From 723e7b2800616a3d0aca5b8d5deb6e0b59606a3c Mon Sep 17 00:00:00 2001
From: Jack Sangdahl <jack@pngu.org>
Date: Tue, 2 Jul 2024 11:21:43 -0600
Subject: 1787. make the xor of all segments equal to zero

---
 make_xor_segment_zero.py | 41 +++++++++++++++++++++++++++++++++++++++++
 1 file changed, 41 insertions(+)
 create mode 100644 make_xor_segment_zero.py

(limited to 'make_xor_segment_zero.py')

diff --git a/make_xor_segment_zero.py b/make_xor_segment_zero.py
new file mode 100644
index 0000000..2174968
--- /dev/null
+++ b/make_xor_segment_zero.py
@@ -0,0 +1,41 @@
+# 1787. Make the XOR of All Segments Equal to Zero
+import collections
+
+"""
+given an array 'nums' and an integer 'k'. the xor of a segment '[left,
+right]' where 'left <= right' is the xor of all the elements with indices
+between 'left' and 'right', inclusive 'nums[left] xor nums[left + 1] xor ...
+xor nums[right]'. return the minimum number of elements to change in the
+array such that the 'xor' of all segments of size 'k' is equal to zero
+"""
+
+
+class Solution(object):
+    def minChanges(self, nums, k):
+        """
+        :type nums: List[int]
+        :type k: int
+        :rtype: int
+        """
+        m = 1 << 10
+        freq = collections.defaultdict(collections.Counter)
+        for i, n in enumerate(nums):
+            freq[i % k][n] += 1
+        dp = [[0] * m for _ in range(k + 1)]
+        for i in range(1, m):
+            dp[0][i] = -float("inf")
+        for i in range(1, k + 1):
+            max_row = max(dp[i - 1])
+            for j in range(m):
+                for mask in freq[i - 1]:
+                    dp[i][j] = max(
+                        dp[i][j], max_row, dp[i - 1][j ^ mask] + freq[i - 1][mask]
+                    )
+        return len(nums) - dp[-1][0]
+
+
+if __name__ == "__main__":
+    obj = Solution()
+    print(obj.minChanges(nums=[1, 2, 0, 3, 0], k=1))
+    print(obj.minChanges(nums=[3, 4, 5, 2, 1, 7, 3, 4, 7], k=3))
+    print(obj.minChanges(nums=[1, 2, 4, 1, 2, 5, 1, 2, 6], k=3))
-- 
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