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UVA 201 Squares

时间:2019-06-16 17:30:35      阅读:38      评论:0      收藏:0      [点我收藏+]

标签:type   msm   pro   复杂度   暴力   其中   ins   inpu   rst   

题目链接:https://vjudge.net/problem/UVA-201

题目翻译摘自《算法禁赛入门经典》

题目大意

  有 n 行 n 列(2 ≤ n ≤ 9)的小黑点,还有 m 条线段连接其中的一些黑点。统计这些线段连成 了多少个正方形(每种边长分别统计)。 行从上到下编号为 1~n,列从左到右编号为 1~n。边用 H i j 和 V i j 表示,分别代表边 (i, j)-(i, j + 1) 和 (i, j)-(i + 1, j)。

分析

  直接暴力时间复杂度是 O(n4),可以扩充矩阵,然后用前缀和优化到 O(n3)。

代码如下

技术分享图片
  1 #include <bits/stdc++.h>
  2 using namespace std;
  3  
  4 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
  5 #define Rep(i,n) for (int i = 0; i < (n); ++i)
  6 #define For(i,s,t) for (int i = (s); i <= (t); ++i)
  7 #define rFor(i,t,s) for (int i = (t); i >= (s); --i)
  8 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
  9 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
 10 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
 11 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 12  
 13 #define pr(x) cout << #x << " = " << x << "  "
 14 #define prln(x) cout << #x << " = " << x << endl
 15  
 16 #define LOWBIT(x) ((x)&(-x))
 17  
 18 #define ALL(x) x.begin(),x.end()
 19 #define INS(x) inserter(x,x.begin())
 20  
 21 #define ms0(a) memset(a,0,sizeof(a))
 22 #define msI(a) memset(a,inf,sizeof(a))
 23 #define msM(a) memset(a,-1,sizeof(a))
 24 
 25 #define MP make_pair
 26 #define PB push_back
 27 #define ft first
 28 #define sd second
 29  
 30 template<typename T1, typename T2>
 31 istream &operator>>(istream &in, pair<T1, T2> &p) {
 32     in >> p.first >> p.second;
 33     return in;
 34 }
 35  
 36 template<typename T>
 37 istream &operator>>(istream &in, vector<T> &v) {
 38     for (auto &x: v)
 39         in >> x;
 40     return in;
 41 }
 42  
 43 template<typename T1, typename T2>
 44 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
 45     out << "[" << p.first << ", " << p.second << "]" << "\n";
 46     return out;
 47 }
 48 
 49 inline int gc(){
 50     static const int BUF = 1e7;
 51     static char buf[BUF], *bg = buf + BUF, *ed = bg;
 52     
 53     if(bg == ed) fread(bg = buf, 1, BUF, stdin);
 54     return *bg++;
 55 } 
 56 
 57 inline int ri(){
 58     int x = 0, f = 1, c = gc();
 59     for(; c<48||c>57; f = c==-?-1:f, c=gc());
 60     for(; c>47&&c<58; x = x*10 + c - 48, c=gc());
 61     return x*f;
 62 }
 63 
 64 template<class T>
 65 inline string toString(T x) {
 66     ostringstream sout;
 67     sout << x;
 68     return sout.str();
 69 }
 70  
 71 typedef long long LL;
 72 typedef unsigned long long uLL;
 73 typedef pair< double, double > PDD;
 74 typedef pair< int, int > PII;
 75 typedef pair< int, PII > PIPII;
 76 typedef pair< string, int > PSI;
 77 typedef pair< int, PSI > PIPSI;
 78 typedef set< int > SI;
 79 typedef set< PII > SPII;
 80 typedef vector< int > VI;
 81 typedef vector< VI > VVI;
 82 typedef vector< PII > VPII;
 83 typedef map< int, int > MII;
 84 typedef map< int, string > MIS;
 85 typedef map< int, PII > MIPII;
 86 typedef map< PII, int > MPIII;
 87 typedef map< string, int > MSI;
 88 typedef map< string, string > MSS;
 89 typedef map< PII, string > MPIIS;
 90 typedef map< PII, PII > MPIIPII;
 91 typedef multimap< int, int > MMII;
 92 typedef multimap< string, int > MMSI;
 93 //typedef unordered_map< int, int > uMII;
 94 typedef pair< LL, LL > PLL;
 95 typedef vector< LL > VL;
 96 typedef vector< VL > VVL;
 97 typedef priority_queue< int > PQIMax;
 98 typedef priority_queue< int, VI, greater< int > > PQIMin;
 99 const double EPS = 1e-6;
100 const LL inf = 0x7fffffff;
101 const LL infLL = 0x7fffffffffffffffLL;
102 const LL mod = 1e9 + 7;
103 const int maxN = 1e4 + 7;
104 const LL ONE = 1;
105 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
106 const LL oddBits = 0x5555555555555555;
107 
108 int T, n, m; 
109 int A[23][23], rowPreSum[23][23], colPreSum[23][23];
110 MII sqr; // size->cnt
111 
112 int main(){
113     //freopen("MyOutput.txt","w",stdout);
114     //freopen("input.txt","r",stdin);
115     //INIT();
116     while(cin >> n >> m) {
117         ms0(A);
118         ms0(rowPreSum);
119         ms0(colPreSum);
120         sqr.clear();
121         n = 2 * n - 1;
122         Rep(i, m) {
123             string str;
124             int x, y;
125             cin >> str >> x >> y;
126             x = 2 * x - 1;
127             y = 2 * y - 1;
128             if(str == "H") For(j, y, y + 2) A[x][j] = 1;
129             else For(j, y, y + 2) A[j][x] = 1;
130         }
131         // 计算矩阵的行列前缀和 
132         For(i, 1, n) {
133             For(j, 1, n) {
134                 rowPreSum[i][j] += rowPreSum[i][j - 1] + A[i][j];
135                 colPreSum[i][j] += colPreSum[i][j - 1] + A[j][i];
136             }
137         }
138         
139         // 枚举所有正方形对角点对 
140         For(i, 1, n) {
141             For(j, 1, n) {
142                 For(k, 2, n) {
143                     if(i + k > n || j + k > n) break;
144                     if(rowPreSum[i][j + k] - rowPreSum[i][j - 1] == k + 1 &&
145                         rowPreSum[i][j + k] - rowPreSum[i][j - 1] == colPreSum[j][i + k] - colPreSum[j][i - 1] &&
146                         colPreSum[j][i + k] - colPreSum[j][i - 1] == rowPreSum[i + k][j + k] - rowPreSum[i + k][j - 1] &&
147                         rowPreSum[i + k][j + k] - rowPreSum[i + k][j - 1] == colPreSum[j + k][i + k] - colPreSum[j + k][i - 1]
148                         ) ++sqr[(k + 1) / 2];
149                 }
150             }
151         }
152         
153         if(T++) printf("\n**********************************\n\n");
154         printf("Problem #%d\n\n", T);
155         if(sqr.empty()) printf("No completed squares can be found.\n");
156         else foreach(i, sqr) printf("%d square (s) of size %d\n", i->sd, i->ft);
157     }
158     return 0;
159 }
View Code

 

UVA 201 Squares

标签:type   msm   pro   复杂度   暴力   其中   ins   inpu   rst   

原文:https://www.cnblogs.com/zaq19970105/p/11032093.html

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