收费公路重建问题(可发现所有同度点集)C语言

  同度点集,就是产生相同的距离集合,但却是不同点集的那些点集.

这个东西,整个白天都在想.到现在,也不是很清楚.但,代码写出来了,回溯部分总是不自信的感觉.

  核心的思想就是:传递给例程一个数组指针,之后用一个 static int 类型变量保存点集的个数.即每次使集合为空,就执行 count++ ;

  无论是否成功产生点集,都进行回溯.通过对决策树的分析,在每次调用 place () 结束之后,都通过上一个点集的内容对 distance 进行恢复.主要的逻辑障碍就在这里了.哎,不深扣了,扣不起啊.

  因为是寻找所有的可能,所以可能会有重复的点集出现.

  注释写得很烂,最近有看英语跟数学.

  好吧,帖.!/* 10-42-11-02-19-23.55.c -- 第十章第四十二题 */ #include <stdio.h> #include <stdlib.h> #define FALSE (0) #define TRUE (1) typedef int Item ; typedef int BOOL ; /* Data is a kind of data structures. */ int turnpike (Item * const * const points, const int column, const int row, Data * const distance) ; int place (Item * const * const points, const int column, const int row, const int left, const int right, Data * const distance) ; Item absoluteValue (const Item value) ; /* It will return the number of lines that can be rebuilded. */ /* In the case where there are some duplicate distances, it is possible that several symmetries will be printed. */ int turnpike (Item * const * const points, const int column, const int row, Data * const distance) { Item max ; int i ; /* To cause the cood expressly, abnegate to optimize the loop. */ /* Set starting point. */ for (i = 0; i < column; i++) points[i][0] = 0 ; max = FindMax (distance) ; for (i = 0; i < column; i++) points[i][row - 1] = max ; Delete (distance, max) ; return place (points, column, row, 1, row - 2, distance) ; } int place (Item * const * const points, const int column, const int row, const int left, const int right, Data * const distance) { static int count = 0 ; BOOL index = FALSE ; Item max_in_distance, temp ; int i, j, k ; if (IsEmpty (distance)) { count++ ; return count ; } max_in_distance = FindMax (distance) ; /* Check if setting points[count][right] = DMax is feasible. */ /* Testing */ for (i = 0; i < left; i++) { temp = absoluteValue (points[count][i] - max_in_distance) ; if (TRUE == Find (distance, temp)) Delete (distance, temp) ; /* If it hasn't found temp in distance. */ else { /* If it has deleted. */ if (i > 0) { /* Recover the items that has been deleted. */ for (k = i - 1; k >= 0; k--) { temp = absoluteValue (points[count][k] - max_in_distance) ; Insert (distance, temp) ; } } /* To guide next step. */ index = TRUE ; break ; } } /* If has passed through the test on last step. */ if (FALSE == index) { /* Testing. */ for (j = right + 1; j < row; j++) { temp = absoluteValue (points[count][j] - max_in_distance) ; if (TRUE == Find (distance, temp)) Delete (distance, temp) ; /* If hasn't found temp in distance. */ else { /* If has deleted. */ if (j > right + 1) { /* Recover the items that has been deleted. */ for (k = j - 1; k > right; k--) { temp = absoluteValue (points[count][k] - max_in_distance) ; Insert (distance, temp) ; } } /* From points[count][i - 1] to points[count][0] has been deleted certainly. */ /* Recover the items that from points[count][i - 1] to points[count][0]. */ for (k = i - 1; k >= 0; k--) { temp = absoluteValue (points[count][k] - max_in_distance) ; Insert (distance, temp) ; } /* To guide next step. */ index = TRUE ; break ; } } /* If has passed through the test on last step. */ if (FALSE == index) { /* Undoubted attempt. */ for (i = count; i < column; i++) points[i][right] = max_in_distance ; count = place (points, column, row, left, right - 1, distance) ; /* Unconditional recall. */ /* Backtrack. */ for (i = 0; i < left; i++) { temp = absoluteValue (points[count][i] - max_in_distance) ; Insert (distance, temp) ; } for (i = right + 1; i < row; i++) { temp = absoluteValue (points[count][i] - max_in_distance) ; Insert (distance, temp) ; } } } /* Even if first attempt is successful, try to setting points[count][left] = points[N] - DMax is feasible. */ /* Initialize "index" again. */ index = FALSE ; for (i = 0; i < left; i++) { /* Make sure you has known that temp is the absolute value of distance. */ temp = absoluteValue (points[count][row - 1] - max_in_distance - points[count][i]) ; if (TRUE == Find (distance, temp)) Delete (distance, temp) ; else { if (i > 0) { for (k = i - 1; k >= 0; k--) { temp = absoluteValue (points[count][row - 1] - max_in_distance - points[count][k]) ; Insert (distance, temp) ; } } index = TRUE ; break ; } } if (FALSE == index) { for (j = right + 1; j < row; j++) { temp = absoluteValue (points[count][row - 1] - max_in_distance - points[count][j]) ; if (TRUE == find (distance, temp)) Delete (distance, temp) ; else { if (j > right + 1) { for (k = j - 1; k > right; k--) { temp = absoluteValue (points[count][row - 1] - max_in_distance - points[count][k]) ; Insert (distance, temp) ; } } for (k = i - 1; k >= 0; k--) { temp = absoluteValue (points[count][row - 1] - max_in_distance - points[count][k]) ; Insert (distance, temp) ; } index = TRUE ; break ; } } } if (FALSE == index) { for (i = count; i < column; i++) points[i][left] = points[count][row - 1] - max_in_distance ; count = place (points, column, row, left + 1, right, distance) ; /* Backtrack. */ for (i = 0; i < left; i++) { temp = absoluteValue (points[count][row - 1] - max_in_distance - points[count][i]) ; Insert (distance, temp) ; } for (i = right + 1; i < row; i++) { temp = absoluteValue (points[count][row - 1] - max_in_distance - points[count][i]) ; Insert (distance, temp) ; } } return count ; } Item absoluteValue (const Item value) { if (value < 0) return 0 - value ; else return value ; }