Given an array of integers nums and a positive integer k, find whether it's possible to divide this array into k non-empty subsets whose sums are all equal.

Example 1:

Input: nums = [4, 3, 2, 3, 5, 2, 1], k = 4
Output: True
Explanation: It's possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums.

Note:

• 1 <= k <= len(nums) <= 16.
• 0 < nums[i] < 10000.

class Solution {
    public boolean canPartitionKSubsets(int[] nums, int k) {
        int sum = 0;
        for(int i=0;i<nums.length;i++){
            sum += nums[i];
        }
        if(sum % k > 0){
            return false;
        }
        int target = sum / k;
        Arrays.sort(nums);
        int row = nums.length - 1;
        /**
        经过排序，最后的元素为该数组的最大数，如果该数大于目标值，则代表该数组无论如何切割都无法达成目标
        **/
        if(nums[row] > target){
            return false;
        }
        while(row>=0 && nums[row] == target) {//为了找到一个小于目标值的数的下标
            row--;
            k--;
        }
        return search(new int[k],row,nums,target);//开始进行搜索
        
    }
    
    public boolean search(int[] groups, int row, int[] nums, int target){
        if(row<0)
            return true;
        int v = nums[row--];
        for(int i = 0;i <groups.length;i++){
            if(groups[i] + v <= target){
                groups[i] += v;
                if(search(groups,row,nums,target))
                    return true;
                groups[i] -= v;//复位
            }
            if(groups[i] == 0){
                break;
            }
        }
        return false;
    }
}