topcoder SRM712 Div1 LR
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题目:
Problem Statement |
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We have a cyclic array A of length n. For each valid i, element i-1 the left neighbor of element i. Additionally, element n-1 is the left neighbor of element 0. You are given two vector<long long>s s and t, each with n elements. Currently, we have A[i] = s[i] for each valid i. Our goal is to have A[i] = t[i] for each valid i. We can use two operations that modify the contents of A:
If there is no way to reach the desired goal state, return "No solution". Otherwise return any valid way of doing so by using at most 100 operations. More precisely, return one valid sequence of operations encoded as a string of ‘L‘s and ‘R‘s. If there are multiple valid solutions, you may return any of them. In particular, you are not required to find the shortest valid solution. Any valid solution will be accepted as long as its length does not exceed 100. We can prove that if there is an valid solution then there must exist one with length at most 100. |
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Definition |
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Limits |
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Constraints |
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- | s will contain between 2 and 50 elements, inclusive. | ||||||||||||
- | s and t will contain the same number of elements. | ||||||||||||
- | Each element in s will be between 0 and 1,000,000,000,000,000 (10^15) inclusive. | ||||||||||||
- | Each element in t will be between 0 and 1,000,000,000,000,000 (10^15) inclusive. | ||||||||||||
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This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2003, TopCoder, Inc. All rights reserved.
思路:因为这是一个圆形数列,所以L和R所得的数列是差不多的,只是左移右移一次的区别。
所以先判断进行sum次操作(通过数列值的和判断)。
然后先进行sum次L操作,再判断把进行sum次操作后的数列k次右平移后能否得到t数列。
能到得到的话则是进行了k次R,sum-k次L操作,LR的先后顺序没有关系。
1 // BEGIN CUT HERE
2
3 #include <conio.h>
4 #include <sstream>
5 /*
6 */
7 #define debuging
8 #ifdef debuging
9 #define FIN {freopen("new.in" , "r" , stdin) ;}
10 #define FOUT {freopen("new.out" , "w" , stdout) ;}
11 #define OUT(x) {cout<< #x << " : " << x <<endl ;}
12 #define ERR(x) {cout<<"#error: "<< x ; while(1) ;}
13 #endif
14 // END CUT HERE
15 #include <bits/stdc++.h>
16
17 using namespace std;
18
19 #define MP make_pair
20 #define PB push_back
21 typedef long long LL;
22 typedef pair<int,int> PII;
23 const double eps=1e-8;
24 const double pi=acos(-1.0);
25 const int K=1e6+7;
26 const int mod=1e9+7;
27
28
29 class LR
30 {
31 public:
32 string construct(vector<long long> s, vector<long long> t)
33 {
34 int cnt=101;
35 LL suma=0,sumb=0,sum=1;
36 string ans;
37 for(int i=0; i<s.size(); i++)
38 suma+=s[i],sumb+=t[i];
39 if(suma==sumb) sum=0;
40 for(int i=1; i<=100&∑ i++)
41 if((suma*=2) == sumb)
42 {
43 sum=i;
44 break;
45 }
46 if(suma!=sumb)
47 return "No solution";
48 for(LL i=0,n=s.size(); i<sum; i++)
49 for(LL j=0,ls=s[n-1],tmp; j<n; j++)
50 tmp=s[j],s[j]+=ls,ls=tmp;
51 for(int i=0; i<=sum; i++)
52 {
53 if(s==t)
54 {
55 cnt=i;break;
56 }
57 s.insert(s.begin(),s[s.size()-1]);
58 s.erase(--s.end());
59 }
60 if(cnt>sum)
61 return "No solution";
62 if(sum==0)
63 return "";
64 for(int i=0; i<cnt; i++)
65 ans+="R";
66 for(int i=cnt; i<sum; i++)
67 ans+="L";
68 return ans;
69 }
70
71
72 // BEGIN CUT HERE
73 public:
74 void run_test(int Case)
75 {
76 if ((Case == -1) || (Case == 0)) test_case_0();
77 if ((Case == -1) || (Case == 1)) test_case_1();
78 if ((Case == -1) || (Case == 2)) test_case_2();
79 if ((Case == -1) || (Case == 3)) test_case_3();
80 if ((Case == -1) || (Case == 4)) test_case_4();
81 if ((Case == -1) || (Case == 5)) test_case_5();
82 if ((Case == -1) || (Case == 6)) test_case_6();
83 }
84 private:
85 template <typename T> string print_array(const vector<T> &V)
86 {
87 ostringstream os;
88 os << "{ ";
89 for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << ‘\"‘ << *iter << "\",";
90 os << " }";
91 return os.str();
92 }
93 void verify_case(int Case, const string &Expected, const string &Received)
94 {
95 cerr << "Test Case #" << Case << "...";
96 if (Expected == Received) cerr << "PASSED" << endl;
97 else
98 {
99 cerr << "FAILED" << endl;
100 cerr << "\tExpected: \"" << Expected << ‘\"‘ << endl;
101 cerr << "\tReceived: \"" << Received << ‘\"‘ << endl;
102 }
103 }
104 void test_case_0()
105 {
106 LL Arr0[] = {0,1,0,0,0};
107 vector<long long> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0])));
108 LL Arr1[] = {0,1,2,1,0};
109 vector<long long> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0])));
110 string Arg2 = "LL";
111 verify_case(0, Arg2, construct(Arg0, Arg1));
112 }
113 void test_case_1()
114 {
115 LL Arr0[] = {0,0,0,1};
116 vector<long long> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0])));
117 LL Arr1[] = {0,1,0,0};
118 vector<long long> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0])));
119 string Arg2 = "No solution";
120 verify_case(1, Arg2, construct(Arg0, Arg1));
121 }
122 void test_case_2()
123 {
124 LL Arr0[] = {1,2,3,4,5,6,7,8,9,10};
125 vector<long long> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0])));
126 LL Arr1[] = {12,24,56,95,12,78,0,100,54,88};
127 vector<long long> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0])));
128 string Arg2 = "No solution";
129 verify_case(2, Arg2, construct(Arg0, Arg1));
130 }
131 void test_case_3()
132 {
133 LL Arr0[] = {1,0,0};
134 vector<long long> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0])));
135 LL Arr1[] = {11,11,10};
136 vector<long long> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0])));
137 string Arg2 = "RRRRR";
138 verify_case(3, Arg2, construct(Arg0, Arg1));
139 }
140 void test_case_4()
141 {
142 LL Arr0[] = {1,1};
143 vector<long long> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0])));
144 LL Arr1[] = {562949953421312,562949953421312};
145 vector<long long> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0])));
146 string Arg2 = "RLLLRRRLLRRRLRLRRLLLLRLLRRLRRRLRRLRRLLRRRLLRRRLLL";
147 verify_case(4, Arg2, construct(Arg0, Arg1));
148 }
149 void test_case_5()
150 {
151 LL Arr0[] = {0,0,0,0,0};
152 vector<long long> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0])));
153 LL Arr1[] = {0,0,0,1,0};
154 vector<long long> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0])));
155 string Arg2 = "No solution";
156 verify_case(5, Arg2, construct(Arg0, Arg1));
157 }
158 void test_case_6()
159 {
160 LL Arr0[] = {123,456};
161 vector<long long> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0])));
162 LL Arr1[] = {123,456};
163 vector<long long> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0])));
164 string Arg2 = "";
165 verify_case(6, Arg2, construct(Arg0, Arg1));
166 }
167
168 // END CUT HERE
169
170 };
171 // BEGIN CUT HERE
172 int main()
173 {
174 LR ___test;
175 ___test.run_test(3);
176 getch() ;
177 return 0;
178 }
179 // END CUT HERE
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