BlockStructure

/*Problem Statement

A group of vertical blocks are placed densely one after another on the ground. The blocks each have a width of 1, but their heights may vary.

For example, if the heights of the vertical blocks are given as {1,5,5,1,6,1}, the configuration would look like the following picture:


　　　　×
　××　×
　××　×
　××　×
　××　×
××××××

Your task is to reproduce the exact shape of this structure using some number of non-intersecting rectangles.

You will be given a int[] heights representing the heights of the vertical blocks from left to right.

Return the minimal number of rectangles necessary to perform this task with the given configuration of blocks.

Definition
Class: BlockStructure
Method: cover
Parameters: int[]
Returns: int
Method signature: int cover(int[] heights)
(be sure your method is public)

Constraints
- heights will have between 1 and 50 elements, inclusive.
- Each element of heights will be between 1 and 1000, inclusive.
Examples
0) {1,5,5,1,6,1} Returns: 3
We can use rectangles with sizes 6x1, 2x4 and 1x5.

　　　　×
　××　×
　××　×
　××　×
　××　×
××××××

1) {2,2,2,4,4} Returns: 2
We can use a 3x2 rectangle and a 2x4 rectangle.

　　　××
　　　××
×××××
×××××

2) {6,6,6,6,6,6} Returns: 1
The structure is a rectangle.

××××××
××××××
××××××
××××××
××××××
××××××

3){71,44,95,16,10,80,12,17,98,61} Returns: 10
It's impossible to use less than 10 rectangles.

4){100,100,97,100,100,100,97,98,99,99}
Returns: 5

This problem statement is the exclusive and proprietary property of TopCoder, Inc.
Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited.
(c)2003, TopCoder, Inc. All rights reserved.*/

package blockStructure;

import java.util.ArrayList;

public class BlockStructure {

public static int cover(int[] heights) {

int[][] records = markRecords(heights);

int result = 0;

int i = 0;
int j = 0;
while(i < records.length && j < records[i].length) {
if(records[i][j] == 1) {
int start_i = i;
int start_j = j;
while(j < records[i].length && records[i][j] == 1) j++;
j--;

while(i < records.length && rangeExist(records, i, start_j, j)) i++;
i--;

result++;
records = removeRecords(records, start_i, start_j, i, j);
i = j = 0;
} else if(records[i][j] == 0) {
if(j < records[i].length - 1) j++;
else {
j = 0;
i++;
}
}
}

return result;
}

//private static int result = 0;

public static int cover_2(int[] heights) {
int result = 0;

if(heights.length == 1) return 1;

deduct(heights);

result++;

if(isEmpty(heights)) return result;

ArrayList zeroList = zeroPos(heights);

int i = 0;
int temp = -1;
while(i < zeroList.size()) {
int position = ((Integer)zeroList.get(i)).intValue();
if(position == 0 || position - temp == 1) {
temp = position;
}
else {
int[] subtree = new int[position - temp - 1];
for(int j = temp + 1; j < position; j++){
subtree[j - temp - 1] = heights[j];
}
result += cover_2(subtree);

temp = position;

}
i++;
}

int position = ((Integer)zeroList.get(zeroList.size() - 1)).intValue();
if(position != heights.length - 1) {
int[] subtree = new int[heights.length - position - 1];
for(int j = position + 1; j < heights.length; j++){
subtree[j - position - 1] = heights[j];
}
result += cover_2(subtree);
}

return result;
}

private static boolean isEmpty(int[] array) {
for(int k = 0; k < array.length; k++) {
if(array[k] != 0) return false;
}

return true;
}

private static ArrayList zeroPos(int[] array) {
ArrayList list = new ArrayList();

for(int i = 0; i < array.length; i++) {
if(array[i] == 0) list.add(i);
}

return list;
}

private static int maxium(int[] array) {
int maxium = 0;
for(int i : array) {
if(i > maxium) maxium = i;
}

return maxium;
}

private static void deduct(int[] array) {
int min = minum(array);

for(int i = 0; i < array.length; i++) {
array[i] = array[i] - min;
}
}

private static int minum(int[] array) {
int min = Integer.MAX_VALUE;
for(int i : array) {
if(i < min) min = i;
}

return min;
}

private static int[][] markRecords(int[] array) {
int largestNum = maxium(array);

int[][] result = new int[largestNum][array.length];

for (int i = 0; i < result.length; i++) {
for (int j = 0; j < result[i].length; j++) {
try{
if(array[j] > i ) result[i][j] = 1;
else result[i][j] = 0;
}catch(Exception e){
e.printStackTrace();
}
}
}

return result;
}

private static int[][] removeRecords(int[][] records, int i, int j, int x, int y) {
for(int k = i; k <= x; k++) {
for(int m = j; m <= y; m++) {
records[k][m] = 0;
}
}
return records;
}

private static boolean rangeExist(int[][] records, int i, int start_j, int j) {
for(int k = start_j; k <= j; k++) {
if(records[i][k] == 0) return false;
}

return true;
}

}