2.1 sort3三值排序

Sorting a Three-Valued Sequence
IOI'96 - Day 2

Sorting is one of the most frequently performed computational tasks.Consider the special sorting problem in which the records to be sortedhave at most three different key values. This happens for instancewhen we sort medalists of a competition according to medal value, thatis, gold medalists come first, followed by silver, and bronze medalistscome last.

In this task the possible key values are the integers 1, 2 and 3.The required sorting order is non-decreasing. However, sorting has tobe accomplished by a sequence of exchange operations. An exchangeoperation, defined by two position numbers p and q, exchanges the elementsin positions p and q.

You are given a sequence of key values. Write a program that computesthe minimal number of exchange operations that are necessary to makethe sequence sorted.

PROGRAM NAME: sort3

INPUT FORMAT

Line 1: N (1 <= N <= 1000), the number ofrecords to be sorted Lines 2-N+1: A single integer from the set {1, 2, 3}

SAMPLE INPUT (file sort3.in)

9
2
2
1
3
3
3
2
3
1

OUTPUT FORMAT

A single line containing the number of exchanges required

SAMPLE OUTPUT (file sort3.out)

4

/*ID: xdzhbin1LANG: C++TASK: sort3*/#include <fstream>#include <vector>#include <algorithm>using namespace std;int max(int a,int b){return a>b?a:b;}int min(int a,int b){return a<b?a:b;}int main(){int n;int i,j;vector<int> v1,v2;int pair[3][3];ifstream in("sort3.in");ofstream out("sort3.out");in>>n;v1.resize(n);for (i=0; i<n; i++){in>>v1[i];}v2 = v1;sort(v2.begin(),v2.end());for (i=0; i<3; i++){for (j=0; j<3; j++){pair[i][j] = 0;}}for (i=0; i<v1.size(); i++){if (v1[i]!=v2[i]){pair[v1[i]-1][v2[i]-1]++;}}int nSwitch = 0;nSwitch += min(pair[0][1],pair[1][0]);nSwitch += min(pair[0][2],pair[2][0]);nSwitch += min(pair[1][2],pair[2][1]);nSwitch += 2*(max(pair[0][1],pair[1][0]) - min(pair[0][1],pair[1][0]));out<<nSwitch<<endl;return 0;}