Uva 10074【遞推dp】
阿新 • • 發佈：2017-08-21
idt lose str img ide mil -- msu nbsp 
UVa 10074
題意:求01矩陣的最大子0矩陣。
http://www.csie.ntnu.edu.tw/~u91029/MaximumSubarray.html#2
這裏說的很清楚。先求Largest Empty Interval,枚舉每個點為矩形的右下角。
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 using namespace std; 6 const int MAXN = 107; 7 int Map[MAXN][MAXN], width[MAXN][MAXN];8 int row, col; 9 10 int main() 11 { 12 while (cin>>row>>col&&!(row==0&&col==0)) 13 { 14 int ans = 0; 15 for(int i=1;i<=row;i++) 16 for (int j = 1; j <= col; j++) { 17 cin >> Map[i][j]; 18 if (Map[i][j]) width[i][j] = 0; 19 else width[i][j] = width[i][j - 1] + 1; 20 } 21 for (int i = 1; i <= row; i++) 22 { 23 for (int j = 1; j <= col; j++) { 24 int w = 1e9; 25 for (int h = 1; i - h + 1 > 0; h++) { 26 if(Map[i][j]) break; 27 w = min(w, width[i - h + 1][j]); 28 ans = max(ans, w*h); 29 } 30 } 31 } 32 cout << ans << endl; 33 } 34 return 0; 35 }
按照下一個更高效的算法寫，不知道為什麽會WA，可能是哪裏有問題。。。
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 using namespace std; 6 const int MAXN = 107; 7 int Map[MAXN][MAXN]; 8 int wl[MAXN], wr[MAXN]; 9 int h[MAXN], l[MAXN], r[MAXN]; 10 int row, col; 11 12 int main() 13 { 14 while (scanf("%d%d", &row, &col) == 2, !(row == 0 && col == 0)) 15 { 16 int ans = 0; 17 for (int i = 1; i <= row; i++) 18 for (int j = 1; j <= col; j++) 19 scanf("%d", &Map[i][j]); 20 for (int i = 1; i <= row; i++) 21 { 22 for (int j = 1; j <= col; j++) 23 if (Map[i][j]) wl[j] = 0; 24 else wl[j] = wl[j - 1] + 1; 25 26 for (int j = col; j >= 1; j--) 27 if (Map[i][j]) wr[j] = 0; 28 else wr[j] = wr[j + 1] + 1; 29 30 for (int j = 1; j <= row; j++) 31 if (Map[i][j]) h[j] = 0; 32 else h[j] = h[j] + 1; 33 34 for (int j = 1; j <= col; j++) 35 if (r[j] == 0) r[j] = wr[j]; 36 else r[j] = min(wr[j], r[j]); 37 38 for (int j = 1; j <= col; j++) 39 if (l[j] == 0) l[j] = wl[j]; 40 else l[j] = min(wl[j], l[j]); 41 42 for (int j = 1; j <= col; j++) 43 ans = max(ans, (l[j] + r[j] - 1)*h[j]); 44 } 45 printf("%d\n", ans); 46 } 47 return 0; 48 }WA1
最高效的按照棧那種方式寫也是WA。。。。。
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 #include<stack> 6 using namespace std; 7 const int MAXN = 107; 8 int a[MAXN][MAXN], h[MAXN][MAXN]; 9 int col, row; 10 11 int main() 12 { 13 while (cin >> row >> col) 14 { 15 if (!col && !row) break; 16 for (int i = 1; i <= row; i++) 17 for (int j = 1; j <= col; j++) 18 cin >> a[i][j]; 19 memset(h, 0, sizeof(h)); 20 for (int i = 1; i <= row; i++) 21 for (int j = 1; j <= col; j++) 22 if (a[i][j]) h[i][j] = 0; 23 else h[i][j] = h[i - 1][j] + 1; 24 25 stack<int> st; 26 int area; 27 int mx = 0; 28 for (int i = 1; i <= row; i++) 29 { 30 int j; 31 for (j = 1; j <= col;) { 32 if (st.empty() || h[i][st.top()] <= h[i][j]) 33 st.push(j++); 34 else { 35 int top = st.top(); 36 st.pop(); 37 if (st.empty()) 38 area = h[i][top] * j; 39 else 40 area = h[i][top] * (j - st.top() - 1); 41 mx = max(mx, area); 42 } 43 } 44 while (!st.empty()) 45 { 46 int top = st.top(); 47 st.pop(); 48 if (st.empty()) area = h[i][top] * j; 49 else 50 area = h[i][top] * (j - st.top() - 1); 51 mx = max(mx, area); 52 } 53 } 54 cout << mx << endl; 55 } 56 return 0; 57 }WA2
Uva 10074【遞推dp】