Largest Rectangle in a Histogram(dp)

http://acm.hdu.edu.cn/showproblem.php?pid=1506

题意：给出n个矩形的高度，每个矩形的宽都为1，求相邻的矩形能组合成的最大的矩形的面积。

思路：求出比第i个矩形大的最左边的矩形的位置 l[i], 及比第i个矩形大的最右边的矩形的位置 r[i], 则第i个矩形的面积 s = (r[i]-l[i]+1)*hign[i]。

如果第i-1个矩形比第i个矩形大，则 l[i] 必定在 l[i-1]的 左边，同理，r[i]必定在 r[i+1]的右边。

 #include <stdio.h>
 #include <string.h>
 #include <algorithm>
 #define LL __int64
 const int N=;
 using namespace std;
 LL high[N],l[N],r[N];
 int main()
 {
     int n;
     while(~scanf("%d",&n)&&n)
     {
         for (int i = ; i <= n; i++)
             scanf("%I64d",&high[i]);
         for (int i = ; i <= n; i++)
         {
             int pos = i;
             while(pos >  && high[pos-] >= high[i])
             {
                 pos = l[pos-];//如果第i个矩形左边的矩形(pos-1)比i高，
                               //则pos移动到l[pos-1](即比第pos-1个矩形高的最左边的矩形的位置)
             }
             l[i] = pos;//l[i]表示比第i个矩形连续高的最左边的矩形位置
         }
         for (int i = n; i >= ; --i)
         {
             int pos = i;
             while(pos < n && high[i] <= high[pos+])
             {
                 pos = r[pos+];
             }
             r[i] = pos;//表示比第i个矩形连续高的最右边的矩形位置
         }
         LL maxn = ;
         for (int i = ; i <= n; i++)
         {
             maxn = max((r[i]-l[i]+)*high[i],maxn);
         }
         printf("%I64d\n",maxn);
     }
     return ;
 }

同类型的题：

http://acm.hdu.edu.cn/showproblem.php?pid=1505

 #include <stdio.h>
 #include <algorithm>
 #include <string.h>
 #define LL __int64
 const int N=;
 using namespace std;
 LL l[N],r[N],high[N];

 LL max_area(int m)
 {
     for (int i = ; i <= m; i++)
     {
         if(i >  && high[i] <= high[i-])
         {
             l[i] = l[i-];
         }
         else
             l[i] = i;
     }
     for (int i = m; i >= ; i--)
     {

         if(i < m && high[i] <= high[i+])
         {
             r[i] = r[i+];
         }
         else
             r[i] = i;
     }
     LL maxn = ;
     for (int i = ; i <= m; i++)
     {
         maxn = max((r[i]-l[i]+)*high[i],maxn);
     }
     return maxn;
 }
 int main()
 {
     int t;
     char s[];
     scanf("%d",&t);
     while(t--)
     {
         int n,m;
         LL ans = ;
         scanf("%d %d",&n,&m);
         memset(high,,sizeof(high));
         for (int i = ; i <= n; i++)
         {
             for (int j = ; j <= m; j++)
             {
                 scanf("%s",s);
                 if (s[]=='F')
                     high[j]++;
                 else
                     high[j] = ;
             }
             ans = max(max_area(m),ans);//第一行到第i行最大的面积
         }
         printf("%I64d\n",ans*);
     }
     return ;
 }