complete 1812.py

zeta_python/completed/1812.py

@@ -0,0 +1,55 @@
+import sys
+
+input = sys.stdin.readline
+
+"""
+A1 + A2 = S1
+A2 + A3 = S2
+...
+AN + A1 = SN
+
+S1 - S2 = A1 - A3
+S3 - S4 = A3 - A5
+..
+S(N-2) - S(N-1) = A(N-2) - AN
+
+S1 - S(N-1) = A1 - AN;
+
+
+S1 = A1 + A2
+S2 = A2 + A3
+S3 = A3 + A1
+
+S1 - S(N=3 - 1) + S(N=3) = 2 * A1
+S2 - S3 + S1 = 2 * A2
+S3 - S1 + S2 = 2 * A3
+S1 - S2 + S3
+S2 - S3 + S1
+S3 - S1
+
+S1 - S2 + S3 - S4 ... + SN
+S2 - S3 ...
+S3 - S4 + 
+
+구하고자 하는 수 r에 대해서
+
+2Ar = Sr - S(r+1) ... (원환 순환) / + S(r-1)
+
+"""
+
+if __name__ == "__main__":
+    N = int(input())
+    S = list(int(input()) for _ in range(N))
+    transformer = lambda x: x % N
+    n = (N - 1) // 2  # N = 2n + 1
+    for i in range(N):
+        print(
+            (
+                sum(
+                    S[transformer(i + 2 * j)] - S[transformer(i + 2 * j + 1)]
+                    for j in range(n)
+                )
+                + S[transformer(i - 1)]
+            )
+            // 2
+        )