I was solving a problem "Sorting a three value sequence" USACO training gateway. I managed to solve the problem on my own. But in analysis section I found a solution given below, I was unable to understand whats the use of 2*(max(s12, s21)- min(s12, s21). plz explain me I am a newbie ?
#include <fstream>
using namespace std;
int min (int a, int b) { return a < b ? a : b; }
int max (int a, int b) { return a > b ? a : b; }
int main () {
int s[1024];
int n;
int sc[4] = {0};
ifstream fin("sort3.in");
ofstream fout("sort3.out");
fin>>n;
for (int i = 0; i < n; i++) {
fin>>s[i];
sc[s[i]]++;
}
int s12 = 0, s13 = 0, s21 = 0, s31 = 0, s23 = 0, s32 = 0;
for (int i = 0; i < sc[1]; i++){
if (s[i] == 2) s12++;
if (s[i] == 3) s13++;
}
for (int i = sc[1]; i < sc[1]+sc[2]; i++){
if (s[i] == 1) s21++;
if (s[i] == 3) s23++;
}
for (int i = sc[1]+sc[2]; i < sc[1]+sc[2]+sc[3]; i++){
if (s[i] == 1) s31++;
if (s[i] == 2) s32++;
}
fout<<min(s12, s21)+min(s13, s31)+min(s23, s32) +
2*(max(s12, s21) - min(s12, s21))<<endl;
return 0;
}