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].
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[] H) {
// write your code in C# 6.0 with .NET 4.5 (Mono)
}
}
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[] H) {
var bestIndex = 0;
var hLength = H.Length;
var firstAreaMaxElement = H.Max();
var secondAreaMaxElement = 0;
decimal firstArea = firstAreaMaxElement * hLength;
decimal secondArea = 0;
decimal bestTotalArea = firstAreaMaxElement * hLength;
//if (H == null || H.Length == 0)
//{
// return 0;
//}
//else if(H.Length == 1)
//{
// return H[0];
//}
// Iterate starting from the end of the array;
// Compare areas on every iteration.
for (int i = H.Length - 1; i >= 0; i--)
{
var checkingPosition = i;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * (H.Length - i);
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
firstAreaMaxElement = H.Max();
secondAreaMaxElement = 0;
firstArea = firstAreaMaxElement * hLength;
secondArea = 0;
// Iterate starting from the beginning of the array;
// Compare areas on every iteration.
for (int i = 0; i < H.Length; i++)
{
var checkingPosition = i + 1;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * checkingPosition;
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
}
}
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[] H) {
var bestIndex = 0;
var hLength = H.Length;
var firstAreaMaxElement = H.Max();
var secondAreaMaxElement = 0;
decimal firstArea = firstAreaMaxElement * hLength;
decimal secondArea = 0;
decimal bestTotalArea = firstAreaMaxElement * hLength;
if (H == null || H.Length == 0)
{
return 0;
}
else if(H.Length == 1)
{
return H[0];
}
// Iterate starting from the end of the array;
// Compare areas on every iteration.
for (int i = H.Length - 1; i >= 0; i--)
{
var checkingPosition = i;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * (H.Length - i);
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
firstAreaMaxElement = H.Max();
secondAreaMaxElement = 0;
firstArea = firstAreaMaxElement * hLength;
secondArea = 0;
// Iterate starting from the beginning of the array;
// Compare areas on every iteration.
for (int i = 0; i < H.Length; i++)
{
var checkingPosition = i + 1;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * checkingPosition;
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
}
}
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[] H) {
var bestIndex = 0;
var hLength = H.Length;
var firstAreaMaxElement = H.Max();
var secondAreaMaxElement = 0;
decimal firstArea = firstAreaMaxElement * hLength;
decimal secondArea = 0;
decimal bestTotalArea = firstAreaMaxElement * hLength;
if (H == null || H.Length == 0)
{
return 0;
}
else if(H.Length == 1)
{
return H[0];
}
// Iterate starting from the end of the array;
// Compare areas on every iteration.
for (int i = H.Length - 1; i >= 0; i--)
{
var checkingPosition = i;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * (H.Length - i);
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
firstAreaMaxElement = H.Max();
secondAreaMaxElement = 0;
firstArea = firstAreaMaxElement * hLength;
secondArea = 0;
// Iterate starting from the beginning of the array;
// Compare areas on every iteration.
for (int i = 0; i < H.Length; i++)
{
var checkingPosition = i + 1;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * checkingPosition;
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
return bestTotalArea;
}
}
Compilation failed: 3 error(s), 0 warnings Solution.cs(13,41): error CS1061: Type `int[]' does not contain a definition for `Max' and no extension method `Max' of type `int[]' could be found. Are you missing `System.Linq' using directive? /opt/lang/mono/lib/mono/4.5/mscorlib.dll (Location of the symbol related to previous error) Solution.cs(59,37): error CS1061: Type `int[]' does not contain a definition for `Max' and no extension method `Max' of type `int[]' could be found. Are you missing `System.Linq' using directive? /opt/lang/mono/lib/mono/4.5/mscorlib.dll (Location of the symbol related to previous error) Solution.cs(93,20): error CS0266: Cannot implicitly convert type `decimal' to `int'. An explicit conversion exists (are you missing a cast?)
using System;
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[] H) {
var bestIndex = 0;
var hLength = H.Length;
var firstAreaMaxElement = H.Max();
var secondAreaMaxElement = 0;
decimal firstArea = firstAreaMaxElement * hLength;
decimal secondArea = 0;
decimal bestTotalArea = firstAreaMaxElement * hLength;
if (H == null || H.Length == 0)
{
return 0;
}
else if(H.Length == 1)
{
return H[0];
}
// Iterate starting from the end of the array;
// Compare areas on every iteration.
for (int i = H.Length - 1; i >= 0; i--)
{
var checkingPosition = i;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * (H.Length - i);
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
firstAreaMaxElement = H.Max();
secondAreaMaxElement = 0;
firstArea = firstAreaMaxElement * hLength;
secondArea = 0;
// Iterate starting from the beginning of the array;
// Compare areas on every iteration.
for (int i = 0; i < H.Length; i++)
{
var checkingPosition = i + 1;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * checkingPosition;
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
return bestTotalArea;
}
}
Compilation failed: 1 error(s), 0 warnings Solution.cs(94,20): error CS0266: Cannot implicitly convert type `decimal' to `int'. An explicit conversion exists (are you missing a cast?)
using System;
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[] H) {
var bestIndex = 0;
var hLength = H.Length;
var firstAreaMaxElement = H.Max();
var secondAreaMaxElement = 0;
int firstArea = firstAreaMaxElement * hLength;
decimal secondArea = 0;
decimal bestTotalArea = firstAreaMaxElement * hLength;
if (H == null || H.Length == 0)
{
return 0;
}
else if(H.Length == 1)
{
return H[0];
}
// Iterate starting from the end of the array;
// Compare areas on every iteration.
for (int i = H.Length - 1; i >= 0; i--)
{
var checkingPosition = i;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * (H.Length - i);
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
firstAreaMaxElement = H.Max();
secondAreaMaxElement = 0;
firstArea = firstAreaMaxElement * hLength;
secondArea = 0;
// Iterate starting from the beginning of the array;
// Compare areas on every iteration.
for (int i = 0; i < H.Length; i++)
{
var checkingPosition = i + 1;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * checkingPosition;
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
return bestTotalArea;
}
}
using System;
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[] H) {
var bestIndex = 0;
var hLength = H.Length;
var firstAreaMaxElement = H.Max();
var secondAreaMaxElement = 0;
int firstArea = firstAreaMaxElement * hLength;
int secondArea = 0;
int bestTotalArea = firstAreaMaxElement * hLength;
if (H == null || H.Length == 0)
{
return 0;
}
else if(H.Length == 1)
{
return H[0];
}
// Iterate starting from the end of the array;
// Compare areas on every iteration.
for (int i = H.Length - 1; i >= 0; i--)
{
var checkingPosition = i;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * (H.Length - i);
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
firstAreaMaxElement = H.Max();
secondAreaMaxElement = 0;
firstArea = firstAreaMaxElement * hLength;
secondArea = 0;
// Iterate starting from the beginning of the array;
// Compare areas on every iteration.
for (int i = 0; i < H.Length; i++)
{
var checkingPosition = i + 1;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * checkingPosition;
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
return bestTotalArea;
}
}
using System;
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[] H) {
var bestIndex = 0;
var hLength = H.Length;
var firstAreaMaxElement = H.Max();
var secondAreaMaxElement = 0;
int firstArea = firstAreaMaxElement * hLength;
int secondArea = 0;
int bestTotalArea = firstAreaMaxElement * hLength;
if (H == null || H.Length == 0)
{
return 0;
}
else if(H.Length == 1)
{
return H[0];
}
// Iterate starting from the end of the array;
// Compare areas on every iteration.
for (int i = H.Length - 1; i >= 0; i--)
{
var checkingPosition = i;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * (H.Length - i);
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
firstAreaMaxElement = H.Max();
secondAreaMaxElement = 0;
firstArea = firstAreaMaxElement * hLength;
secondArea = 0;
// Iterate starting from the beginning of the array;
// Compare areas on every iteration.
for (int i = 0; i < H.Length; i++)
{
var checkingPosition = i + 1;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * checkingPosition;
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
return bestTotalArea;
}
}
using System;
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[] H) {
var bestIndex = 0;
var hLength = H.Length;
var firstAreaMaxElement = H.Max();
var secondAreaMaxElement = 0;
int firstArea = firstAreaMaxElement * hLength;
int secondArea = 0;
int bestTotalArea = firstAreaMaxElement * hLength;
if (H == null || H.Length == 0)
{
return 0;
}
else if(H.Length == 1)
{
return H[0];
}
// Iterate starting from the end of the array;
// Compare areas on every iteration.
for (int i = H.Length - 1; i >= 0; i--)
{
var checkingPosition = i;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * (H.Length - i);
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
firstAreaMaxElement = H.Max();
secondAreaMaxElement = 0;
firstArea = firstAreaMaxElement * hLength;
secondArea = 0;
// Iterate starting from the beginning of the array;
// Compare areas on every iteration.
for (int i = 0; i < H.Length; i++)
{
var checkingPosition = i + 1;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * checkingPosition;
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
return bestTotalArea;
}
}
using System;
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[] H) {
var bestIndex = 0;
var hLength = H.Length;
var firstAreaMaxElement = H.Max();
var secondAreaMaxElement = 0;
int firstArea = firstAreaMaxElement * hLength;
int secondArea = 0;
int bestTotalArea = firstAreaMaxElement * hLength;
if (H == null || H.Length == 0)
{
return 0;
}
else if(H.Length == 1)
{
return H[0];
}
// Iterate starting from the end of the array;
// Compare areas on every iteration.
for (int i = H.Length - 1; i >= 0; i--)
{
var checkingPosition = i;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * (H.Length - i);
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
firstAreaMaxElement = H.Max();
secondAreaMaxElement = 0;
firstArea = firstAreaMaxElement * hLength;
secondArea = 0;
// Iterate starting from the beginning of the array;
// Compare areas on every iteration.
for (int i = 0; i < H.Length; i++)
{
var checkingPosition = i + 1;
var checkingElement = H[i];
if (checkingElement == firstAreaMaxElement)
{
break;
}
if (checkingElement > secondAreaMaxElement)
{
secondAreaMaxElement = checkingElement;
}
firstArea -= firstAreaMaxElement;
secondArea = secondAreaMaxElement * checkingPosition;
var currrentTotalArea = firstArea + secondArea;
if (currrentTotalArea < bestTotalArea)
{
bestIndex = checkingPosition;
bestTotalArea = currrentTotalArea;
}
}
return bestTotalArea;
}
}
The solution obtained perfect score.
Values in the tests are arranged into ascending or descending pyramids. N=100,000.