I, entitled Description
Title 84. Largest Rectangle in Histogram, to form a histogram, find the largest area of the graph given n non-negative integers (a width of each column 1). Difficulty of the subject is Hard!
Second, my answer
This is a look easy, but doing it is easy to mistake the title . I started to use the word "digging Law", unfortunately, always Time Limit Exceeded . After 10 sub-optimal, or difficult to see.
class Solution{
public:
int largestRectangleArea(vector<int>& heights){
int len = heights.size();
if(len<1) return 0;
if(len==1) return heights[0];
int result = 0;
int start=len-1,end=0;
int cnt = 0,sum=0;
int min;
while(1){
min = INT_MAX;
for(int i=0;i<len;i++){
if(heights[i]>0 && heights[i]<min){
min = heights[i];
}
}
//找到第1个正的
while(end<len && heights[end]<=0){
end++;
}
while(start>0 && heights[start]<=0){
start--;
}
if(start==end){
sum = heights[start];
if(sum>result) result = sum;
break;
}else if(end>start) {
break;
}
sum = 0;
cnt = 0;
//一次遍历,求大于0的连续长度 最大值
while(end<len){
cnt = 0;
sum = 0;
while(end<len && heights[end]>=min){
if(heights[end]==min) heights[end] = 0;
cnt++;
end++;
}
sum = cnt * min;
if(sum>result) result = sum;
if(end<len) end++;
}
end = 0;
start = len-1;
}
return result;
}
};
performance:
Runtime: 1536 ms, faster than 4.53% of C++ online submissions for Largest Rectangle in Histogram.
Memory Usage: 9.9 MB, less than 94.29% of C++ online submissions for Largest Rectangle in Histogram.
The method can also think of violence calculations, performance is also similar:
class Solution{
public:
//brute force
int largestRectangleArea(vector<int>& heights){
int len = heights.size();
if(len<1) return 0;
if(len==1) return heights[0];
int result = 0;
bool allthesame = true;
for(int i=0;i<len-1;i++){
if(heights[i]!=heights[i+1]){
allthesame = false;
}
}
if(allthesame){
return heights[0]*len;
}
for(int i=0;i<len;i++){
int minHeight = INT_MAX;
for(int j=i;j<len;j++){
minHeight = min(minHeight,heights[j]);
result = max(result,minHeight * (j-i+1));
}
}
return result;
}
};
Runtime: 1040 ms, faster than 5.03% of C++ online submissions for Largest Rectangle in Histogram.
Memory Usage: 10 MB, less than 94.29% of C++ online submissions for Largest Rectangle in Histogram.
Third, the optimization measures
Stack with a monotonically increasing method, as follows:
class Solution{
public:
//单调递增栈
int largestRectangleArea(vector<int>& heights){
int result = 0;
stack<int> st;
st.push(-1);//-1 放进栈的顶部来表示开始
//按照从左到右的顺序,我们不断将柱子的序号放进栈中,直到 heights[i]<heights[st.top]
//将栈中的序号弹出,直到heights[stack[j]]≤heights[i]
for(int i=0;i<heights.size();i++){
while(st.top()!=-1 && heights[i]<heights[st.top()]){
int h = st.top();
st.pop();
result = max(result,heights[h]*(i - st.top() -1));
}
st.push(i);
}
// 遍历完了,但是没计算完
while(st.top() != -1){
int h = st.top();
st.pop();
int len = heights.size() - st.top() -1;
result = max(result,heights[h]*len);
}
return result;
}
};
Runtime: 16 ms, faster than 53.51% of C++ online submissions for Largest Rectangle in Histogram.
Memory Usage: 10.4 MB, less than 91.43% of C++ online submissions for Largest Rectangle in Histogram.
Continue to optimize:
class Solution{
public:
//单调递增栈 ,借用i当栈
int largestRectangleArea(vector<int>& heights){
int result = 0;
int len, wid;
for (int i = 0; i < heights.size(); i++) {
if(i != heights.size() - 1 && heights[i] <= heights[i + 1]) continue; //这一步的判断很玄妙
wid = heights[i];
for (int j = i; j >= 0; j--) {
len = i - j + 1;
wid = min(wid, heights[j]);
result = max(result, len * wid);
}
}
return result;
}
};
Runtime: 12 ms, faster than 89.13% of C++ online submissions for Largest Rectangle in Histogram.
Memory Usage: 10 MB, less than 94.29% of C++ online submissions for Largest Rectangle in Histogram.
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