Merge 28594f05a2 into fcf82a1eda

hashes/array_pairs_divisibility.py

@@ -0,0 +1,84 @@
+"""
+check-if-array-pairs-are-divisible-by-k
+
+Problem statement:
+Given an array of integers arr of even length n and an integer k.
+
+Divide the array into n / 2 pairs such that the sum of each pair is divisible by k.
+
+Return true If you can find a way to do that or false otherwise.
+
+Example 1:
+
+Input: arr = [1,2,3,4,5,10,6,7,8,9], k = 5
+Output: true
+Explanation: Pairs are (1,9),(2,8),(3,7),(4,6) and (5,10).
+Example 2:
+
+Input: arr = [1,2,3,4,5,6], k = 7
+Output: true
+Explanation: Pairs are (1,6),(2,5) and(3,4).
+Example 3:
+
+Input: arr = [1,2,3,4,5,6], k = 10
+Output: false
+Explanation: You can try all possible pairs.
+See that there is no way to divide arr into 3 pairs each with sum divisible by 10.
+
+Constraints:
+
+arr.length == n
+1 <= n <= 105
+n is even.
+-109 <= arr[i] <= 109
+1 <= k <= 105
+"""
+
+# Time complexity: O(n)
+# Space complexity: O(k)
+
+# Approach:
+# 1. Create a list of size k with all elements as 0.
+# 2. For each element in the array, increment the element at index i%k.
+# 3. If the element at index 0 is odd, return False.
+# 4. Check if the number of elements at index i and k-i are equal.
+# 5. If not, return False.
+# 6. If all the conditions are satisfied, return True.
+
+
+class Solution:
+    def can_arrange(self, arr: list[int], input_num: int) -> bool:
+        """
+        Function to check if array pairs are divisible by k
+        :param arr: List of integers
+        :param k: Integer
+        :return: Boolean
+
+        Example:
+        >>> obj = Solution()
+        >>> obj.can_arrange([1, 2, 3, 4, 5, 10, 6, 7, 8, 9], 5)
+        True
+        >>> obj.can_arrange([1, 2, 3, 4, 5, 6], 7)
+        True
+        """
+        sol_arr = [0 for i in range(input_num)]
+        for i in arr:
+            sol_arr[i % input_num] += 1
+        if sol_arr[0] % 2 != 0:
+            return False
+        i, j = 1, input_num - 1
+        while j > i:
+            if sol_arr[i] == sol_arr[j]:
+                j -= 1
+                i += 1
+            else:
+                return False
+        return True
+
+
+# Driver code
+if __name__ == "__main__":
+    arr = [1, 2, 3, 4, 5, 10, 6, 7, 8, 9]
+    input_num = 5
+    s = Solution()
+    print(s.can_arrange(arr, input_num))  # Output: True