Create determine-the-minimum-sum-of-a-k-avoiding-array.py

Author: kamyu104

Python/determine-the-minimum-sum-of-a-k-avoiding-array.py

@@ -0,0 +1,17 @@
+# Time:  O(1)
+# Space: O(1)
+
+# constructive algorithms, math
+class Solution(object):
+    def minimumSum(self, n, k):
+        """
+        :type n: int
+        :type k: int
+        :rtype: int
+        """
+        def arithmetic_progression_sum(a, d, n):
+            return (a+(a+(n-1)*d))*n//2
+    
+        a = min(k//2, n)
+        b = n-a
+        return arithmetic_progression_sum(1, 1, a)+arithmetic_progression_sum(k, 1, b)