Suppose we have a number N; we have to find factors of N and return only the product of four factors of N such that −
The sum of the four factors is same as N.
The product of the four factors is maximum.
All four factors can be equal to each other to maximize the product.
So, if the input is like N = 60, then the output will be 50625 as all the factors are → 1 2 3 4 5 6 10 12 15 20 30 60 and their product is 50625, as we 15 has been selected four times to make product largest.
To solve this, we will follow these steps −
my_map := a new map
v := a new list, v1 := a new list
for i in range 1 to the ceiling of square root of (n) + 1, do
if n mod i is same as 0, then
insert i at the end of v
if i is not same as integer part of (n / i) and i is not same as 1, then
insert integer part of (n / i) at the end of v
s := size of v
maximum := -1
map1 := an array of size (n + 5) fill this with 0
for i in range 0 to s, do
for j in range i to s, do
if v[i] + v[j] < n , then
insert v[i] + v[j] at the end of v1
map1[v[i] + v[j]] := [v[i], v[j]]
my_map[v[i] + v[j]] := 1
s := size of v1
for i in range 0 to s, do
element := n - (v1[i])
if element in my_map, then
a := map1[v1[i], 0]
b := map1[v1[i], 1]
c := map1[n - v1[i], 0]
d := map1[n - v1[i], 1]
maximum := maximum of a * b * c * d, maximum
if maximum is same as -1, then
display "Not Possible"
otherwise,
display maximum
Example
Let us see the following implementation to get better understanding −
from math import sqrt, ceil, floor
def get_product(n):
my_map = dict()
v = []
v1 = []
for i in range(1,ceil(sqrt(n)) + 1):
if (n % i == 0):
v.append(i)
if (i != (n // i) and i != 1):
v.append(n // i)
s = len(v)
maximum = -1
map1 = [0]*(n + 5)
for i in range(s):
for j in range(i, s):
if (v[i] + v[j] < n):
v1.append(v[i] + v[j])
map1[v[i] + v[j]] =[v[i], v[j]]
my_map[v[i] + v[j]] = 1
s = len(v1)
for i in range(s):
element = n - (v1[i])
if (element in my_map):
a = map1[v1[i]][0]
b = map1[v1[i]][1]
c = map1[n - v1[i]][0]
d = map1[n - v1[i]][1]
maximum = max(a * b * c * d, maximum)
if (maximum == -1):
print("Not Possible")
else :
print("Maximum product", maximum)
n = 60
get_product(n)Input
60
Output
Maximum product 50625