Problem:
Minimum Cost Sort You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times. Write a program which reports the minimal total cost to sort the given integers. Input In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0, 1, 2, ... n-1)$ separated by space characters are given. Output Print the minimal cost in a line. Constraints  $1 \leq n \leq 1,000$  $0 \leq w_i\leq 10^4$  $w_i$ are all different  Sample Input 1 5
1 5 3 4 2 Sample Output 1 7 Sample Input 2 4
4 3 2 1 Sample Output 2 10

Solution (Python):
def solve(a, n):
    vmax = 10000
    ans = 0
    all_min = min(a)
    b = sorted(a)
    v = [False] * n

    t = {}
    for i in range(n):
        t[b[i]] = i
    for i in range(n):
        if v[i]:
            continue
        cur = i
        w_sum = 0
        w_min = vmax
        an = 0
        while True:
            v[cur] = True
            an += 1
            v_cur = a[cur]
            w_min = min(w_min, v_cur)
            w_sum += v_cur
            cur = t[v_cur]
            if v[cur]:
                break
        ans += min(w_sum + (an-2) * w_min, w_min + w_sum + (an+1) * all_min)

    return ans


n = int(input())
a = [int(v) for v in input().split()]

ans = solve(a, n)
print(ans)

Solution (Python):
n = int(input())
A = [int(i) for i in input().split()]
B = A.copy()
B.sort()
ans = 0
for i in B:
    ixB = B.index(i)
    counter = 0
    while(True):
        ixA = A.index(i)
        if ixA == ixB:
            break
        else:
            counter += 1
            num = B[ixA]
            ixN = A.index(num)
            A[ixA],A[ixN] = A[ixN],A[ixA]
            ans += A[ixA] + A[ixN]
    tmp = (B[0] - i)*counter + (B[0]+i)*2
    if tmp < 0:
        ans += tmp
print(ans)

Solution (Python):


import sys
import math
import itertools as it
from collections import deque

sys.setrecursionlimit(10000000)

N = input()
A_ = map(int, raw_input().split())
minA = min(A_)
lst = []
for i in range(N):
    lst.append((A_[i], i))
lst.sort()

A = [0] * N
for i in range(N):
    A[lst[i][1]] = (lst[i][0], i)

flag = [False] * N

def func(pos, lst):
    if flag[pos]:
        return
    lst.append(A[pos][0])
    flag[pos] = True
    func(A[pos][1], lst)

ans = 0
for i in range(N):
    if not flag[i]:
        ret = []
        func(i, ret)
        ans += min(min(ret) * (len(ret) - 2) + sum(ret), sum(ret) + min(ret) + minA * (len(ret) + 1))

print ans