HDOJ4328 Cut the cake

Posted 2020-06-13

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。

  1 /* 4328 */
  2 #include <iostream>
  3 #include <sstream>
  4 #include <string>
  5 #include <map>
  6 #include <queue>
  7 #include <set>
  8 #include <stack>
  9 #include <vector>
 10 #include <deque>
 11 #include <algorithm>
 12 #include <cstdio>
 13 #include <cmath>
 14 #include <ctime>
 15 #include <cstring>
 16 #include <climits>
 17 #include <cctype>
 18 #include <cassert>
 19 #include <functional>
 20 #include <iterator>
 21 #include <iomanip>
 22 using namespace std;
 23 //#pragma comment(linker,"/STACK:102400000,1024000")
 24 
 25 #define sti                set<int>
 26 #define stpii            set<pair<int, int> >
 27 #define mpii            map<int,int>
 28 #define vi                vector<int>
 29 #define pii                pair<int,int>
 30 #define vpii            vector<pair<int,int> >
 31 #define rep(i, a, n)     for (int i=a;i<n;++i)
 32 #define per(i, a, n)     for (int i=n-1;i>=a;--i)
 33 #define clr                clear
 34 #define pb                 push_back
 35 #define mp                 make_pair
 36 #define fir                first
 37 #define sec                second
 38 #define all(x)             (x).begin(),(x).end()
 39 #define SZ(x)             ((int)(x).size())
 40 #define lson            l, mid, rt<<1
 41 #define rson            mid+1, r, rt<<1|1
 42 
 43 const int maxn = 1005;
 44 char s[maxn][maxn];
 45 int a[maxn][maxn];
 46 int L[maxn][maxn], R[maxn][maxn], T[maxn][maxn];
 47 int n, m;
 48 
 49 int calc() {
 50     int ret = 0;
 51     
 52     rep(j, 0, m+1) {
 53         T[0][j] = 0;
 54         L[0][j] = 1;
 55         R[0][j] = m;
 56     }
 57     
 58     rep(i, 1, n+1) {
 59         int l;
 60         l = 0;
 61         rep(j, 1, m+1) {
 62             if (a[i][j] == 1) {
 63                 T[i][j] = T[i-1][j] + 1;
 64                 L[i][j] = max(L[i-1][j], l+1);
 65             } else {
 66                 T[i][j] = 0;
 67                 L[i][j] = 1;
 68                 l = j;
 69             }
 70         }
 71         
 72         int r;
 73         r = m + 1;
 74         per(j, 1, m+1) {
 75             if (a[i][j] == 1) {
 76                 R[i][j] = min(R[i-1][j], r-1);
 77             } else {
 78                 R[i][j] = m;
 79                 r = j;
 80             }
 81         }
 82         
 83         rep(j, 1, m+1) {
 84             if (a[i][j]) {
 85                 int h = T[i][j];
 86                 int w = R[i][j] - L[i][j] + 1;
 87                 ret = max(ret, w+h);
 88             }
 89         }
 90     }
 91     
 92     return ret << 1;
 93 }
 94 
 95 void solve() {
 96     int ans = 0, tmp;
 97     
 98     // blue
 99     rep(i, 1, n+1)
100         rep(j, 1, m+1)
101             a[i][j] = s[i][j] == ‘B‘;
102     tmp = calc();
103     ans = max(ans, tmp);
104     
105     // red
106     rep(i, 1, n+1)
107         rep(j, 1, m+1)
108             a[i][j] = s[i][j] == ‘R‘;
109     tmp = calc();
110     ans = max(ans, tmp);
111     
112     rep(i, 1, n+1) {
113         rep(j, 1, m+1) {
114             if ((i+j) & 1) {
115                 a[i][j] = s[i][j]!=‘R‘;
116             } else {
117                 a[i][j] = s[i][j]==‘R‘;
118             }
119         }
120     }
121     tmp = calc();
122     ans = max(ans, tmp);
123     
124     rep(i, 1, n+1) {
125         rep(j, 1, m+1) {
126             if ((i+j) & 1) {
127                 a[i][j] = s[i][j]==‘R‘;
128             } else {
129                 a[i][j] = s[i][j]!=‘R‘;
130             }
131         }
132     }
133     tmp = calc();
134     ans = max(ans, tmp);
135     
136     printf("%d\n", ans);
137 }
138 
139 int main() {
140     ios::sync_with_stdio(false);
141     #ifndef ONLINE_JUDGE
142         freopen("data.in", "r", stdin);
143         freopen("data.out", "w", stdout);
144     #endif
145     
146     int t;
147     
148     scanf("%d", &t);
149     rep(tt, 1, t+1) {
150         scanf("%d %d", &n, &m);
151         rep(i, 1, n+1)
152             scanf("%s", s[i]+1);
153         printf("Case #%d: ", tt);
154         solve();
155     }
156     
157     #ifndef ONLINE_JUDGE
158         printf("time = %d.\n", (int)clock());
159     #endif
160     
161     return 0;
162 }

数据生成器。

 1 from copy import deepcopy
 2 from random import randint, shuffle
 3 import shutil
 4 import string
 5 
 6 
 7 def GenDataIn():
 8     with open("data.in", "w") as fout:
 9         t = 10
10         bound = 10**18
11         op = "RB"
12         fout.write("%d\n" % (t))
13         for tt in xrange(t):
14             n = randint(100, 1000)
15             m = randint(100, 1000)
16             fout.write("%d %d\n" % (n, m))
17             for i in xrange(n):
18                 line = ""
19                 for j in xrange(m):
20                     idx = randint(0, 1)
21                     line += op[idx]
22                 fout.write("%s\n" % (line))
23             
24                 
25 def MovDataIn():
26     desFileName = "F:\eclipse_prj\workspace\hdoj\data.in"
27     shutil.copyfile("data.in", desFileName)
28 
29     
30 if __name__ == "__main__":
31     GenDataIn()
32     MovDataIn()