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Find the maximum number of composite summands of a number in Python
Suppose we have a given number N that in range (1<=N<=10^9), we have to represent N as a sum of the largest possible number of composite summands and return this largest number, otherwise when we cannot find any split, then return -1.
So, if the input is like 16, then the output will be 4 as 16 can be written as 4 + 4 + 4 + 4 or 8 + 8, but (4 + 4 + 4 + 4) has maximum summands.
To solve this, we will follow these steps −
max_val := 16
Define a function pre_calc() . This will take
table := a list of size max_val, then store -1 at each position
table[0] := 0
v := [4, 6, 9]
for i in range 1 to max_val, increase by 1, do
for k in range 0 to 2, do
j := v[k]
if i >= j and table[i - j] is not -1, then
table[i] := maximum of table[i], table[i - j] + 1
return table
Define a function max_summ() . This will take table, n
if n < max_val, then
return table[n]
otherwise,
t := integer of ((n - max_val) / 4) + 1
return t + table[n - 4 * t]
From the main method, do the following −
table := pre_calc()
display max_summ(table, n)
Example
Let us see the following implementation to get better understanding −
global max_val max_val = 16 def pre_calc(): table = [-1 for i in range(max_val)] table[0] = 0 v = [4, 6, 9] for i in range(1, max_val, 1): for k in range(3): j = v[k] if (i >= j and table[i - j] != -1): table[i] = max(table[i], table[i - j] + 1) return table def max_summ(table, n): if (n < max_val): return table[n] else: t = int((n - max_val) / 4)+ 1 return t + table[n - 4 * t] n = 16 table = pre_calc() print(max_summ(table, n))
Input
16
Output
4
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