Look at the data structure write code (33) Tree and backtracking method (a) subset tree

Backtracking is a kind of branch which does not satisfy the condition in the exhaustive lifting, and has reached the method of improving efficiency. Its basic prototype is the first sequence traversal of a tree, and the path from the root to the leaf is a solution to the problem.

The basic framework of backtracking = determining the solution space + depth-first traversal + clipping function + Determining the result function

Where the solution space is divided into subsets tree and sort tree.

Detailed concept: Reference click to open the link and click the Open link

The generic template for recursive algorithms is as follows:

The backtracking method is a depth-first search for the solution space, so the backtracking method is implemented by recursive method in the general case.

Recursive backtracking method for n-fork Tree

void backtrack (int t)

{

if (T > N) {

Reach the leaf node and output the result.

Output (x);

}

else {

Traverse all sub-nodes of a node T

for (int i = f (n,t); I <= g (n,t); i + +) {

X[T] = H[i];

If the pruning condition is not met, continue traversing

if (constraint (t) && bound (t))

Backtrack (t + 1);

}

}

}

The following three examples are written according to this template.

Backtrack.cpp: Defines the entry point of the console application. #include "stdafx.h" #include <cstring> #define SET_MAX_SIZE 1000static bool set[set_max_size];//get power set//times representation  The number of layers of the current recursive layer, starting at 0 levels//n represents the number of sets void Getpowset (int times,int n) {if (Times >= N) {for (int i = 0; i < n; i++) {if (set[i] = = true) {printf ("%d\t", I+1);}} printf ("\ n");} else{for (int i = 0; i < 2; i++) {Set[times] = I;getpowset (times+1,n);}}} Prints all substrings of a string//times represents the current recursive layer void Getallsubchar (int Times,char * string) {int len = strlen (string); if (Times >= len) { for (int i = 0; i < len; i++) {if (set[i] = = True) {printf ("%c\t", String[i]);}} printf ("\ n");} else{for (int i = 0; i < 2; i++) {Set[times] = I;getallsubchar (times+1,string);}}} Prints all combinations of equals N in the collection. void getallequal (int times,int arraylen,int * array,int equal) {int len = arraylen;if (Times >= len) {i NT sum = 0;for (int i = 0; i < len; i++) {if (set[i] = = True) {sum + = Array[i];}} if (sum = = equal) {for (int i = 0; i < len; i++) {if (set[i] = true) {printf ("%d\t", Array[i]);}} printf ("\ n");}} else{for (int i = 0; i < 2; i++) {Set[times] = i;int sum = 0;//cropping. Cut out the non-conforming conditions. for (int i = 0; I <= times; i++) {if (set[i]== true) {sum + = Array[i];}} if (sum <= equal) {getallequal (times+1,arraylen,array,equal);}}}} int _tmain (int argc, _tchar* argv[]) {printf ("The power set of 1~ N, enter N value:"), int n;scanf ("%d", &n);p rintf ("The power set of 1~%d is: \ n", "N."); Getpowset (0,n); char string[set_max_size];p rintf ("Enter string:"), scanf ("%s", string);p rintf ("All substrings of '%s are as follows: \ n", string); Getallsubchar (0,string);p rintf (the combination of "lookup set (3,2,5,6,7,8,10,20,4,15) equals 10 \ n"); int array[] = {3,2,5,6,7,8,10,20,4,15}; Getallequal (0,sizeof (array)/sizeof (int), array,10); return 0;}

Look at the data structure write code (33) Tree and backtracking method (a) subset tree