Uva 10074【递推dp】

UVa 10074

题意:求01矩阵的最大子0矩阵。

http://www.csie.ntnu.edu.tw/~u91029/MaximumSubarray.html#2

这里说的很清楚。先求Largest Empty Interval,枚举每个点为矩形的右下角。

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 using namespace std;
 const int MAXN = ;
 int Map[MAXN][MAXN], width[MAXN][MAXN];
 int row, col;

 int main()
 {
     while (cin>>row>>col&&!(row==&&col==))
     {
         int ans = ;
         for(int i=;i<=row;i++)
             for (int j = ; j <= col; j++) {
                 cin >> Map[i][j];
                 if (Map[i][j]) width[i][j] = ;
                 else width[i][j] = width[i][j - ] + ;
             }
         for (int i = ; i <= row; i++)
         {
             for (int j = ; j <= col; j++) {
                 int w = 1e9;
                 for (int h = ; i - h +  > ; h++) {
                     if (Map[i][j]) break;
                     w = min(w, width[i - h + ][j]);
                     ans = max(ans, w*h);
                 }
             }
         }
         cout << ans << endl;
     }
     return ;
 }

按照下一个更高效的算法写，不知道为什么会WA，可能是哪里有问题。。。

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 using namespace std;
 const int MAXN = ;
 int Map[MAXN][MAXN];
 int wl[MAXN], wr[MAXN];
 int h[MAXN], l[MAXN], r[MAXN];
 int row, col;

 int main()
 {
     while (scanf("%d%d", &row, &col) == , !(row ==  && col == ))
     {
         int ans = ;
         for (int i = ; i <= row; i++)
             for (int j = ; j <= col; j++)
                 scanf("%d", &Map[i][j]);
         for (int i = ; i <= row; i++)
         {
             for (int j = ; j <= col; j++)
                 if (Map[i][j]) wl[j] = ;
             else wl[j] = wl[j - ] + ;

             for (int j = col; j >= ; j--)
                 if (Map[i][j]) wr[j] = ;
             else wr[j] = wr[j + ] + ;

             for (int j = ; j <= row; j++)
                 if (Map[i][j]) h[j] = ;
             else h[j] = h[j] + ;

             for (int j = ; j <= col; j++)
                 if (r[j] == ) r[j] = wr[j];
             else r[j] = min(wr[j], r[j]);

             for (int j = ; j <= col; j++)
                 if (l[j] == ) l[j] = wl[j];
             else l[j] = min(wl[j], l[j]);

             for (int j = ; j <= col; j++)
                         ans = max(ans, (l[j] + r[j] - )*h[j]);
         }
         printf("%d\n", ans);
     }
     return ;
 }

WA1

最高效的按照栈那种方式写也是WA。。。。。

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<stack>
 using namespace std;
 const int MAXN = ;
 int a[MAXN][MAXN], h[MAXN][MAXN];
 int col, row;

 int main()
 {
     while (cin >> row >> col)
     {
         if (!col && !row) break;
         for (int i = ; i <= row; i++)
             for (int j = ; j <= col; j++)
                 cin >> a[i][j];
         memset(h, , sizeof(h));
         for (int i = ; i <= row; i++)
             for (int j = ; j <= col; j++)
                 if (a[i][j]) h[i][j] = ;
                 else h[i][j] = h[i - ][j] + ;

                 stack<int> st;
                 int area;
                 int mx = ;
                 for (int i = ; i <= row; i++)
                 {
                     int j;
                     for (j = ; j <= col;) {
                         if (st.empty() || h[i][st.top()] <= h[i][j])
                             st.push(j++);
                         else {
                             int top = st.top();
                             st.pop();
                             if (st.empty())
                                 area = h[i][top] * j;
                             else
                                 area = h[i][top] * (j - st.top() - );
                             mx = max(mx, area);
                         }
                     }
                     while (!st.empty())
                     {
                         int top = st.top();
                         st.pop();
                         if (st.empty()) area = h[i][top] * j;
                         else
                             area = h[i][top] * (j - st.top() - );
                         mx = max(mx, area);
                     }
                 }
                 cout << mx << endl;
     }
     return ;
 }

WA2