acm/icpc live archive 2481, world final 2002 problem h. silly sort

Your younger brother has an assignment and needs some help. His teacher gave him a sequence of numbers to be sorted in ascending order. During the sorting process, the places of two numbers can be interchanged. Each interchange has a cost, which is the sum of the two numbers involved.

You must write a program that determines the minimal cost to sort the sequence of numbers.

Input 

The input file contains several test cases. Each test case consists of two lines. The first line contains a single integer n (n >1), representing the number of items to be sorted. The second line contains n different integers (each positive and less than 1000), which are the numbers to be sorted.

The input is terminated by a zero on a line by itself.

Output 

For each test case, the output is a single line containing the test case number and the minimal cost of sorting the numbers in the test case.

Place a blank line after the output of each test case.

Sample Input 

3 
3 2 1 
4 
8 1 2 4 
5 
1 8 9 7 6 
6 
8 4 5 3 2 7 
0 

Sample Output 

Case 1: 4 

Case 2: 17 

Case 3: 41 

Case 4: 34 

黑書 247 頁

把數據排序，分割成若干個羣，在羣裏，每個置換操作恢復一個數字的位置。

恢復一個羣有兩種辦法：

1。引入全局最小值到羣裏，用最小值每次置換恢復一個數字的位置；

2。不引入全局最小值，用羣裏最小值，每次置換恢復一個數字的位置。

#include <cstdio>
#include <cstdlib>
#include <cassert>
#include <cstring>
#include <algorithm>

#define SZ_MAX 100000

int num [SZ_MAX];
int sorted [SZ_MAX];
int sz;
int globMin;

#define NUM_MAX 1010

void Sort () {
    static int cnt [1010];
    memset (cnt, 0, sizeof (cnt));
    for (int i=0; i<sz; ++i) {
        ++cnt [num [i]];
    }
    int ind = 0;
    for (int i=0; i<NUM_MAX; ++i) {
        while (cnt[i]--) {
            sorted [ind++] = i;
        }
    }
    assert (ind == sz);
#ifdef _DEBUG
    for (int i=0; i<sz; ++i) {
        printf ("%d%s", sorted[i], i==sz-1 ? "\n" : " ");
    }
#endif
}

int BinSearch (int n) {
    int lo = 0;
    int hi = sz - 1;
    while (lo < hi) {
        int mid = (lo + hi) / 2;
        if (sorted [mid] < n) {
            lo = mid + 1;
        } else {
            hi = mid;
        }
    }
    assert (sorted [lo] >= n);
    assert (lo == 0 || sorted [lo - 1] < n);
    return lo;
}

void Solve () {
    if (scanf ("%d", &sz) == EOF || !sz) {
        exit (0);
    }
    globMin = 100000;
    for (int i=0; i<sz; ++i) {
        scanf ("%d", &num[i]);
        globMin = std::min (globMin, num [i]);
    }
    Sort ();

    static bool marked [SZ_MAX];
    memset (marked, 0, sizeof (marked));

    int cost = 0;

    for (int i=0; i<sz; ++i) {
        if (marked [i] || sorted [i] == num [i]) {
            continue;
        }
        int k = i;
        int sum = 0;
        int troopMin = 100000;
        int troopSz = 0;
        do {
#ifdef _DEBUG
            printf ("i = %d, k = %d\n", i, k);
#endif
            troopMin = std::min (troopMin, sorted [k]);
            sum += sorted [k];
            assert (! marked [k]);
            marked [k] = true;
            ++troopSz;
            k = BinSearch (num [k]);
            while (k < sz && (sorted [k] == num [k] || marked [k]) && i != k) {
                ++k;
            }
            assert (k < sz);
        } while (k != i);

        cost += sum + std::min ((troopSz + 1) * globMin + troopMin, (troopSz - 2) * troopMin);
#ifdef _DEBUG
        printf ("cost = %d\n", cost);
#endif
    }

    static int cs = 0;
    printf ("Case %d: %d\n\n", ++cs, cost);
}

int main () {
    while (true) {
        Solve ();
    }
    return 0;
}