A factorial multiplies every positive integer from one through a given nonnegative integer. Written n!, it counts the permutations generated from n items. section 8.2
Permutation growth
A brute-force traveling-salesman solver evaluates n! possible city orders. Five cities produce 5! = 120 orders; adding a sixth multiplies the work by 6, and adding a seventh multiplies it by 7 again. section 8.2
Factorial growth matters when:
- Generating every permutation for a brute-force search. section 8.2
- Recognizing when exhaustive evaluation becomes infeasible and approximation or other techniques are needed. section 8.2
