1  2  3  4  5  KEY
1  0 65 95 80 49  11
2 65  0 78 69 16   9
3 95 78  0 55 88   6
4 80 69 55  0 87  18
5 49 16 88 87  0   2

exept0_a = df[2] != 0
point_a = (df.loc[exept0_a, 2] / df.loc[exept0_a, 'KEY']).idxmin()
exept0_b = (df[point_a] != 0) & ~df.index.isin([point_a])
point_b = (df.loc[exept0_b, point_a] / df.loc[exept0_b, 'KEY']).idxmin()
exept0_c = (df[point_b] != 0) & ~df.index.isin([point_a, point_b])
point_c = (df.loc[exept0_c, point_b] / df.loc[exept0_c, 'KEY']).idxmin()

list = [point_a, point_b, point_c]
[4, 1, 2]

import pandas as pd
import numpy as np

d = df.drop('KEY',1).div(df['KEY'], axis=0)
d.values[np.diag_indices_from(d)] = np.inf

In [42]: d
Out[42]:
           1          2          3          4          5
1        inf   5.909091   8.636364   7.272727   4.454545
2   7.222222        inf   8.666667   7.666667   1.777778
3  15.833333  13.000000        inf   9.166667  14.666667
4   4.444444   3.833333   3.055556        inf   4.833333
5  24.500000   8.000000  44.000000  43.500000        inf

res = []

def f(col):
    ret = col.loc[~col.index.isin(res)].idxmin()
    if ret not in res:
        res.append(ret)

_ = d.apply(f)

print(res)

[4, 1, 2, 3, 5]

print(res[:3])

# [4, 1, 2]

exept0[0] = df[2] != 0
point[0] = (df.loc[exept0[0], 2] / df.loc[exept0[0], 'KEY']).idxmin()

exept0[1] = (df[point[0]] != 0) & ~df.index.isin([point[0]])
point[1] = (df.loc[exept0[1], point[0]] / df.loc[exept0[1], 'KEY']).idxmin()

exept0[2] = (df[point[1]] != 0) & ~df.index.isin([point[0], point[1]])
point[2] = (df.loc[exept0[2], point[1]] / df.loc[exept0[2], 'KEY']).idxmin()

exept0 = []
point = []

exept0.append(df[2] != 0)
point.append((df.loc[exept0[0], 2] / df.loc[exept0[-1], 'KEY']).idxmin())

exept0.append((df[point[-1]] != 0) & ~df.index.isin([point[0]]))
point.append((df.loc[exept0[-1], point[-1]] / df.loc[exept0[-1], 'KEY']).idxmin())

exept0.append((df[point[-1]] != 0) & ~df.index.isin([point[0], point[1]]))
point.append((df.loc[exept0[-1], point[-1]] / df.loc[exept0[-1], 'KEY']).idxmin())

exept0 = []
point = []

exept0.append(df[2] != 0)
point.append((df.loc[exept0[0], 2] / df.loc[exept0[-1], 'KEY']).idxmin())

exept0.append((df[point[-1]] != 0) & ~df.index.isin(point))
point.append((df.loc[exept0[-1], point[-1]] / df.loc[exept0[-1], 'KEY']).idxmin())

exept0.append((df[point[-1]] != 0) & ~df.index.isin(point))
point.append((df.loc[exept0[-1], point[-1]] / df.loc[exept0[-1], 'KEY']).idxmin())

# Нулевой этап объединили с инициализацией
exept0 = [df[2] != 0]
point = [(df.loc[exept0[0], 2] / df.loc[exept0[-1], 'KEY']).idxmin()]

# Остались этапы от 1 до n
for i in range(1, n):
    exept0.append((df[point[-1]] != 0) & ~df.index.isin(point))
    point.append((df.loc[exept0[-1], point[-1]] / df.loc[exept0[-1], 'KEY']).idxmin())

# На выходе списки длиной n