Create Partition to K Equal Sum Subsets.py

Author: sugia

Partition to K Equal Sum Subsets.py

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+'''
+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:
+    def canPartitionKSubsets(self, nums: List[int], k: int) -> bool:
+        sum_nums = sum(nums)
+        if sum_nums % k != 0:
+            return False
+        target = sum_nums // k
+        visited = [False for i in range(len(nums))]
+        return self.valid(nums=nums,
+                          visited=visited,
+                          start=0,
+                          group=k,
+                          tmp_sum=0,
+                          target_sum=target)
+    
+    def valid(self, nums: List[int], visited: List[bool], start: int, group: int, tmp_sum: int, target_sum: int):
+        if group == 1:
+            return True
+        if tmp_sum == target_sum:
+            return self.valid(nums=nums,
+                              visited=visited,
+                              start=0,
+                              group=group-1,
+                              tmp_sum=0,
+                              target_sum=target_sum)
+        
+        for i in range(start, len(nums)):
+            if visited[i]:
+                continue
+            
+            visited[i] = True
+            if self.valid(nums=nums,
+                         visited=visited,
+                         start=i+1,
+                         group=group,
+                         tmp_sum=tmp_sum+nums[i],
+                         target_sum=target_sum):
+                return True
+            visited[i] = False
+            
+        return False