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  1. \begin{minipage}{.5\textwidth}
  2. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1},scale=.45]
  3. \node [vertex] (r){$6$}
  4.  child {
  5.    node [vertex] (a) {$13$}
  6.    child {
  7.      node [vertex] {$35$}
  8.      child {
  9.        node [vertex] {$8$}
  10.      }
  11.      child {node [vertex] {$3$}}
  12.    }
  13.          child {node [vertex] {$7$}}
  14.  }
  15.      child {
  16.      node [vertex] {$2$}
  17.      child {node [vertex] {$17$}}
  18.      child {node [vertex] {$20$}}
  19.    }
  20. %  child {
  21. %    node [vertex] {$9$}
  22. %    child {
  23. %      node [vertex] {$8$}
  24. %      child {node [vertex] {$2$}}
  25. %    }
  26. %    child {
  27. %      node [vertex] {$11$}
  28. %      child {node [vertex] {$17$}}
  29. %      child {node [vertex] {$-4$}}
  30. %    }
  31. %  };
  32. ;
  33. \end{tikzpicture}
  34. \caption{(a)}
  35. \caption{\;\;\;\;\;\;\;(b)}
  36. \end{minipage}
  37. \begin{minipage}{.3\textwidth}
  38. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.45]
  39. \node [vertex] (r){$6$}
  40.  child {
  41.    node [vertex] (a) {$13$}
  42.    child {
  43.      node [vertex] {$35$}
  44.      child {node [vertex] {$8$}}
  45.      child {node [vertex] {$3$}}
  46.    }
  47.          child {node [vertex] {$7$}}
  48.  }
  49.      child {
  50.      node [vertex] {$20$}
  51.      child {node [vertex] {$17$}}
  52.      child {node [vertex] {$2$}}
  53.    }
  54. ;
  55. \end{tikzpicture}
  56. \end{minipage}
  57.  
  58. \begin{minipage}{.35\textwidth}
  59. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  60. \node [vertex] (r){$6$}
  61.  child {
  62.    node [vertex] (a) {$35$}
  63.    child {
  64.      node [vertex] {$13$}
  65.      child {node [vertex] {$8$}}
  66.      child {node [vertex] {$3$}}
  67.    }
  68.    child {node [vertex] {$7$}}
  69.  }
  70.      child {
  71.      node [vertex] {$20$}
  72.      child {node [vertex] {$17$}}
  73.      child {node [vertex] {$2$}}
  74.    }
  75. ;
  76. \end{tikzpicture}
  77. \end{minipage}
  78. \caption{(c)}
  79. \caption{\;\;\;\;\;\;\;(d)}
  80. \begin{minipage}{.3\textwidth}
  81. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  82. \node [vertex] (r){$35$}
  83.  child {
  84.    node [vertex] (a) {$13$}
  85.    child {
  86.      node [vertex] {$8$}
  87.      child {node [vertex] {$6$}}
  88.      child {node [vertex] {$3$}}
  89.    }
  90.    child {node [vertex] {$7$}}
  91.  }
  92.      child {
  93.      node [vertex] {$20$}
  94.      child {node [vertex] {$17$}}
  95.      child {node [vertex] {$2$}}
  96.    }
  97. ;
  98. \end{tikzpicture}
  99. \end{minipage}
  100.  
  101. \caption{(e)}
  102. \begin{minipage}{.2\textwidth}
  103. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  104. \node [vertex] (r){$20$}
  105.  child {
  106.    node [vertex] (a) {$13$}
  107.    child {
  108.      node [vertex] {$8$}
  109.      child {node [vertex] {$6$}}
  110.      child {node [vertex] {$3$}}
  111.    }
  112.    child {node [vertex] {$7$}}
  113.  }
  114.  child {
  115.      node [vertex] {$17$}
  116.      child {node [vertex] {$2$}}
  117.   }
  118.   ;
  119. \end{tikzpicture}
  120. \end{minipage}
  121. \begin{minipage}{.2\textwidth}
  122. \vspace{70px}
  123. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  124. \node [vertex] (r){$35$};
  125. \end{tikzpicture}
  126. \end{minipage}
  127. \caption{(f)}
  128. \begin{minipage}{.2\textwidth}
  129. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  130. \node [vertex] (r){$17$}
  131.  child {
  132.    node [vertex] (a) {$13$}
  133.    child {
  134.      node [vertex] {$8$}
  135.      child {node [vertex] {$6$}}
  136.      child {node [vertex] {$3$}}
  137.    }
  138.    child {node [vertex] {$7$}}
  139.  }
  140.  child {node [vertex] {$2$}};
  141. \end{tikzpicture}
  142. \end{minipage}
  143. \begin{minipage}{.04\textwidth}
  144. \vspace{70px}
  145. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  146. \node [vertex] (r){$20$};
  147. \end{tikzpicture}
  148. \end{minipage}
  149. \begin{minipage}{.2\textwidth}
  150. \vspace{70px}
  151. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  152. \node [vertex] (r){$35$};
  153. \end{tikzpicture}
  154. \end{minipage}
  155.  
  156. \caption{(g)}
  157. \begin{minipage}{.2\textwidth}
  158. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.6]
  159. \node [vertex] (r){$13$}
  160.  child {
  161.    node [vertex] (a) {$8$}
  162.    child {
  163.      node [vertex] {$6$}
  164.      child {node [vertex] {$3$}}
  165.    }
  166.          child {node [vertex] {$7$}}
  167.  }
  168.  child {node [vertex] {$2$}};
  169. \end{tikzpicture}
  170. \end{minipage}
  171. \begin{minipage}{.04\textwidth}
  172. \vspace{70px}
  173. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  174. \node [vertex] (r){$17$};
  175. \end{tikzpicture}
  176. \end{minipage}
  177. \begin{minipage}{.04\textwidth}
  178. \vspace{70px}
  179. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  180. \node [vertex] (r){$20$};
  181. \end{tikzpicture}
  182. \end{minipage}
  183. \begin{minipage}{.1\textwidth}
  184. \vspace{70px}
  185. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  186. \node [vertex] (r){$35$};
  187. \end{tikzpicture}
  188. \end{minipage}
  189. \caption{(h)}
  190. \begin{minipage}{.1\textwidth}
  191. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.6]
  192. \node [vertex] (r){$8$}
  193.  child {
  194.    node [vertex] (a) {$7$}
  195.    child {
  196.      node [vertex] {$6$}
  197.        child {node [vertex] {$3$}}
  198.    }
  199.  }
  200.  child {node [vertex] {$2$}};
  201. \end{tikzpicture}
  202. \end{minipage}
  203. \begin{minipage}{.04\textwidth}
  204. \vspace{70px}
  205. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  206. \node [vertex] (r){$13$};
  207. \end{tikzpicture}
  208. \end{minipage}
  209. \begin{minipage}{.04\textwidth}
  210. \vspace{70px}
  211. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  212. \node [vertex] (r){$17$};
  213. \end{tikzpicture}
  214. \end{minipage}
  215. \begin{minipage}{.04\textwidth}
  216. \vspace{70px}
  217. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  218. \node [vertex] (r){$20$};
  219. \end{tikzpicture}
  220. \end{minipage}
  221. \begin{minipage}{.1\textwidth}
  222. \vspace{70px}
  223. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  224. \node [vertex] (r){$35$};
  225. \end{tikzpicture}
  226. \end{minipage}
  227.  
  228. \caption{(i)}
  229. \begin{minipage}{.1\textwidth}
  230. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.6]
  231. \node [vertex] (r){$7$}
  232.  child {
  233.    node [vertex] (a) {$6$}
  234.    child {node [vertex] {$3$}}
  235.  }
  236.  child {node [vertex] {$2$}};
  237. \end{tikzpicture}
  238. \end{minipage}
  239. \begin{minipage}{.04\textwidth}
  240. \vspace{70px}
  241. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  242. \node [vertex] (r){$8$};
  243. \end{tikzpicture}
  244. \end{minipage}
  245. \begin{minipage}{.04\textwidth}
  246. \vspace{70px}
  247. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  248. \node [vertex] (r){$13$};
  249. \end{tikzpicture}
  250. \end{minipage}
  251. \begin{minipage}{.04\textwidth}
  252. \vspace{70px}
  253. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  254. \node [vertex] (r){$17$};
  255. \end{tikzpicture}
  256. \end{minipage}
  257. \begin{minipage}{.04\textwidth}
  258. \vspace{70px}
  259. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  260. \node [vertex] (r){$20$};
  261. \end{tikzpicture}
  262. \end{minipage}
  263. \begin{minipage}{.1\textwidth}
  264. \vspace{70px}
  265. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  266. \node [vertex] (r){$35$};
  267. \end{tikzpicture}
  268. \end{minipage}
  269. \caption{(j)}
  270. \begin{minipage}{.1\textwidth}
  271. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.6]
  272. \node [vertex] (r){$6$}
  273.  child {node [vertex] (a) {$3$}}
  274.  child {node [vertex] {$2$}};
  275. \end{tikzpicture}
  276. \end{minipage}
  277. \begin{minipage}{.04\textwidth}
  278. \vspace{70px}
  279. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  280. \node [vertex] (r){$7$};
  281. \end{tikzpicture}
  282. \end{minipage}
  283. \begin{minipage}{.04\textwidth}
  284. \vspace{70px}
  285. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  286. \node [vertex] (r){$8$};
  287. \end{tikzpicture}
  288. \end{minipage}
  289. \begin{minipage}{.04\textwidth}
  290. \vspace{70px}
  291. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  292. \node [vertex] (r){$13$};
  293. \end{tikzpicture}
  294. \end{minipage}
  295. \begin{minipage}{.04\textwidth}
  296. \vspace{70px}
  297. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  298. \node [vertex] (r){$17$};
  299. \end{tikzpicture}
  300. \end{minipage}
  301. \begin{minipage}{.04\textwidth}
  302. \vspace{70px}
  303. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  304. \node [vertex] (r){$20$};
  305. \end{tikzpicture}
  306. \end{minipage}
  307. \begin{minipage}{.1\textwidth}
  308. \vspace{70px}
  309. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  310. \node [vertex] (r){$35$};
  311. \end{tikzpicture}
  312. \end{minipage}
  313.  
  314. \caption{(j)}
  315. \begin{minipage}{.06\textwidth}
  316. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.6]
  317. \node [vertex] (r){$3$}
  318.  child {node [vertex] (a) {$2$}};
  319. \end{tikzpicture}
  320. \end{minipage}
  321. \begin{minipage}{.04\textwidth}
  322. \vspace{40px}
  323. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  324. \node [vertex] (r){$6$};
  325. \end{tikzpicture}
  326. \end{minipage}
  327. \begin{minipage}{.04\textwidth}
  328. \vspace{40px}
  329. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  330. \node [vertex] (r){$7$};
  331. \end{tikzpicture}
  332. \end{minipage}
  333. \begin{minipage}{.04\textwidth}
  334. \vspace{40px}
  335. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  336. \node [vertex] (r){$8$};
  337. \end{tikzpicture}
  338. \end{minipage}
  339. \begin{minipage}{.04\textwidth}
  340. \vspace{40px}
  341. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  342. \node [vertex] (r){$13$};
  343. \end{tikzpicture}
  344. \end{minipage}
  345. \begin{minipage}{.04\textwidth}
  346. \vspace{40px}
  347. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  348. \node [vertex] (r){$17$};
  349. \end{tikzpicture}
  350. \end{minipage}
  351. \begin{minipage}{.04\textwidth}
  352. \vspace{40px}
  353. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  354. \node [vertex] (r){$20$};
  355. \end{tikzpicture}
  356. \end{minipage}
  357. \begin{minipage}{.1\textwidth}
  358. \vspace{40px}
  359. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  360. \node [vertex] (r){$35$};
  361. \end{tikzpicture}
  362. \end{minipage}
  363. \caption{(k)}
  364. \begin{minipage}{.05\textwidth}
  365. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.6]
  366. \node [vertex] (r){$2$};
  367. \end{tikzpicture}
  368. \end{minipage}
  369. \begin{minipage}{.04\textwidth}
  370. \vspace{40px}
  371. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  372. \node [vertex] (r){$3$};
  373. \end{tikzpicture}
  374. \end{minipage}
  375. \begin{minipage}{.04\textwidth}
  376. \vspace{40px}
  377. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  378. \node [vertex] (r){$6$};
  379. \end{tikzpicture}
  380. \end{minipage}
  381. \begin{minipage}{.04\textwidth}
  382. \vspace{40px}
  383. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  384. \node [vertex] (r){$7$};
  385. \end{tikzpicture}
  386. \end{minipage}
  387. \begin{minipage}{.04\textwidth}
  388. \vspace{40px}
  389. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  390. \node [vertex] (r){$8$};
  391. \end{tikzpicture}
  392. \end{minipage}
  393. \begin{minipage}{.04\textwidth}
  394. \vspace{40px}
  395. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  396. \node [vertex] (r){$13$};
  397. \end{tikzpicture}
  398. \end{minipage}
  399. \begin{minipage}{.04\textwidth}
  400. \vspace{40px}
  401. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  402. \node [vertex] (r){$17$};
  403. \end{tikzpicture}
  404. \end{minipage}
  405. \begin{minipage}{.04\textwidth}
  406. \vspace{40px}
  407. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  408. \node [vertex] (r){$20$};
  409. \end{tikzpicture}
  410. \end{minipage}
  411. \begin{minipage}{.1\textwidth}
  412. \vspace{40px}
  413. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  414. \node [vertex] (r){$35$};
  415. \end{tikzpicture}
  416. \end{minipage}
  417.  
  418. \centering
  419. \caption{(l)}
  420. \begin{minipage}{.04\textwidth}
  421. \vspace{40px}
  422. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  423. \node [vertex] (r){$2$};
  424. \end{tikzpicture}
  425. \end{minipage}
  426. \begin{minipage}{.04\textwidth}
  427. \vspace{40px}
  428. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  429. \node [vertex] (r){$3$};
  430. \end{tikzpicture}
  431. \end{minipage}
  432. \begin{minipage}{.04\textwidth}
  433. \vspace{40px}
  434. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  435. \node [vertex] (r){$6$};
  436. \end{tikzpicture}
  437. \end{minipage}
  438. \begin{minipage}{.04\textwidth}
  439. \vspace{40px}
  440. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  441. \node [vertex] (r){$7$};
  442. \end{tikzpicture}
  443. \end{minipage}
  444. \begin{minipage}{.04\textwidth}
  445. \vspace{40px}
  446. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  447. \node [vertex] (r){$8$};
  448. \end{tikzpicture}
  449. \end{minipage}
  450. \begin{minipage}{.04\textwidth}
  451. \vspace{40px}
  452. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  453. \node [vertex] (r){$13$};
  454. \end{tikzpicture}
  455. \end{minipage}
  456. \begin{minipage}{.04\textwidth}
  457. \vspace{40px}
  458. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  459. \node [vertex] (r){$17$};
  460. \end{tikzpicture}
  461. \end{minipage}
  462. \begin{minipage}{.04\textwidth}
  463. \vspace{40px}
  464. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  465. \node [vertex] (r){$20$};
  466. \end{tikzpicture}
  467. \end{minipage}
  468. \begin{minipage}{.1\textwidth}
  469. \vspace{40px}
  470. \begin{tikzpicture}[very thick,level/.style={sibling distance=60mm/#1}, scale=.5]
  471. \node [vertex] (r){$35$};
  472. \end{tikzpicture}
  473. \end{minipage}
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