How to use backtracking algorithm to solve subset problem in PHP

The backtracking algorithm is actually a search attempt process similar to enumeration. It mainly searches for the solution to the problem during the search attempt process. When it is found that the solution conditions are no longer met, it will "backtrack" and return to try other paths. The backtracking method is a optimization search method that searches forward according to the optimization conditions to achieve the goal.

When you reach a certain step in exploration and find that the original choice is not optimal or fails to achieve the goal, you will take a step back and choose again. This is a technique of going back and trying again if it doesn't work. It is a backtracking method, and the point in a certain state that satisfies the backtracking condition is called a "backtracking point". Many complex and large-scale problems can use the backtracking method, which is known as the "universal problem-solving method".

Subset

Given a set of integer array nums without duplicate elements, return all possible subsets (power set) of the array ).

Note: The solution set cannot contain repeated subsets.

Example:

输入: nums = [1,2,3]
输出:[  [3],  
[1],  
[2],  
[1,2,3], 
[1,3],  
[2,3], 
[1,2],  
[]]

Problem-solving ideas 1

Direct reference to the backtracking algorithm group elimination permutation/combination/subset problem

Code

class Solution {
    public $result = [];
    /** 
    * @param Integer[] $nums 
    * @return Integer[][] 
    */
    function subsets($nums) {
       $this->dfs(0, $nums, []);
       return $this->result;
    }
    // 递归部分 
    function dfs($start, $nums, $array){
        $this->result[] = $array;
        for ($i = $start; $i < count($nums); $i++) {
            $array[] = $nums[$i];
            $this->dfs($i + 1, $nums, $array);
            array_pop($array);
        }
    }}

Problem-solving idea 2 Iteration method

The initialization result is a two-dimensional empty array and iterates through each element in the given array. During each traversal, the result set is processed. Each element in the result set adds the number traversed to, and the length of the result set continues to increase.

class Solution {
  /** 
  * @param Integer[] $nums 
  * @return Integer[][] 
  */
    function subsets($nums) {
        $result = [];
        $result[] = [];
        $numsCount = count($nums);
        for ($i = 0; $i < $numsCount; $i++) {
            $resultCount = count($result);
            for ($j = 0; $j < $resultCount; $j++) {
                $tmp = $result[$j];
                $tmp[] = $nums[$i];
                $result[] = $tmp;
            }
        }
        return $result;
    }}

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