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  • SRM 408(1-250pt, 1-500pt)

    DIV1 250pt

    题意：每天晚上需要点蜡烛，且每晚蜡烛燃烧1cm，第i天晚上需要点i根蜡烛。第一天白天的时候，拥有一些蜡烛，用vector<int>can表示他们的长度，问最多能烧几个晚上。

    解法：模拟+贪心，每次烧长度最长的k支蜡烛即可。

    tag:simulation, greedy

      1 // BEGIN CUT HERE
  2 /*
  3  * Author:  plum rain
  4  * score :
  5  */
  6 /*
  7 
  8  */
  9 // END CUT HERE
 10 #line 11 "OlympicCandles.cpp"
 11 #include <sstream>
 12 #include <stdexcept>
 13 #include <functional>
 14 #include <iomanip>
 15 #include <numeric>
 16 #include <fstream>
 17 #include <cctype>
 18 #include <iostream>
 19 #include <cstdio>
 20 #include <vector>
 21 #include <cstring>
 22 #include <cmath>
 23 #include <algorithm>
 24 #include <cstdlib>
 25 #include <set>
 26 #include <queue>
 27 #include <bitset>
 28 #include <list>
 29 #include <string>
 30 #include <utility>
 31 #include <map>
 32 #include <ctime>
 33 #include <stack>
 34 
 35 using namespace std;
 36 
 37 #define clr0(x) memset(x, 0, sizeof(x))
 38 #define clr1(x) memset(x, -1, sizeof(x))
 39 #define pb push_back
 40 #define sz(v) ((int)(v).size())
 41 #define all(t) t.begin(),t.end()
 42 #define zero(x) (((x)>0?(x):-(x))<eps)
 43 #define out(x) cout<<#x<<":"<<(x)<<endl
 44 #define tst(a) cout<<a<<" "
 45 #define tst1(a) cout<<#a<<endl
 46 #define CINBEQUICKER std::ios::sync_with_stdio(false)
 47 
 48 typedef vector<int> vi;
 49 typedef vector<string> vs;
 50 typedef vector<double> vd;
 51 typedef pair<int, int> pii;
 52 typedef long long int64;
 53 
 54 const double eps = 1e-8;
 55 const double PI = atan(1.0)*4;
 56 const int inf = 2139062143 / 2;
 57 
 58 bool cmp(int a, int b)
 59 {
 60     return a > b;
 61 }
 62 
 63 class OlympicCandles
 64 {
 65     public:
 66         int numberOfNights(vector <int> can){
 67             int ans = 1;
 68             while (ans <= 55){
 69                 if (ans > sz(can)) return sz(can);
 70                 sort(all(can), cmp);
 71                 for (int i = 0; i < ans; ++ i){
 72                     if (can[i]) can[i] --;
 73                     else return ans - 1;
 74                 }
 75                 ++ ans;
 76             }
 77             return ans;
 78         }
 79         
 80 // BEGIN CUT HERE
 81     public:
 82     void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); if ((Case == -1) || (Case == 4)) test_case_4(); }
 83     private:
 84     template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '"' << *iter << "","; os << " }"; return os.str(); }
 85     void verify_case(int Case, const int &Expected, const int &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "	Expected: "" << Expected << '"' << endl; cerr << "	Received: "" << Received << '"' << endl; } }
 86     void test_case_0() { int Arr0[] = {2, 2, 2}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 3; verify_case(0, Arg1, numberOfNights(Arg0)); }
 87     void test_case_1() { int Arr0[] = {2, 2, 2, 4}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 4; verify_case(1, Arg1, numberOfNights(Arg0)); }
 88     void test_case_2() { int Arr0[] = {5, 2, 2, 1}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 3; verify_case(2, Arg1, numberOfNights(Arg0)); }
 89     void test_case_3() { int Arr0[] = {1, 2, 3, 4, 5, 6}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 6; verify_case(3, Arg1, numberOfNights(Arg0)); }
 90     void test_case_4() { int Arr0[] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 4; verify_case(4, Arg1, numberOfNights(Arg0)); }
 91 
 92 // END CUT HERE
 93 
 94 };
 95 
 96 // BEGIN CUT HERE
 97 int main()
 98 {
 99 //    freopen( "a.out" , "w" , stdout );    
100     OlympicCandles ___test;
101     ___test.run_test(-1);
102        return 0;
103 }
104 // END CUT HERE
    View Code

    DIV1 500pt

    题意：做一个游戏，在一个无向图上，每个点上有一些糖果，每次可以选择任意一个糖果数大等于2的点i，拿出其中两个糖果，吃掉一个，将剩下的一个放在i点的一个相邻点上。初始时，每个点上有一些糖果，有一个特定点k，要求无论如何操作，都不能使k点出现有且仅有一个糖果的情况，问初始时图上最多有多少个糖果。如果可以有多余2*10^9个糖果，直接输出-1。

    解法：首先，若图不联通，则可以放无数糖果，输出-1。

    　　　考虑末态，要使糖果数量最多，末态肯定为除了k点，每个点一个糖果。考虑末态向初态转移。将无向图转化成以k点为根的树，则每个父亲节点的1个糖果可以有它的某个子节点的两个糖果变出来，所以，应该尽量将所有糖果都放在非叶子节点。下面考虑，从树的顶端把所有糖果放回底端，即是考虑这个游戏的逆过程。

    　　　如果某个父亲节点仅有一个子节点，直接将父亲节点的k个糖果变为子节点的2*k个糖果即可。若父亲节点有多个子节点，有两种处理方式，父亲节点的k个糖果均由一个某一个子节点转移得到，或者由多个子节点转移得到。显然，前者更优。那么，要选择哪个子节点呢？子树深度最深的那个自己子节点。

    　　　至此，问题得到完整解决。这是一道想法非常自然，而且所用结论均为简单贪心的题，稍微想一下即可明白。

    tag:greedy, tree

      1 // BEGIN CUT HERE
  2 /*
  3  * Author:  plum rain
  4  * score :
  5  */
  6 /*
  7 
  8  */
  9 // END CUT HERE
 10 #line 11 "CandyGame.cpp"
 11 #include <sstream>
 12 #include <stdexcept>
 13 #include <functional>
 14 #include <iomanip>
 15 #include <numeric>
 16 #include <fstream>
 17 #include <cctype>
 18 #include <iostream>
 19 #include <cstdio>
 20 #include <vector>
 21 #include <cstring>
 22 #include <cmath>
 23 #include <algorithm>
 24 #include <cstdlib>
 25 #include <set>
 26 #include <queue>
 27 #include <bitset>
 28 #include <list>
 29 #include <string>
 30 #include <utility>
 31 #include <map>
 32 #include <ctime>
 33 #include <stack>
 34 
 35 using namespace std;
 36 
 37 #define clr0(x) memset(x, 0, sizeof(x))
 38 #define clr1(x) memset(x, -1, sizeof(x))
 39 #define pb push_back
 40 #define sz(v) ((int)(v).size())
 41 #define all(t) t.begin(),t.end()
 42 #define zero(x) (((x)>0?(x):-(x))<eps)
 43 #define out(x) cout<<#x<<":"<<(x)<<endl
 44 #define tst(a) cout<<a<<" "
 45 #define tst1(a) cout<<#a<<endl
 46 #define CINBEQUICKER std::ios::sync_with_stdio(false)
 47 
 48 typedef vector<int> vi;
 49 typedef vector<string> vs;
 50 typedef vector<double> vd;
 51 typedef pair<int, int> pii;
 52 typedef long long int64;
 53 
 54 const double eps = 1e-8;
 55 const double PI = atan(1.0)*4;
 56 const int inf = 2139062143 / 2;
 57 const int maxx = 2000000000; 
 58 
 59 class CandyGame
 60 {
 61     public:
 62         vs g;
 63         int64 ans;
 64         vi son[100];
 65         int64 an[100];
 66         int len[100];
 67         bool v[100];
 68 
 69         void dfs (int tar)
 70         {
 71             len[tar] = 0; v[tar] = 1;
 72             for (int i = 0; i < sz(g); ++ i) 
 73                 if (g[i][tar] == 'Y' && !v[i]){
 74                     son[tar].pb (i);
 75                     dfs (i); 
 76                     len[tar] = max(len[tar], len[i]);
 77                 }
 78             ++ len[tar];
 79         }
 80 
 81         void gao(int tar, int64 num)
 82         {
 83             bool ok = 0;
 84             an[tar] = num > maxx ? -1 : num;
 85             for (int i = 0; i < sz(son[tar]); ++ i){
 86                 if (ok || len[son[tar][i]]+1 != len[tar])
 87                     gao (son[tar][i], 1);
 88                 else
 89                     ok = 1, gao (son[tar][i], 2*num>1 ? 2*num : 1);
 90 
 91                 if (an[tar] != -1){
 92                     if(an[son[tar][i]] == -1) an[tar] = -1;
 93                     else an[tar] += an[son[tar][i]];
 94 
 95                     if (an[tar] > maxx) an[tar] = -1;
 96                 }
 97             }
 98         }
 99          
100         int maximumCandy(vector <string> G, int tar){
101             g = G;
102             clr0 (v);
103             for (int i = 0; i < sz(g); ++ i) son[i].clear();
104             dfs (tar);
105             for (int i = 0; i < sz(g); ++ i) if (!v[i]) return -1;
106             if (sz(g) == 2) return 2;
107             if (sz(g) == 1) return 0;
108             gao(tar, 0);
109             return an[tar];
110         }
111         
112 // BEGIN CUT HERE
113     public:
114     void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); if ((Case == -1) || (Case == 4)) test_case_4(); if ((Case == -1) || (Case == 5)) test_case_5(); }
115     //void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_1();}
116     private:
117     template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '"' << *iter << "","; os << " }"; return os.str(); }
118     void verify_case(int Case, const int &Expected, const int &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "	Expected: "" << Expected << '"' << endl; cerr << "	Received: "" << Received << '"' << endl; } }
119     void test_case_0() { string Arr0[] = {"NYN", "YNY", "NYN"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 1; int Arg2 = 2; verify_case(0, Arg2, maximumCandy(Arg0, Arg1)); }
120     void test_case_1() { string Arr0[] = {"NYN", "YNY", "NYN"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 2; int Arg2 = 3; verify_case(1, Arg2, maximumCandy(Arg0, Arg1)); }
121     void test_case_2() { string Arr0[] = {"NYYY", "YNNN", "YNNN", "YNNN"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 0; int Arg2 = 3; verify_case(2, Arg2, maximumCandy(Arg0, Arg1)); }
122     void test_case_3() { string Arr0[] = {"NYYY", "YNNN", "YNNN", "YNNN"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 1; int Arg2 = 4; verify_case(3, Arg2, maximumCandy(Arg0, Arg1)); }
123     void test_case_4() { string Arr0[] = {"NYNNNYN",
124  "YNYNYNN",
125  "NYNYNNN",
126  "NNYNNNN",
127  "NYNNNNN",
128  "YNNNNNY",
129  "NNNNNYN"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 0; int Arg2 = 11; verify_case(4, Arg2, maximumCandy(Arg0, Arg1)); }
130     void test_case_5() { string Arr0[] = {"NYNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN",
131  "YNYNNNNNNNNNNNNNNNNNNNNNNNNNNNNN",
132  "NYNYNNNNNNNNNNNNNNNNNNNNNNNNNNNN",
133  "NNYNYNNNNNNNNNNNNNNNNNNNNNNNNNNN",
134  "NNNYNYNNNNNNNNNNNNNNNNNNNNNNNNNN",
135  "NNNNYNYNNNNNNNNNNNNNNNNNNNNNNNNN",
136  "NNNNNYNYNNNNNNNNNNNNNNNNNNNNNNNN",
137  "NNNNNNYNYNNNNNNNNNNNNNNNNNNNNNNN",
138  "NNNNNNNYNYNNNNNNNNNNNNNNNNNNNNNN",
139  "NNNNNNNNYNYNNNNNNNNNNNNNNNNNNNNN",
140  "NNNNNNNNNYNYNNNNNNNNNNNNNNNNNNNN",
141  "NNNNNNNNNNYNYNNNNNNNNNNNNNNNNNNN",
142  "NNNNNNNNNNNYNYNNNNNNNNNNNNNNNNNN",
143  "NNNNNNNNNNNNYNYNNNNNNNNNNNNNNNNN",
144  "NNNNNNNNNNNNNYNYNNNNNNNNNNNNNNNN",
145  "NNNNNNNNNNNNNNYNYNNNNNNNNNNNNNNN",
146  "NNNNNNNNNNNNNNNYNYNNNNNNNNNNNNNN",
147  "NNNNNNNNNNNNNNNNYNYNNNNNNNNNNNNN",
148  "NNNNNNNNNNNNNNNNNYNYNNNNNNNNNNNN",
149  "NNNNNNNNNNNNNNNNNNYNYNNNNNNNNNNN",
150  "NNNNNNNNNNNNNNNNNNNYNYNNNNNNNNNN",
151  "NNNNNNNNNNNNNNNNNNNNYNYNNNNNNNNN",
152  "NNNNNNNNNNNNNNNNNNNNNYNYNNNNNNNN",
153  "NNNNNNNNNNNNNNNNNNNNNNYNYNNNNNNN",
154  "NNNNNNNNNNNNNNNNNNNNNNNYNYNNNNNN",
155  "NNNNNNNNNNNNNNNNNNNNNNNNYNYNNNNN",
156  "NNNNNNNNNNNNNNNNNNNNNNNNNYNYNNNN",
157  "NNNNNNNNNNNNNNNNNNNNNNNNNNYNYNNN",
158  "NNNNNNNNNNNNNNNNNNNNNNNNNNNYNYNN",
159  "NNNNNNNNNNNNNNNNNNNNNNNNNNNNYNYN",
160  "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNYNY",
161  "NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNYN"}; vector <string> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arg1 = 0; int Arg2 = -1; verify_case(5, Arg2, maximumCandy(Arg0, Arg1)); }
162 
163 // END CUT HERE
164 
165 };
166 
167 // BEGIN CUT HERE
168 int main()
169 {
170     //freopen( "a.out" , "w" , stdout );    
171     CandyGame ___test;
172     ___test.run_test(-1);
173        return 0;
174 }
175 // END CUT HERE
    View Code
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  • 原文地址：https://www.cnblogs.com/plumrain/p/srm_408.html
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