import pandas as pd
import numpy as np

n_rows = 10000  # number of rows in dataframe
n_cat  = 5      # number of categories per column; gives a total of n_cat*n_cat unique combinations

# Dataframe en dictionary used for replacement
convert_df = pd.DataFrame(columns=['c1','c2','value'])
convert_dict = {}

for i in range(n_cat):
    for j in range(n_cat):
        value = int(0.5*(i+j)*(i+j+1)+j)
        convert_dict[(i,j)] = value
        convert_df.loc[j+i*n_cat] = {'c1':i, 'c2':j, 'value':value}

def convert_with_df(df, convert_df):
    df = df.merge(convert_df, on=["c1", "c2"], how="left")
    return df

def convert_with_dict(df, convert_dict):
    # Added copy to preserve original df.
    df = df.copy()
    df['value'] = list(map(convert_dict.get, map(tuple, df[['c1', 'c2']].values)))
    return df

# Create some data and dataframe
data = np.random.randint(low=0, high=n_cat, size=[n_rows, 2])
df1 = pd.DataFrame(data, columns=['c1','c2'])

# Test test..
#df2 = convert_with_df  (df1, convert_df)
#df3 = convert_with_dict(df1, convert_dict)

# --------------------------
# Timing results in iPython:
# In [97]: timeit convert_with_df  (df1, convert_df)
# 6.73 ms ± 79.2 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

# In [98]: timeit convert_with_dict(df1, convert_dict)
# 24.5 ms ± 176 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)