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0. Leave f and g alone capacities from positive numbers to positive numbers. f(n) is O(g(n)) if there
are positive constants C and k with the end goal that:
f(n) ≤ C g(n) at whatever point n > k
f(n) is O(g(n)) ≡ ∃C ∃k ∀n (n > k → f(n) ≤ C g(n)) To demonstrate enormous Oh, pick esteems for C and k and demonstrate n > k suggests f(n) ≤ C g(n).
1. a.
An enchantment square of request n is a plan of n2 numbers, typically unmistakable whole numbers, in a square, with the end goal that the n numbers in all lines, all sections, and the two diagonals aggregate to a similar steady. An enchantment square contains the whole numbers from 1 to n2. The consistent total in each line, segment and askew are known as the sorcery steady or wizardry total, M. The enchantment consistent of a typical wizardry square relies just upon n and has the accompanying worth:
M = n(n2+1)/2
For typical sorcery squares of request n = 3, 4, 5, ...,
the enchantment constants are: 15, 34, 65, 111, 175, 260, ...
Here will talk about how automatically we can create an enchantment square of size n. This methodology just considers odd upsides of n and doesn't work for even numbers. Before we go further, consider the underneath models:
Wizardry Square of size 3
- - - - - - - - - - - -
2 7 6
9 5 1
4 3 8
Total in each line and every section = 3*(32+1)/2 = 15
Enchantment Square of size 5
- - - - - - - - - - -
9 3 22 16 15
2 21 20 14 8
25 19 13 7 1
18 12 6 5 24
11 10 4 23 17
Total in each line and every section = 5*(52+1)/2 = 65
Enchantment Square of size 7
- - - - - - - - - - -
20 12 4 45 37 29 28
11 3 44 36 35 27 19
2 43 42 34 26 18 10
49 41 33 25 17 9 1
40 32 24 16 8 7 48
31 23 15 14 6 47 39
22 21 13 5 46 38 30
Total in each line and every section = 7*(72+1)/2 = 175
b. Pseudocode is regularly utilized in all different fields of...