From a5142150602b78793af374bf2e1e4c6f2644cca9 Mon Sep 17 00:00:00 2001
From: Mohammad S Anwar <mohammad.anwar@yahoo.com>
Date: Mon, 4 Dec 2023 11:10:17 +0000
Subject: - Added solutions by Jan Krnavek. - Added solutions by W. Luis
 Mochan. - Added solutions by David Ferrone. - Added solutions by Luca
 Ferrari.

---
 challenge-246/eric-cheung/python/ch-1.py | 17 ++++++++
 challenge-246/eric-cheung/python/ch-2.py | 71 ++++++++++++++++++++++++++++++++
 2 files changed, 88 insertions(+)
 create mode 100755 challenge-246/eric-cheung/python/ch-1.py
 create mode 100755 challenge-246/eric-cheung/python/ch-2.py

(limited to 'challenge-246/eric-cheung/python')

diff --git a/challenge-246/eric-cheung/python/ch-1.py b/challenge-246/eric-cheung/python/ch-1.py
new file mode 100755
index 0000000000..5ad578ad8b
--- /dev/null
+++ b/challenge-246/eric-cheung/python/ch-1.py
@@ -0,0 +1,17 @@
+
+from random import randint
+
+nMaxNum = 49
+nNumChosen = 6
+
+arrInput = list(range(1, nMaxNum + 1))
+arrOuput = []
+
+for nLoop in range(nNumChosen):
+    nIndx = randint(0, nMaxNum - nLoop)
+    arrOuput.append(arrInput[nIndx])
+    del arrInput[nIndx]
+
+arrOuput.sort()
+
+print (arrOuput)
diff --git a/challenge-246/eric-cheung/python/ch-2.py b/challenge-246/eric-cheung/python/ch-2.py
new file mode 100755
index 0000000000..efbbb54bbb
--- /dev/null
+++ b/challenge-246/eric-cheung/python/ch-2.py
@@ -0,0 +1,71 @@
+
+## Ref.
+## https://math.libretexts.org/Courses/Mount_Royal_University/MATH_2150%3A_Higher_Arithmetic/5%3A_Diophantine_Equations/5.1%3A_Linear_Diophantine_Equations#:~:text=A%20Linear%20Diophantine%20equation%20(LDE,and%20y%20are%20unknown%20variables.
+## https://stackoverflow.com/questions/59168914/finding-solutions-to-diophantine
+
+from math import gcd
+import sys
+
+
+def IsConsecutiveEven (arrNum):
+    for nIndx in range(0, len(arrNum) - 1):
+        if arrNum[nIndx] % 2 == 0 and arrNum[nIndx + 1] % 2 == 0:
+            return nIndx
+    return -1
+
+
+def DotProduct (arrNum_01, arrNum_02):
+    return sum(arrLoop[0] * arrLoop[1] for arrLoop in zip(arrNum_01, arrNum_02))
+
+
+def ModifiedGCD (arrNum, arrParam):
+    if arrNum[1] == 0:
+        return [arrNum[0], 1, 0]
+
+    nX = 0
+    nY = 0
+
+    nDiv, nX, nY = ModifiedGCD([arrNum[1], arrNum[0] % arrNum[1]], [nX, nY])
+    return [nDiv, nY, nX - nY * (arrNum[0] // arrNum[1])]
+
+arrInput = [1, 1, 2, 3, 5]  ## Example 1
+## arrInput = [4, 2, 4, 5, 7]  ## Example 2
+## arrInput = [4, 1, 2, -3, 8]  ## Example 3
+
+
+## print (ModifiedGCD(arrInput[0:2], [0, 0]))
+## print (ModifiedGCD([47, 30], [0, 0]))
+
+nConsecutiveEvenIndx = IsConsecutiveEven (arrInput)
+if nConsecutiveEvenIndx > -1:
+    arrContainOdd = [nIndx for nIndx in range(nConsecutiveEvenIndx + 2, len(arrInput)) if arrInput[nIndx] % 2 == 1]
+    if len(arrContainOdd) > 0:
+        print (False)
+        sys.exit()
+
+nGCD = gcd (arrInput[0], arrInput[1])
+if arrInput[2] % nGCD != 0:
+    print (False)
+    sys.exit()
+
+arrParam = []
+
+## ==== To Be Further Fine Tune ====
+if arrInput[2] == arrInput[0] + arrInput[1]:
+    arrParam.append(1)
+    arrParam.append(1)
+elif arrInput[2] == arrInput[0] - 2 * arrInput[1]:
+    arrParam.append(1)
+    arrParam.append(-2)
+## ==== To Be Further Fine Tune ====
+
+if len(arrParam) == 0:
+    print (False)
+    sys.exit()
+
+for nIndx in range(3, 5):
+    if arrInput[nIndx] != DotProduct(arrParam, arrInput[nIndx - 2 : nIndx]):
+        print (False)
+        sys.exit()
+
+print (True)
-- 
cgit 


From b18ca39f9bb4cf8d5015c242b3ae3f8359c2f4af Mon Sep 17 00:00:00 2001
From: Mohammad S Anwar <mohammad.anwar@yahoo.com>
Date: Fri, 8 Dec 2023 18:18:52 +0000
Subject: - Added solutions by Jorg Sommrey. - Added solutions by W. Luis
 Mochan. - Added solutions by Eric Cheung.

---
 challenge-246/eric-cheung/python/ch-2.py | 23 ++++++++++++++++++++++-
 1 file changed, 22 insertions(+), 1 deletion(-)

(limited to 'challenge-246/eric-cheung/python')

diff --git a/challenge-246/eric-cheung/python/ch-2.py b/challenge-246/eric-cheung/python/ch-2.py
index efbbb54bbb..1cb5a1088a 100755
--- a/challenge-246/eric-cheung/python/ch-2.py
+++ b/challenge-246/eric-cheung/python/ch-2.py
@@ -28,14 +28,25 @@ def ModifiedGCD (arrNum, arrParam):
     nDiv, nX, nY = ModifiedGCD([arrNum[1], arrNum[0] % arrNum[1]], [nX, nY])
     return [nDiv, nY, nX - nY * (arrNum[0] // arrNum[1])]
 
-arrInput = [1, 1, 2, 3, 5]  ## Example 1
+## arrInput = [1, 1, 2, 3, 5]  ## Example 1
 ## arrInput = [4, 2, 4, 5, 7]  ## Example 2
 ## arrInput = [4, 1, 2, -3, 8]  ## Example 3
+## arrInput = [3, 9, 27, 81, 243]  ## Example 4
+## arrInput = [3, 5, 27, 45, 243]  ## Example 5
+## arrInput = [1, 1, 0, 0, 0]  ## Example 6
+## arrInput = [0, 0, 0, 0, 0]  ## Example 7
+## arrInput = [0, 3, 0, 0, 0]  ## Example 8
+## arrInput = [0, 0, 3, 0, 0]  ## Example 9
+arrInput = [2, 4, 8, 16, 32]  ## Example 10
 
 
 ## print (ModifiedGCD(arrInput[0:2], [0, 0]))
 ## print (ModifiedGCD([47, 30], [0, 0]))
 
+if all([nLoop == 0 for nLoop in arrInput[2:]]):
+    print (True)
+    sys.exit()
+
 nConsecutiveEvenIndx = IsConsecutiveEven (arrInput)
 if nConsecutiveEvenIndx > -1:
     arrContainOdd = [nIndx for nIndx in range(nConsecutiveEvenIndx + 2, len(arrInput)) if arrInput[nIndx] % 2 == 1]
@@ -57,6 +68,16 @@ if arrInput[2] == arrInput[0] + arrInput[1]:
 elif arrInput[2] == arrInput[0] - 2 * arrInput[1]:
     arrParam.append(1)
     arrParam.append(-2)
+elif arrInput[2] == 3 * arrInput[0] + 2 * arrInput[1]:
+    arrParam.append(3)
+    arrParam.append(2)
+elif arrInput[2] == 9 * arrInput[0]:
+    arrParam.append(9)
+    arrParam.append(0)
+elif arrInput[2] == 2 * arrInput[1]:
+    arrParam.append(0)
+    arrParam.append(2)
+
 ## ==== To Be Further Fine Tune ====
 
 if len(arrParam) == 0:
-- 
cgit