minimumSwap.py

# You are given an unordered array consisting of consecutive integers  [1, 2, 3, ..., n] without any duplicates. You are allowed to swap any two elements. Find the minimum number of swaps required to sort the array in ascending order.

# Example


# Perform the following steps:

# i   arr                         swap (indices)
# 0   [7, 1, 3, 2, 4, 5, 6]   swap (0,3)
# 1   [2, 1, 3, 7, 4, 5, 6]   swap (0,1)
# 2   [1, 2, 3, 7, 4, 5, 6]   swap (3,4)
# 3   [1, 2, 3, 4, 7, 5, 6]   swap (4,5)
# 4   [1, 2, 3, 4, 5, 7, 6]   swap (5,6)
# 5   [1, 2, 3, 4, 5, 6, 7]
# It took  swaps to sort the array.

# Function Description

# Complete the function minimumSwaps in the editor below.

# minimumSwaps has the following parameter(s):

# int arr[n]: an unordered array of integers
# Returns

# int: the minimum number of swaps to sort the array
# Input Format

# The first line contains an integer, , the size of .
# The second line contains  space-separated integers .

# Constraints

# Sample Input 0

# 4
# 4 3 1 2
# Sample Output 0

# 3
# Explanation 0

# Given array 
# After swapping  we get 
# After swapping  we get 
# After swapping  we get 
# So, we need a minimum of  swaps to sort the array in ascending order.

# Sample Input 1

# 5
# 2 3 4 1 5
# Sample Output 1

# 3
# Explanation 1

# Given array 
# After swapping  we get 
# After swapping  we get 
# After swapping  we get 
# So, we need a minimum of  swaps to sort the array in ascending order.

# Sample Input 2

# 7
# 1 3 5 2 4 6 7
# Sample Output 2

# 3
# Explanation 2

# Given array 
# After swapping  we get 
# After swapping  we get 
# After swapping  we get 
# So, we need a minimum of  swaps to sort the array in ascending order.

# my solution
#!/bin/python3

import math
import os
import random
import re
import sys

# Complete the minimumSwaps function below.
def minimumSwaps(arr):
    min_swap = 0
    for i in range(len(arr)):
        min_index = i
        for j in range(i+1, len(arr)):
            if arr[min_index] > arr[j]:
                min_index = j
        if arr != sorted(arr) and arr[i] > arr[min_index]:
            arr[i], arr[min_index] = arr[min_index], arr[i]
            min_swap += 1
    return min_swap

It passes the test on Hackerrank but when I submit it times out because the code takes too long to run.
How can improve this code to make it more efficient so it can run in a shorter time?