# TopCoder SRM 733 Easy. MinimizeAbsoluteDifferenceDiv1

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## solution

${}_5C4 \cdot 4!$個すべて試して間に合う。$O(1)$。

## note

• overflowを警戒してPythonで検証コード書いたけど何事もなかった
• そのままPythonを提出できればもっと安心なんだけど対応versionすら知らないのでかえって危険かなと思った
• 「unused code多いんだけど」と怒られた。「いや多くないだろ」と言いながら削った。納得がいかない
• editorial: https://www.topcoder.com/blog/single-round-match-733-editorials/

## implementation

#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; (i) < int(n); ++ (i))
#define ALL(x) begin(x), end(x)
typedef long long ll;
using namespace std;
class MinimizeAbsoluteDifferenceDiv1 { public: vector<int> findTuple(vector<int> x); };

struct rational { int num, den; };
rational make_rational(int num, int den = 1) { return (rational) { num, den }; }
rational operator - (rational a, rational b) { return make_rational(a.num *(ll) b.den - b.num *(ll) a.den, a.den *(ll) b.den); }
bool operator < (rational a, rational b) { return a.num *(ll) b.den < b.num *(ll) a.den; }
bool operator == (rational a, rational b) { return a.num == b.num and a.den == b.den; }

rational get_score(int a, int b, int c, int d) {
auto r = make_rational(a, b) - make_rational(c, d);
if (r < make_rational(0)) r = make_rational(0) - r;
return r;
}
vector<int> MinimizeAbsoluteDifferenceDiv1::findTuple(vector<int> x) {
vector<int> result;
rational highscore;
REP (choose, 5) {
vector<int> perm;
REP (i, 5) if (i != choose) {
perm.push_back(i);
}
do {
rational score = get_score(x[perm[0]], x[perm[1]], x[perm[2]], x[perm[3]]);
if (result.empty() or score < highscore or (score == highscore and perm < result)) {
result = perm;
highscore = score;
}
} while (next_permutation(ALL(perm)));
}
return result;
}