Time: 3650 ms (100%), Space: 38.1 MB (100%) - LeetHub

Author: hogan-tech

3752-lexicographically-smallest-negated-permutation-that-sums-to-target/3752-lexicographically-smallest-negated-permutation-that-sums-to-target.py

@@ -0,0 +1,48 @@
+# time complexity: O(n)
+# space complexity: O(n)
+from typing import List
+
+
+class Solution:
+    def lexSmallestNegatedPerm(self, n: int, target: int) -> List[int]:
+        S = n * (n + 1) // 2
+        if (S - target) < 0 or (S - target) % 2 != 0:
+            return []
+        sumPNeg = (S - target) // 2
+        if sumPNeg < 0 or sumPNeg > S:
+            return []
+        pNeg = set()
+        currSum = 0
+
+        for i in range(n, 0, -1):
+            if currSum + i <= sumPNeg:
+                pNeg.add(i)
+                currSum += i
+        if currSum != sumPNeg:
+            return []
+        pNegList = sorted(list(pNeg), reverse=True)
+        pPosSet = set(range(1, n + 1)) - pNeg
+        pPosList = sorted(list(pPosSet), reverse=True)
+        result = []
+        for _ in range(n):
+            candidateNeg = float('inf')
+            if pNegList:
+                candidateNeg = -pNegList[0]
+            candidatePos = float('inf')
+            if pPosList:
+                candidatePos = pPosList[-1]
+            if candidateNeg <= candidatePos:
+                result.append(candidateNeg)
+                pNegList.pop(0)
+            else:
+                result.append(candidatePos)
+                pPosList.pop()
+        return result
+
+
+n = 3
+target = 0
+print(Solution().lexSmallestNegatedPerm(n, target))
+n = 1
+target = 10000000000
+print(Solution().lexSmallestNegatedPerm(n, target))