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Program to find expected growth of virus after time t in Python
Suppose there is a dangerous virus and that grows rapidly. The probability of number of virus cells growing by a factor x is 0.5 and also the probability of number of virus cells growing by a factor y is 0.5. Now if there was a single cell of virus at beginning, then calculate the expected number of virus cells after t time. If the answer is too large, then mod result by 10^9+7.
So, if the input is like x = 2, y = 4, t = 1, then the output will be 3, because initially, the virus has only one cell. After x time, with probability 0.5, its size is doubled (x2) and, with probability of the other 0.5, its size grows by 4 times. Thus, the expected number of virus cell after time t = 1 is: 0.5*2*1 + 0.5*4*1 = 3.
To solve this, we will follow these steps −
- m = 10^9+7
- factor := floor of (x+y)/2
- res:= 1
- while t > 0, do
- if t is odd, then
- res :=(res*factor) mod m
- factor :=(factor*factor) mod m
- t := floor of t/2
- if t is odd, then
- return res
Example
Let us see the following implementation to get better understanding −
m=10**9+7
def solve(x, y, t):
factor=(x+y)//2
res=1
while t > 0:
if t % 2:
res = (res*factor) % m
factor = (factor*factor) % m
t = t// 2
return res
x = 2
y = 4
t = 1
print(solve(x, y, t))Input
2, 4, 1
Output
3
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