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Given two numbers base value and the exponential value, the task is to find the power of base and exponent modular 10^9+7
Examples:
Example1:
Input:
Given base value = 5 Given exponent value = 3
Output:
The value of the power of base and exponent modular 10^9+7 = 125
Example2:
Input:
Given base value = 3 Given exponent value = 10000
Output:
The value of the power of base and exponent modular 10^9+7 = 895629451
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Below are the ways to find the power of base and exponent modular 10^9+7 for the given base and exponential values:
Method #1: Using While Loop (Static Input)
Approach:
- Give the base value as static input and store it in a variable.
- Give the exponential value as static input and store it in another variable.
- Pass the given base and exponential values as the arguments to the exponentl_squaring() function and store it in a variable.
- Take a variable to say numb and initialize its value with 1000000007(10^9+7).
- Create a function to say exponentl_squaring() which takes the given two base and exponential values as the arguments and returns the value of the power of base and exponent modular 10^9+7.
- Inside the function, take a variable say p, and initialize its value to 1.
- Loop until the given exponential value is greater than 0 using the while loop.
- Check if the given exponential value is odd using the if conditional statement.
- If it is true, multiply p with the given base value and store it in another variable.
- Calculate the value of the above result modulus numb(10^9+7) and store it in the same variable p.
- Multiply the given base value with itself and apply the modulus operator with 10^9+7(numb).
- Store it in the same variable given base value.
- Divide the given exponential value by 2 and convert it to an integer using the int() function.
- Store it in the same variable given exponential value.
- Return the value of p modulus 10^9+7.
- Print the value of the power of base and exponent modular 10^9+7.
- The Exit of the Program.
Below is the implementation:
# Take a variable to say numb and initialize its value with 1000000007(10^9+7).
numb = 1000000007
# Create a function to say exponentl_squaring() which takes the given two base and
# exponential values as the arguments and returns the value of the power of base and
# exponent modular 10^9+7.
def exponentl_squaring(gvn_baseval, gvn_exponentlval):
# Inside the function, take a variable say p, and initialize its value to 1.
p = 1
# Loop until the given exponential value is greater than 0 using the while loop.
while(gvn_exponentlval > 0):
# Check if the given exponential value is odd using the if conditional statement.
if (gvn_exponentlval % 2 != 0):
# If it is true, multiply p with the given base value and store it in another
# variable.
k = p * gvn_baseval
# Calculate the value of the above result modulus numb(10^9+7) and store it in the
# same variable p.
p = k % numb
# Multiply the given base value with itself and apply the modulus operator with
# 10^9+7(numb).
# Store it in the same variable given base value.
gvn_baseval = (gvn_baseval * gvn_baseval) % numb
# Divide the given exponential value by 2 and convert it to an integer using the
# int() function.
# Store it in the same variable given exponential value.
gvn_exponentlval = int(gvn_exponentlval / 2)
# Return the value of p modulus 10^9+7.
return p % numb
# Give the base value as static input and store it in a variable.
gvn_baseval = 5
# Give the exponential value as static input and store it in another variable.
gvn_exponentlval = 3
# Pass the given base and exponential values as the arguments to the exponentl_squaring()
# function and store it in a variable.
rslt = exponentl_squaring(gvn_baseval, gvn_exponentlval)
# Print the value of the power of base and exponent modular 10^9+7.
print("The value of the power of base and exponent modular 10^9+7 = ", rslt)
Output:
The value of the power of base and exponent modular 10^9+7 = 125
Method #2: Using While loop (User Input)
Approach:
- Give the base value as user input using the int(input()) function and store it in a variable.
- Give the exponential value as user input using the int(input()) function and store it in another variable.
- Pass the given base and exponential values as the arguments to the exponentl_squaring() function and store it in a variable.
- Take a variable to say numb and initialize its value with 1000000007(10^9+7).
- Create a function to say exponentl_squaring() which takes the given two base and exponential values as the arguments and returns the value of the power of base and exponent modular 10^9+7.
- Inside the function, take a variable say p, and initialize its value to 1.
- Loop until the given exponential value is greater than 0 using the while loop.
- Check if the given exponential value is odd using the if conditional statement.
- If it is true, multiply p with the given base value and store it in another variable.
- Calculate the value of the above result modulus numb(10^9+7) and store it in the same variable p.
- Multiply the given base value with itself and apply the modulus operator with 10^9+7(numb).
- Store it in the same variable given the base value.
- Divide the given exponential value by 2 and convert it to an integer using the int() function.
- Store it in the same variable given exponential value.
- Return the value of p modulus 10^9+7.
- Print the value of the power of base and exponent modular 10^9+7.
- The Exit of the Program.
Below is the implementation:
# Take a variable to say numb and initialize its value with 1000000007(10^9+7).
numb = 1000000007
# Create a function to say exponentl_squaring() which takes the given two base and
# exponential values as the arguments and returns the value of the power of base and
# exponent modular 10^9+7.
def exponentl_squaring(gvn_baseval, gvn_exponentlval):
# Inside the function, take a variable say p, and initialize its value to 1.
p = 1
# Loop until the given exponential value is greater than 0 using the while loop.
while(gvn_exponentlval > 0):
# Check if the given exponential value is odd using the if conditional statement.
if (gvn_exponentlval % 2 != 0):
# If it is true, multiply p with the given base value and store it in another
# variable.
k = p * gvn_baseval
# Calculate the value of the above result modulus numb(10^9+7) and store it in the
# same variable p.
p = k % numb
# Multiply the given base value with itself and apply the modulus operator with
# 10^9+7(numb).
# Store it in the same variable given base value.
gvn_baseval = (gvn_baseval * gvn_baseval) % numb
# Divide the given exponential value by 2 and convert it to an integer using the
# int() function.
# Store it in the same variable given exponential value.
gvn_exponentlval = int(gvn_exponentlval / 2)
# Return the value of p modulus 10^9+7.
return p % numb
# Give the base value as user input using the int(input()) function and store it in a variable.
gvn_baseval = int(input("Enter some random number = "))
# Give the exponential value as user input using the int(input()) function and
# store it in another variable.
gvn_exponentlval = int(input("Enter some random number = "))
# Pass the given base and exponential values as the arguments to the exponentl_squaring()
# function and store it in a variable.
rslt = exponentl_squaring(gvn_baseval, gvn_exponentlval)
# Print the value of the power of base and exponent modular 10^9+7.
print("The value of the power of base and exponent modular 10^9+7 = ", rslt)
Output:
Enter some random number = 3 Enter some random number = 10000 The value of the power of base and exponent modular 10^9+7 = 895629451