How to Generate All 5-Number Combinations Containing Adjacent Values Using Python

Introduction

The author, a Python enthusiast, shares a solution to a fan’s combinatorial question about selecting numbers that contain a pair of consecutive values.

Problem Statement

Given a list of 15 distinct random numbers, choose any 5 numbers such that the selection includes a number a and its immediate successor a+1, where a can be any element of the original list.

Idea

The problem can be tackled in two steps: first generate a set of random numbers, then check whether a randomly chosen pair of consecutive numbers appears together in a 5‑element subset. The author references a Monte Carlo approach to enumerate valid combinations.

Solution

1) Pseudocode

The following pseudocode outlines the overall workflow: generate 14 unique random numbers, add the successor of a randomly chosen number to form 15 numbers, then repeatedly sample 5 numbers and keep those containing both the target pair.

2) Code 1

# coding: utf-8
import random

def quchong(list_data):
    list2 = []
    for i in list_data:
        if i not in list2:
            list2.append(i)
    return list2

# generate 14 unique random numbers
random_14 = random.sample(range(100), 14)
print(random_14)
random_1 = random.choice(random_14)
random_2 = random_1 + 1
random_14.append(random_2)
random_15 = random_14
print(random_1, random_2)

final_list = []
for i in range(100):
    select = [random.choice(random_15) for j in range(5)]
    quchong_select = set(select)
    if random_1 in quchong_select and random_2 in quchong_select:
        final_list.append(quchong_select)

fina_result = quchong(final_list)
print(len(fina_result))

3) Code 2

# -*- coding: utf-8 -*-
import numpy as np
import random

def quchong(list_data):
    list2 = []
    for i in list_data:
        if i not in list2:
            list2.append(i)
    return list2

random_14 = random.sample(range(100), 14)
print(random_14)
random_1 = random.choice(random_14)
random_2 = random_1 + 1
random_14.append(random_2)
random_15 = random_14
print(random_1, random_2)

final_list = []
for i in range(100):
    sub_random_data = np.random.choice(random_15, 5)
    quchong_select = set(sub_random_data)
    if random_1 in quchong_select and random_2 in quchong_select:
        final_list.append(quchong_select)

fina_result = quchong(final_list)
print(len(fina_result))

4) Code 3

# -*- coding: utf-8 -*-
import random
import numpy as np

def get_random15():
    random_14 = random.sample(range(1000), 14)
    print(random_14)
    random_1 = random.choice(random_14)
    random_2 = random_1 + 1
    random_14.append(random_2)
    random_15 = random_14
    print(random_1, random_2)
    get_final_result(random_1, random_2, random_15)

def get_final_result(random_1, random_2, random_15):
    final_list = []
    for i in range(1000):
        sub_random_data = np.random.choice(random_15, 5)
        quchong_select = set(sub_random_data)
        if random_1 in quchong_select and random_2 in quchong_select:
            final_list.append(quchong_select)
    fina_result = quchong(final_list)
    print(len(fina_result))

def quchong(list_data):
    list2 = []
    for i in list_data:
        if i not in list2:
            list2.append(i)
    return list2

if __name__ == '__main__':
    get_random15()

5) Code 4

import random
import numpy as np

def get_random15():
    for i in range(2):
        random_15 = random.sample(range(20), 15)
        get_random5(random_15)

def get_random5(random_15):
    random_5 = []
    for i in range(5):
        random_data = np.random.choice(random_15)
        random_5.append(random_data)
        random_15.remove(random_data)
    for num in random_5:
        random_1 = num
        random_2 = random_1 + 1
        get_final_result(random_1, random_2, random_5)

def get_final_result(random_1, random_2, random_5):
    final_list = []
    if random_1 in random_5 and random_2 in random_5:
        print(random_5)
        final_list.append(random_1)
    result = quchong(final_list)
    print(result)

def quchong(list_data):
    list = []
    for i in list_data:
        if i not in list:
            list.append(i)
    return list

if __name__ == '__main__':
    get_random15()

6) Code 5

# -*- coding: utf-8 -*-
import random
import numpy as np
import time

def get_random15():
    for i in range(100000):
        random_15 = random.sample(range(2000), 15)
        get_random5(random_15)

def get_random5(random_15):
    random_5 = []
    for i in range(5):
        random_data = np.random.choice(random_15)
        random_5.append(random_data)
        random_15.remove(random_data)
    for num in random_5:
        random_1 = num
        random_2 = random_1 + 1
        get_final_result(random_1, random_2, random_5)

def get_final_result(random_1, random_2, random_5):
    final_list = []
    if random_1 in random_5 and random_2 in random_5:
        final_list.append(random_5)
    result = quchong(final_list)
    if result:
        if len(result[0]) == 5:
            final_result.append(result)

def quchong(list_data):
    list = []
    for i in list_data:
        if i not in list:
            list.append(i)
    return list

if __name__ == '__main__':
    start_time = time.time()
    global final_result
    final_result = []
    get_random15()
    final_result = quchong(final_result)
    print("共%d个符合题意的列表" % len(final_result))
    print("分别是：%s" % final_result)
    end_time = time.time()
    used_time = end_time - start_time
    print()
    print("本次程序用时：{}".format(time.strftime('%H(小时):%M（分钟）:%S（秒）', time.gmtime(used_time))))

Conclusion

The Monte Carlo‑based Python solution successfully generates all 5‑element subsets that contain a consecutive pair, but the runtime grows quickly with larger iteration counts or value ranges, highlighting a trade‑off between completeness and performance.