Compile error
Solution.java:12: error: cannot find symbol
for(int i=0; i<nums.length;i++) {
^
symbol: variable nums
location: class Solution
Solution.java:14: error: cannot find symbol
if(max < nums[i]) {
^
symbol: variable nums
location: class Solution
Solution.java:15: error: cannot find symbol
max = nums[i];
^
symbol: variable nums
location: class Solution
Solution.java:27: error: cannot find symbol
for(int k=j; k < nums.length; k++) {
^
symbol: variable nums
location: class Solution
Solution.java:28: error: cannot find symbol
if(maxInTheRemainingPosition < nums[k]) {
^
symbol: variable nums
location: class Solution
Solution.java:29: error: cannot find symbol
maxInTheRemainingPosition = nums[k];
^
symbol: variable nums
location: class Solution
6 errors
Code: 08:44:43 UTC,
java,
verify,
result: Passed
// 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[] nums) {
// write your code in Java SE 8
int max = 0;
int minSize = 0;
for(int i=0; i<nums.length;i++) {
int currentSize = 0;
if(max < nums[i]) {
max = nums[i];
}
int j=0;int width = 1;
for(; j<=i; j++) {
if(j==i) {
currentSize = width * max;
} else {
width++;
}
}
width = 0;
int maxInTheRemainingPosition = 0;
for(int k=j; k < nums.length; k++) {
if(maxInTheRemainingPosition < nums[k]) {
maxInTheRemainingPosition = nums[k];
}
width++;
}
currentSize += (width * maxInTheRemainingPosition);
if(minSize == 0) {
minSize = currentSize;
}
else if(currentSize < minSize) {
minSize = currentSize;
}
}
return minSize;
}
}
Code: 08:45:24 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
int max = 0;
int minSize = 0;
for(int i=0; i<nums.length;i++) {
int currentSize = 0;
if(max < nums[i]) {
max = nums[i];
}
int j=0;int width = 1;
for(; j<=i; j++) {
if(j==i) {
currentSize = width * max;
} else {
width++;
}
}
width = 0;
int maxInTheRemainingPosition = 0;
for(int k=j; k < nums.length; k++) {
if(maxInTheRemainingPosition < nums[k]) {
maxInTheRemainingPosition = nums[k];
}
width++;
}
currentSize += (width * maxInTheRemainingPosition);
if(minSize == 0) {
minSize = currentSize;
}
else if(currentSize < minSize) {
minSize = currentSize;
}
}
return minSize;
}
}
Code: 08:45:41 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
int max = 0;
int minSize = 0;
for(int i=0; i<H.length;i++) {
int currentSize = 0;
if(max < H[i]) {
max = H[i];
}
int j=0;int width = 1;
for(; j<=i; j++) {
if(j==i) {
currentSize = width * max;
} else {
width++;
}
}
width = 0;
int maxInTheRemainingPosition = 0;
for(int k=j; k < nums.length; k++) {
if(maxInTheRemainingPosition < nums[k]) {
maxInTheRemainingPosition = nums[k];
}
width++;
}
currentSize += (width * maxInTheRemainingPosition);
if(minSize == 0) {
minSize = currentSize;
}
else if(currentSize < minSize) {
minSize = currentSize;
}
}
return minSize;
}
}
Code: 08:45:51 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
int max = 0;
int minSize = 0;
for(int i=0; i<H.length;i++) {
int currentSize = 0;
if(max < H[i]) {
max = H[i];
}
int j=0;int width = 1;
for(; j<=i; j++) {
if(j==i) {
currentSize = width * max;
} else {
width++;
}
}
width = 0;
int maxInTheRemainingPosition = 0;
for(int k=j; k < H.length; k++) {
if(maxInTheRemainingPosition < H[k]) {
maxInTheRemainingPosition = H[k];
}
width++;
}
currentSize += (width * maxInTheRemainingPosition);
if(minSize == 0) {
minSize = currentSize;
}
else if(currentSize < minSize) {
minSize = currentSize;
}
}
return minSize;
}
}
Code: 08:45:54 UTC,
java,
verify,
result: Passed
// 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
int max = 0;
int minSize = 0;
for(int i=0; i<H.length;i++) {
int currentSize = 0;
if(max < H[i]) {
max = H[i];
}
int j=0;int width = 1;
for(; j<=i; j++) {
if(j==i) {
currentSize = width * max;
} else {
width++;
}
}
width = 0;
int maxInTheRemainingPosition = 0;
for(int k=j; k < H.length; k++) {
if(maxInTheRemainingPosition < H[k]) {
maxInTheRemainingPosition = H[k];
}
width++;
}
currentSize += (width * maxInTheRemainingPosition);
if(minSize == 0) {
minSize = currentSize;
}
else if(currentSize < minSize) {
minSize = currentSize;
}
}
return minSize;
}
}
Code: 09:09:53 UTC,
java,
verify,
result: Passed
// 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
int max = 0;
int minSize = 0;
for(int i=0; i<H.length;i++) {
int currentSize = 0;
if(max < H[i]) {
max = H[i];
}
int j=0;int width = 1;
for(; j<=i; j++) {
if(j==i) {
currentSize = width * max;
} else {
width++;
}
}
width = 0;
int maxInTheRemainingPosition = 0;
for(int k=j; k < H.length; k++) {
if(maxInTheRemainingPosition < H[k]) {
maxInTheRemainingPosition = H[k];
}
width++;
}
currentSize += (width * maxInTheRemainingPosition);
if(minSize == 0) {
minSize = currentSize;
}
else if(currentSize < minSize) {
minSize = currentSize;
}
}
return minSize;
}
}
Code: 09:09:58 UTC,
java,
final,
score:
50
// 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
int max = 0;
int minSize = 0;
for(int i=0; i<H.length;i++) {
int currentSize = 0;
if(max < H[i]) {
max = H[i];
}
int j=0;int width = 1;
for(; j<=i; j++) {
if(j==i) {
currentSize = width * max;
} else {
width++;
}
}
width = 0;
int maxInTheRemainingPosition = 0;
for(int k=j; k < H.length; k++) {
if(maxInTheRemainingPosition < H[k]) {
maxInTheRemainingPosition = H[k];
}
width++;
}
currentSize += (width * maxInTheRemainingPosition);
if(minSize == 0) {
minSize = currentSize;
}
else if(currentSize < minSize) {
minSize = currentSize;
}
}
return minSize;
}
}
Analysis summary
The following issues have been detected: timeout errors.
Analysis
Detected time complexity:
O(N**2)
expand all
Correctness tests
1.
0.004 s
OK
2.
0.004 s
OK
3.
0.004 s
OK
4.
0.004 s
OK
5.
0.004 s
OK
6.
0.004 s
OK
1.
0.008 s
OK
2.
0.004 s
OK
3.
0.004 s
OK
4.
0.004 s
OK
5.
0.004 s
OK
1.
0.004 s
OK
2.
0.004 s
OK
1.
0.004 s
OK
2.
0.004 s
OK
3.
0.004 s
OK
4.
0.004 s
OK
5.
0.004 s
OK
1.
0.004 s
OK
2.
0.004 s
OK
3.
0.004 s
OK
4.
0.004 s
OK
5.
0.004 s
OK
6.
0.004 s
OK
1.
0.008 s
OK
2.
0.008 s
OK
3.
0.008 s
OK
4.
0.008 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: 0.736 sec., time limit: 0.100 sec.
running time: 0.736 sec., time limit: 0.100 sec.
1.
0.736 s
TIMEOUT ERROR,
running time: 0.736 sec., time limit: 0.100 sec.
2.
0.732 s
TIMEOUT ERROR,
running time: 0.732 sec., time limit: 0.100 sec.
3.
0.732 s
TIMEOUT ERROR,
running time: 0.732 sec., time limit: 0.100 sec.
4.
0.732 s
TIMEOUT ERROR,
running time: 0.732 sec., time limit: 0.100 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.
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.
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.
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.
7.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 7.000 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.
7.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 7.000 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.
7.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 7.000 sec.
7.
6.000 s
TIMEOUT ERROR,
Killed. Hard limit reached: 6.000 sec.