#! /usr/bin/env python
# -*- coding: utf-8 -*-
#
def pprint(A):
  for i in A:
    print(i)
  print("")
data = [
  [1, 2, 1, 2],
  [3, 8, 1, 12],
  [0, 4, 1, 2]
]
n = len(data)
print("輸入數(shù)據(jù)")
pprint(data)
for i in range(n):
  print("第{}次操作".format(i))
  maxE = abs(data[i][i])
  # 最大值在第幾行
  maxRow = i
  for k in range(i + 1, n):
    if abs(data[k][i] > maxE):
      maxE = abs(data[k][i])
      maxRow = k
  # 當前行交換最大的行
  for k in range(i, n + 1):
    data[maxRow][k], data[i][k] = data[i][k], data[maxRow][k]
  print("當前行交換最大的行 交換結果")
  pprint(data)
  # 改0
  for k in range(i + 1, n):
    c = -data[k][i] / data[i][i]
    print(-data[k][i] ,"/", data[i][i])
    for j in range(i, n + 1):
      if i == j:
        data[k][j] = 0
      else:
        data[k][j] += c * data[i][j]
  print("改0結果")
  pprint(data)
# 化簡后結果
print("化簡結果")
pprint(data)
# 結果計算
result = [0 for i in range(n)]
for i in range(n - 1, -1, -1):
  result[i] = data[i][n] / data[i][i]
  for k in range(i - 1, -1, -1):
    data[k][n] -= data[k][i] * result[i]
print(result)