leetCode 84.Largest Rectangle in Histogram （最大矩形直方图） 解题思路和方法

Given n non-negative integers representing the histogram's bar height where the width of each bar is 1, find the area of largest rectangle in the histogram.



Above is a histogram where width of each bar is 1, given height =

[2,1,5,6,2,3]

.



The largest rectangle is shown in the shaded area, which has area =

10

unit.

For example,

Given height =

[2,1,5,6,2,3]

,

return

10

.

思路：此题还是有一些难度的。刚開始想的双指针，前后扫描，可是每次求最小的高度的时候都须要遍历一次。效率上不是非常高。为o(n2)。

代码例如以下：

public class Solution {
public int largestRectangleArea(int[] height) {

int max = 0;//最大值
int i = 0;//左指针
int j = height.length - 1;//右指针
boolean isMinChange = true;

//双指针扫描
while(i <= j){
int minHeight = Integer.MAX_VALUE;//范围内最小值
if(isMinChange){//最小值是否改变
isMinChange = false;
//又一次得到最小值
for(int k = i ; k <= j;k++){
if(height[k] < minHeight){
minHeight = height[k];
}
}
}
//面积
int area = (j - i + 1)*minHeight;
if(max < area){
max = area;
}
if(i == j){//假设相等，则结束
break;
}
if(height[i] < height[j]){//左指针添加，直到比当前大
int k = i;
while(k <= j && height[k] <= height[i]){
if(height[k] == minHeight){//推断最小值是否改变
isMinChange = true;
}
k++;
}
i = k;
}else{//右指针减小，直到比当前大
int k = j;
while( k >= i && height[k] <= height[j]){
if(height[k] == minHeight){//推断最小值是否改变
isMinChange = true;
}
k--;
}
j = k;
}
}
return max;
}
}

解法上过不了OJ,所以仅仅能在网上參看资料，最后找到资料例如以下，是用栈解决的。

public class Solution {
public int largestRectangleArea(int[] height) {
if (height == null || height.length == 0) return 0;

Stack<Integer> stHeight = new Stack<Integer>();
Stack<Integer> stIndex = new Stack<Integer>();
int max = 0;

for(int i = 0; i < height.length; i++){
if(stHeight.isEmpty() || height[i] > stHeight.peek()){
stHeight.push(height[i]);
stIndex.push(i);
}else if(height[i] < stHeight.peek()){
int lastIndex = 0;
while(!stHeight.isEmpty() && height[i] < stHeight.peek()){
lastIndex = stIndex.pop();
int area = stHeight.pop()*(i - lastIndex);
if(max < area){
max = area;
}
}
stHeight.push(height[i]);
stIndex.push(lastIndex);
}
}
while(!stHeight.isEmpty()){
int area = stHeight.pop()*(height.length - stIndex.pop());
max = max < area ? area:max;
}

return max;
}
}