Generate All Unique 3‑Digit Numbers and Compute Tiered Bonuses with Python

Example 1

Problem: With the digits 1, 2, 3, 4, how many distinct three‑digit numbers without repeated digits can be formed, and what are they?

Analysis: All three positions (hundreds, tens, units) can be filled by 1‑4. Generate every permutation and keep only those where the three digits differ.

<code>#!/usr/bin/python
# -*- coding: UTF-8 -*-
for i in range(1,5):
    for j in range(1,5):
        for k in range(1,5):
            if i != k and i != j and j != k:
                print i, j, k
</code>

Output:

<code>1 2 3
1 2 4
1 3 2
1 3 4
1 4 2
1 4 3
2 1 3
2 1 4
2 3 1
2 3 4
2 4 1
2 4 3
3 1 2
3 1 4
3 2 1
3 2 4
3 4 1
3 4 2
4 1 2
4 1 3
4 2 1
4 2 3
4 3 1
4 3 2
</code>

Example 2

Problem: A company distributes bonuses based on profit I with tiered percentages: up to 100,000 ¥ at 10%; the next 100,000 ¥ at 7.5%; 200,000‑400,000 ¥ at 5%; 400,000‑600,000 ¥ at 3%; 600,000‑1,000,000 ¥ at 1.5%; any amount above 1,000,000 ¥ at 1%. Write a program that reads the monthly profit and outputs the total bonus.

Analysis: Use a number line to locate the profit segment. Define the bonus as a long integer and apply the appropriate rate for each segment.

<code>#!/usr/bin/python
# -*- coding: UTF-8 -*-
i = int(raw_input('净利润:'))
arr = [1000000,600000,400000,200000,100000,0]
rat = [0.01,0.015,0.03,0.05,0.075,0.1]
r = 0
for idx in range(0,6):
    if i > arr[idx]:
        r += (i - arr[idx]) * rat[idx]
        print (i - arr[idx]) * rat[idx]
        i = arr[idx]
print r
</code>

Sample Output (profit = 120,000 ¥):

<code>净利润:120000
1500.0
10000.0
11500.0
</code>