【HDOJ】4328 Cut the cake

将原问题转化为求完全由1组成的最大子矩阵。
挺经典的通过dp将n^3转化为n^2。

 /* 4328 */
 #include <iostream>
 #include <sstream>
 #include <string>
 #include <map>
 #include <queue>
 #include <set>
 #include <stack>
 #include <vector>
 #include <deque>
 #include <algorithm>
 #include <cstdio>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <climits>
 #include <cctype>
 #include <cassert>
 #include <functional>
 #include <iterator>
 #include <iomanip>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,1024000")

 #define sti                set<int>
 #define stpii            set<pair<int, int> >
 #define mpii            map<int,int>
 #define vi                vector<int>
 #define pii                pair<int,int>
 #define vpii            vector<pair<int,int> >
 #define rep(i, a, n)     for (int i=a;i<n;++i)
 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 #define clr                clear
 #define pb                 push_back
 #define mp                 make_pair
 #define fir                first
 #define sec                second
 #define all(x)             (x).begin(),(x).end()
 #define SZ(x)             ((int)(x).size())
 #define lson            l, mid, rt<<1
 #define rson            mid+1, r, rt<<1|1

 const int maxn = ;
 char s[maxn][maxn];
 int a[maxn][maxn];
 int L[maxn][maxn], R[maxn][maxn], T[maxn][maxn];
 int n, m;

 int calc() {
     int ret = ;

     rep(j, , m+) {
         T[][j] = ;
         L[][j] = ;
         R[][j] = m;
     }

     rep(i, , n+) {
         int l;
         l = ;
         rep(j, , m+) {
             if (a[i][j] == ) {
                 T[i][j] = T[i-][j] + ;
                 L[i][j] = max(L[i-][j], l+);
             } else {
                 T[i][j] = ;
                 L[i][j] = ;
                 l = j;
             }
         }

         int r;
         r = m + ;
         per(j, , m+) {
             if (a[i][j] == ) {
                 R[i][j] = min(R[i-][j], r-);
             } else {
                 R[i][j] = m;
                 r = j;
             }
         }

         rep(j, , m+) {
             if (a[i][j]) {
                 int h = T[i][j];
                 int w = R[i][j] - L[i][j] + ;
                 ret = max(ret, w+h);
             }
         }
     }

     return ret << ;
 }

 void solve() {
     int ans = , tmp;

     // blue
     rep(i, , n+)
         rep(j, , m+)
             a[i][j] = s[i][j] == 'B';
     tmp = calc();
     ans = max(ans, tmp);

     // red
     rep(i, , n+)
         rep(j, , m+)
             a[i][j] = s[i][j] == 'R';
     tmp = calc();
     ans = max(ans, tmp);

     rep(i, , n+) {
         rep(j, , m+) {
             if ((i+j) & ) {
                 a[i][j] = s[i][j]!='R';
             } else {
                 a[i][j] = s[i][j]=='R';
             }
         }
     }
     tmp = calc();
     ans = max(ans, tmp);

     rep(i, , n+) {
         rep(j, , m+) {
             if ((i+j) & ) {
                 a[i][j] = s[i][j]=='R';
             } else {
                 a[i][j] = s[i][j]!='R';
             }
         }
     }
     tmp = calc();
     ans = max(ans, tmp);

     printf("%d\n", ans);
 }

 int main() {
     ios::sync_with_stdio(false);
     #ifndef ONLINE_JUDGE
         freopen("data.in", "r", stdin);
         freopen("data.out", "w", stdout);
     #endif

     int t;

     scanf("%d", &t);
     rep(tt, , t+) {
         scanf("%d %d", &n, &m);
         rep(i, , n+)
             scanf("%s", s[i]+);
         printf("Case #%d: ", tt);
         solve();
     }

     #ifndef ONLINE_JUDGE
         printf("time = %d.\n", (int)clock());
     #endif

     return ;
 }

数据生成器。

 from copy import deepcopy
 from random import randint, shuffle
 import shutil
 import string

 def GenDataIn():
     with open("data.in", "w") as fout:
         t = 10
         bound = 10**18
         op = "RB"
         fout.write("%d\n" % (t))
         for tt in xrange(t):
             n = randint(100, 1000)
             m = randint(100, 1000)
             fout.write("%d %d\n" % (n, m))
             for i in xrange(n):
                 line = ""
                 for j in xrange(m):
                     idx = randint(0, 1)
                     line += op[idx]
                 fout.write("%s\n" % (line))

 def MovDataIn():
     desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
     shutil.copyfile("data.in", desFileName)

 if __name__ == "__main__":
     GenDataIn()
     MovDataIn()