POJ 1804 Brainman

Brainman

Time Limit: 1000MS Memory Limit: 30000K
Total Submissions: 8755 Accepted: 4723

Description

Background

Raymond Babbitt drives his brother Charlie mad. Recently Raymond counted 246 toothpicks spilled all over the floor in an instant just by glancing at them. And he can even count Poker cards. Charlie would love to be able to do cool things like that, too. He wants to beat his brother in a similar task.

Problem

Here’s what Charlie thinks of. Imagine you get a sequence of N numbers. The goal is to move the numbers around so that at the end the sequence is ordered. The only operation allowed is to swap two adjacent numbers. Let us try an example:
Start with: 2 8 0 3
swap (2 8) 8 2 0 3
swap (2 0) 8 0 2 3
swap (2 3) 8 0 3 2
swap (8 0) 0 8 3 2
swap (8 3) 0 3 8 2
swap (8 2) 0 3 2 8
swap (3 2) 0 2 3 8
swap (3 8) 0 2 8 3
swap (8 3) 0 2 3 8

So the sequence (2 8 0 3) can be sorted with nine swaps of adjacent numbers. However, it is even possible to sort it with three such swaps:
Start with: 2 8 0 3
swap (8 0) 2 0 8 3
swap (2 0) 0 2 8 3
swap (8 3) 0 2 3 8

The question is: What is the minimum number of swaps of adjacent numbers to sort a given sequence?Since Charlie does not have Raymond’s mental capabilities, he decides to cheat. Here is where you come into play. He asks you to write a computer program for him that answers the question. Rest assured he will pay a very good prize for it.

Input

The first line contains the number of scenarios.
For every scenario, you are given a line containing first the length N (1 <= N <= 1000) of the sequence,followed by the N elements of the sequence (each element is an integer in [-1000000, 1000000]). All numbers in this line are separated by single blanks.

Output

Start the output for every scenario with a line containing “Scenario #i:”, where i is the number of the scenario starting at 1. Then print a single line containing the minimal number of swaps of adjacent numbers that are necessary to sort the given sequence. Terminate the output for the scenario with a blank line.

Sample Input

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3
4
5
4
4 2 8 0 3
10 0 1 2 3 4 5 6 7 8 9
6 -42 23 6 28 -100 65537
5 0 0 0 0 0

Sample Output

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5
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7
8
9
10
11
Scenario #1:
3

Scenario #2:
0

Scenario #3:
5

Scenario #4:
0

Idea

这题求逆序对,可以用改动归并排序来解决。POJ上的题目,原题地址:http://poj.org/problem?id=1804

Code

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#include <stdio.h>
#define MAXN 1005
#define MAX 1000005

void MergeInversion(int a[], int p, int r);
void Merge(int a[], int p, int q, int r);

int ans;

int main(void)
{
int i , j, n, x;
int ar[MAXN];
//freopen("input.txt", "r", stdin);
scanf("%d", &x);
for(i = 1; i <= x; i++)
{
ans = 0;
scanf("%d", &n);
for(j = 1; j <= n; j++)
scanf("%d", &ar[j]);
MergeInversion(ar, 1, n);
printf("Scenario #%d:\n%d\n\n", i, ans);
}
}

void MergeInversion(int a[], int p, int r)
{
int q;
if(p < r)
{
q = (p + r) / 2;
MergeInversion(a, p, q);
MergeInversion(a, q + 1, r);
Merge(a, p, q, r);
}
}

void Merge(int a[], int p, int q, int r)
{
int i, j, k;
int m[q - p + 2], n[r - q + 1];

for(i = 0; i < q - p + 1; i++)
m[i] = a[p + i];

for(j = 0; j < r - q; j++)
n[j] = a[q + j + 1];

m[i] = n[j] = MAX;
i = j = 0;
for( k = p; k <= r; k++)
{
if(m[i] <= n[j])
a[k] = m[i++];
else
{
a[k] = n[j++];
ans += q - (p + i) + 1;
}
}
}
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