Program Overview
This Python program receives a list of numbers and checks all possible 3-number combinations.
It determines which combinations can form a valid triangle using the triangle inequality rule:
For any three numbers a, b, c, they form a triangle if:
\[
a + b > c,\quad a + c > b,\quad b + c > a
\]
Python Code:
from itertools import combinations
def is_valid_triangle(a, b, c):
return a + b > c and a + c > b and b + c > a
def find_valid_sets(numbers):
valid = []
for combo in combinations(numbers, 3):
if is_valid_triangle(*combo):
valid.append(combo)
return valid
# Run the program
nums = list(map(int, input("Enter numbers separated by space: ").split()))
valid_sets = find_valid_sets(nums)
print(f"Number of valid sets: {len(valid_sets)}")
for s in valid_sets:
print(f"Valid set: {s}")
Sample Output:
Enter numbers separated by space: 3 4 5 6 10
Number of valid sets: 4
Valid set: (3, 4, 5)
Valid set: (3, 5, 6)
Valid set: (4, 5, 6)
Valid set: (5, 6, 10)
Step-by-Step Explanation:
- All 3-number combinations are generated using itertools.combinations
- Each combination is checked against the triangle inequality condition
- Valid sets are collected and displayed