HDU 1056 Largest Rectangle in a Histogram（dp）（求最大的矩形面積），hduhistogram

HDU 1056 Largest Rectangle in a Histogram（dp）（求最大的矩形面積），hduhistogram

Problem DescriptionA histogram is a polygon composed of a sequence of rectangles aligned at a common base line. The rectangles have equal widths but may have different heights. For example, the figure on the left shows the histogram that consists of rectangles with the heights 2, 1, 4, 5, 1, 3, 3, measured in units where 1 is the width of the rectangles:

Usually, histograms are used to represent discrete distributions, e.g., the frequencies of characters in texts. Note that the order of the rectangles, i.e., their heights, is important. Calculate the area of the largest rectangle in a histogram that is aligned at the common base line, too. The figure on the right shows the largest aligned rectangle for the depicted histogram. 
InputThe input contains several test cases. Each test case describes a histogram and starts with an integer n, denoting the number of rectangles it is composed of. You may assume that 1 <= n <= 100000. Then follow n integers h1, ..., hn, where 0 <= hi <= 1000000000. These numbers denote the heights of the rectangles of the histogram in left-to-right order. The width of each rectangle is 1. A zero follows the input for the last test case. 
OutputFor each test case output on a single line the area of the largest rectangle in the specified histogram. Remember that this rectangle must be aligned at the common base line. 
Sample Input

7 2 1 4 5 1 3 34 1000 1000 1000 10000

 
Sample Output

84000

 
SourceUniversity of Ulm Local Contest 2003 
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思路：以每一行的高度為高，看左右分別可以延伸到哪裡，算出面積求優解

代碼：

#include<iostream>#include<algorithm>#include<cstdio>#include<cstring>using namespace std;#define N 100005__int64 h[N],le[N],ri[N];int main(){    __int64 n,i;    while(scanf("%I64d",&n),n)    {        for(i=1;i<=n;i++)        {            scanf("%I64d",&h[i]);            le[i]=ri[i]=i;        }        for(i=1;i<=n;i++)            while(le[i]>1&&h[le[i]-1]>=h[i])               le[i]=le[le[i]-1];        for(i=n;i>=1;i--)            while(ri[i]<n&&h[ri[i]+1]>=h[i])            ri[i]=ri[ri[i]+1];        __int64 ans=0;        for(i=1;i<=n;i++)        {            __int64 temp=((ri[i]-le[i]+1)*h[i]);            if(temp>ans)                ans=temp;        }        printf("%I64d\n",ans);    }    return 0;}

杭電1506，Largest Rectangle in a Histogram，幫忙看看

#include<stdio.h>__int64 h[100001],dp[100001],m1[100001],m2[100001];//數組太大了要放外面，其他的沒錯__int64 n,s,m,i,j,k;int main(){ while(scanf("%I64d",&n)!=EOF&&n!=0) { for(i=1;i<=n;i++) scanf("%I64d",&h[i]); m1[1]=1; for(i=1;i<=n;i++) { k=i; while(k>1) { if(h[k-1]>=h[i]) { m1[i]=m1[k-1]; k=m1[k-1]; } else { m1[i]=k; break; } } } m2[n]=n; for(i=n;i>=1;i--) { k=i; while(k<n) { if(h[k+1]>=h[i]) { m2[i]=m2[k+1]; k=m2[k+1]; } else { m2[i]=k; break; } } } for(i=1;i<=n;i++) dp[i]=(m2[i]-m1[i]+1)*h[i]; m=0; for(i=1;i<=n;i++) if(dp[i]>m) m=dp[i]; printf("%I64d\n",m); } return 0;}看了 很久剛剛開始我幫你驗證了一下，結果沒發執行，然後我就想可能是數組的原因吧，所以這問題以後注意一下就好了，，希望對你有協助