Recursive and backtracking methods for subset sums

A subset and an instance of the problem are <S, C> 〉. S = {x1, x2 ,..., Xn} is a set of positive integers, and C is a positive integer. The subset and the problem determine whether a subset S1 of s exists, so that Σ x = C (X in S1 ). Try to design a method to solve the subset and problem. You can assume that the processing range does not exceed the int type.

Recursive Solution

// Subset and problem (recursion). cpp: defines the entry point of the console application. // # Include "stdafx. H "# include <iostream> # include <vector> using namespace STD; void subsetsum (int A [], int level, int total, vector <bool> & frame, int N) {If (level <n) {If (Total = A [level]) {frame [level] = true; For (INT I = 0; I <N; I ++) {If (frame [I]) cout <A [I] <"" ;}cout <Endl; return ;} if (total> A [level]) {frame [level] = true; subsetsum (A, level + 1, total-A [level], frame, n );} if (total <A [level]) {frame [level] = false; subsetsum (A, level + 1, total, frame, n );}} else {While (frame [level-1] = false) level --; frame [level] = false; subsetsum (A, level + 1, total + A [level], frame, n) ;}int _ tmain (INT argc, _ tchar * argv []) {int arr [] = {2, 5, 15, 8, 20}; vector <bool> frame (); subsetsum (ARR, frame, 5); Return 0 ;}

Backtracking

// Subset and problem (rollback). cpp: defines the entry point of the console application. // # Include "stdafx. H "# include <iostream> # include <vector> # include <algorithm> # include <string> using namespace STD; // find if the given Subset sum exists.int findsubsetsum (vector <int> & arr, int given, vector <bool> & bounded DED) {int cur = 0; // points to the current value. int sum = 0; // current Subset sum. while (cur> = 0) {// if current one is not supported ded if (false = supported ded [cur]) {// include current one supported ded [cur] = true; s Um + = arr [cur]; // find the given Subset sum if (sum = given) {return 1;} else if (sum> given) // exceed the given sum {encoded ded [cur] = false; sum-= arr [cur];} cur ++;} // backtrace if (cur> = arr. size ()) {/*** the following two cycles exclude the ** elements included in the result and not included in the result ** In the result in sequence until the next element included in the result is found. element ** example: use 1 and 0 to indicate including and not including ** if the result is 1110011, then the third 1 is the element found ** to change it to 0, but the traversal starts from 4th 0. **/While (true = encoded ded [cur-1]) {cur --; encoded ded [cur] = false; sum-= arr [cur]; // backtrace to the head if (cur <1) return 0;} while (false = encoded ded [cur-1]) {cur --; If (cur <1) return 0;} // change the status of current-1, not current! Encoded ded [cur-1] = false; sum-= arr [cur-1];} return 0;} int _ tmain (INT argc, _ tchar * argv []) {int arr [] = {2, 5, 15, 8, 20}; vector <int> V (ARR, arr + sizeof (ARR)/sizeof (INT )); vector <bool> included (sizeof (ARR)/sizeof (INT), false); int given = 33; // 5 + 8 + 20 if (findsubsetsum (v, given, encoded DED) {vector <bool>: iterator iterb = encoded ded. begin (); vector <int >:: iterator iteri = v. begin (); For (; I Terb! = Included ded. End (); iterb ++, iteri ++) {If (* iterb) cout <* iteri <Endl ;}} return 0 ;}