The sign triangle problem of backtracking method

2. /* Backtracking to solve symbolic triangle problems
6. Problem Description:
8. As a symbolic triangle consisting of 14 "+" and 14 "-", 2 are "+" under the same number, and 2 are "-" below.
10. - + + - + + +
12. - + - - + +
14. - - + - +
16. + - - -
18. - + +
20. - +
22. -
24. In general, the first line of the symbol triangle has n symbols, and the sign triangle problem requires a given n,
26. Calculates how many different symbol triangles have the same number of "+" and "-" contained.
30. Problem Solving Ideas:
32. 1, constantly change the first line of each symbol, search for a solution that meets the criteria, you can use recursive backtracking
34. For ease of operation, set + to 0,-to 1, which allows you to use an XOR operator to represent the relationship of the symbol triangle
36. + + is 0^0=0,--for + that is 1^1=0, +--that is, 0^1=1,-+-that is, 1^0=1;
40. 2, because the number of two symbols is the same, you can prune the tree,
42. When the total number of symbols is odd, there is no solution when a symbol exceeds half of the total
46. Refer to the learning materials, re-implementation to practice, there are omissions please correct [email protected].
48. Yang Xiaojin, 17:13 2009-8-5
50. */
52. #include "iostream"
54. Using namespace std;
56. typedef unsigned char uchar;
60. Char cc[2]={' + ','-'}; //Easy to output
62. int n, //Total number of first line symbols
64. Half, //Total symbols in half
66. Counter //1 count, i.e. "-" number count
70. Uchar **p; //Symbol storage space
72. Long sum; //Meet the criteria for the triangle Count
76. T, the first line of the T-symbol
78. void BackTrace (int t)
80. {
82. int I, J;
86. if (T > N)
88. {//symbol fills complete
90. sum++;
94. //Print symbols
96. cout << "<< sum << " A:/n ";
98. For (i=1; i<=n; ++i)
100. {
102. For (j=1; j<i; ++j)
104. {
106. cout << "";
108. }
112. For (j=1; j<=n-i+1; ++j)
114. {
116. cout << cc[P[i][j]] << "";
118. }
120. cout << "/n";
122. }
124. }
126. Else
128. {
130. For (i=0; i<2; ++i)
132. {
134. P[1][t] = i; //First line of T-symbol
136. Counter + = i; //"-" number statistics
140. for (j=2; j<=t; ++j) //When the first line of the symbol >=2, you can calculate some of the symbols in the following line
142. {
144. P[J][T-J+1] = p[j-1][t-j+1]^p[j-1][t-j+2]; //Via XOR or op-downlink symbol
146. Counter + = p[j][t-j+1];
148. }
152. if ((counter <= half) && (t* (t+1)/2-counter <= half))
154. {//If the symbol statistics are not more than half, and the other symbol is not more than half
156. BackTrace (t+1); //Add the next symbol in the first line
158. }
162. //backtracking, judging another symbol situation
164. For (j=2; j<=t; ++j)
166. {
168. Counter-= p[j][t-j+1];
170. }
174. Counter-= i;
176. }
178. }
180. }
184. int main ()
186. {
188. cout << "Please enter the first line of the number of symbols N:";
190. CIN >> N;
192. Counter = 0;
194. sum = 0;
196. Half = N (n+1)/2;
198. int i=0;
202. if (half%2 = = 0)
204. {//Total number must be even, if odd, no solution
206. Half/= 2;
208. p = new Uchar *[n+1];
212. For (i=0; i<=n; ++i)
214. {
216. P[i] = new uchar[n+1];
218. memset (P[i], 0, sizeof (UCHAR) * (n+1));
220. }
224. BackTrace (1);
226. For (i=0; i<=n; ++i)
228. {
230. delete[] p[i];
232. }
234. delete[] p;
236. }
240. cout << "/n Total" << sum << "x" << Endl;
242. return 0;
244. }

The sign triangle problem of backtracking method