CodeChef: Easy Problems

Author: OmkarPathak

CompetitiveProgramming/CodeChef/P35_AMSGAME1.py

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+# Chef is playing a game on a sequence of N positive integers, say A1, A2, ... AN. The game is played as
+# follows.
+# If all the numbers are equal, the game ends.
+# Otherwise
+# Select two numbers which are unequal
+# Subtract the smaller number from the larger number
+# Replace the larger number with the result from above (see the explanation section for clarity)
+# Chef has already figured out that the game always terminates. He also knows, for a given sequence of
+# integers, the game will always terminate on the same value, no matter how the game is played. Chef wants
+# you to simulate the game for him and tell him on which value will the game terminate for a given sequence
+# of integers.
+#
+# Input
+# The first line of the input contains an integer T, the number of test cases. Then follow the
+# description of T test cases. The first line of each test case contains a single integer N, the length of
+# the sequence. The second line contains N positive integers, each separated by a single space.
+#
+# Output
+# For each test case, output a single integer - the value of all the numbers when they are equal (and the game terminates), on a line by itself.
+#
+# Constraints
+# 1 ≤ T ≤ 100
+# 1 ≤ N ≤ 1000
+# 1 ≤ Ai ≤ 109
+#
+# Sample
+# Input
+# 3
+# 2
+# 10 12
+# 2
+# 5 9
+# 3
+# 6 10 15
+#
+# Output
+# 2
+# 1
+# 1
+#
+# Explanation
+# Test Case 1: Since there are only two numbers, the operations are forced.
+#
+# { 10, 12 } => Replace 12 with ( 12 - 10 = 2 ) => { 10, 2 }
+# { 10, 2 } => Replace 10 with ( 10 - 2 = 8 ) => { 8, 2 }
+# { 8, 2 } => Replace 8 with ( 8 - 2 = 6 ) => { 6, 2 }
+# { 6, 2 } => Replace 6 with ( 6 - 2 = 4 ) => { 4, 2 }
+# { 4, 2 } => Replace 4 with ( 4 - 2 = 2 ) => { 2, 2 }
+# The value of all the numbers when the game ends is 2.
+#
+# Test Case 2: Since there are only two numbers, the operations are forced.
+#
+# { 5, 9 } => Replace 9 with ( 9 - 5 = 4 ) => { 5, 4 }
+# { 5, 4 } => Replace 5 with ( 5 - 4 = 1 ) => { 1, 4 }
+# { 1, 4 } => Replace 4 with ( 4 - 1 = 3 ) => { 1, 3 }
+# { 1, 3 } => Replace 3 with ( 3 - 1 = 2 ) => { 1, 2 }
+# { 1, 2 } => Replace 2 with ( 2 - 1 = 1 ) => { 1, 1 }
+# The value of all the numbers when the game ends is 1.
+#
+# Test Case 3: One way to play the game is
+#
+# { 6, 10, 15 } => Replace 15 with ( 15 - 6 = 9 ) => { 6, 10, 9 }
+# { 6, 10, 9 } => Replace 10 with ( 10 - 6 = 4 ) => { 6, 4, 9 }
+# { 6, 4, 9 } => Replace 9 with ( 9 - 6 = 3 ) => { 6, 4, 3 }
+# { 6, 4, 3 } => Replace 6 with ( 6 - 4 = 2 ) => { 2, 4, 3 }
+# { 2, 4, 3 } => Replace 3 with ( 3 - 2 = 1 ) => { 2, 4, 1 }
+# { 2, 4, 1 } => Replace 4 with ( 4 - 2 = 2 ) => { 2, 2, 1 }
+# { 2, 2, 1 } => Replace first 2 with ( 2 - 1 = 1 ) => { 1, 2, 1 }
+# { 1, 2, 1 } => Replace 2 with ( 2 - 1 = 1 ) => { 1, 1, 1 }
+
+for _ in range(int(input())):
+  n = int(input())
+  numbers = [int(i) for i in input().split()]
+  res = 0
+  while True:
+    maxi = max(numbers)
+    mini = min(numbers)
+    res = maxi - mini
+    numbers[numbers.index(maxi)] = res
+    if(n == numbers.count(res)):
+      print(res)
+      break