20161022 Noip Simulation Game T2 Problem Solving report

Traveler questions

"Problem description"

Lahub is a fan of the traveler who wants to be a real traveler, so he plans to start a trip. Lahub wanted to visit n destinations (all on a straight line). Lahub began his travels at the beginning. The distance between the first destination and the starting point is ai km (AI is a nonnegative integer). There are no two destinations and the same distance from the starting point.

The journey from the I destination to the first J destination is |ai-aj| km. We call the order of visits to n destinations a "trip". Lahub can visit any order he wants to visit, but each destination has and can only be visited once (the order of visits is N).

Lahub writes all possible "travels" on a piece of paper and notes the distance each "trip" is going to take. He is interested in the average value of the sum of all "travel" distances. But he thought the calculation was too dull, so he asked you for help.

"Input Format"

The first line is a positive integer n.

The second row n non-negative integers a1,a2,...., an (1≤ai≤10^7).

"Output Format"

Two integers, the answer is output in the simplest fractional form, the first is the numerator and the second is the denominator.

"Input Sample"

3

2 3 5

"Output Example"

22 3

the sample Tips "

There are 6 possible travel examples:

[2, 3, 5]: The distance to travel: |2–0| + |3–2| + |5–3| = 5;

[2, 5, 3]: |2–0| + |5–2| + |3–5| = 7;

[3, 2, 5]: |3–0| + |2–3| + |5–2| = 7;

[3, 5, 2]: |3–0| + |5–3| + |2–5| = 8;

[5, 2, 3]: |5–0| + |2–5| + |3–2| = 9;

[5, 3, 2]: |5–0| + |3–5| + |2–3| = 8.

The answer is 1/6 * (5+7+7+8+9+8) =44/6=22/3

"Data Range"

30% n<=10

50% n<=1000

100% n<=100000

————————————— Split Line —————————————

Each point contributes to the answer:

Answer:

1#include"bits/stdc++.h"2 3 using namespacestd;4typedefLong LongQaq;5 Const intMAXN = 1e6 +1e3;6 7 Qaq GCD (Qaq x, Qaq y) {8          while(x ^= y ^= x ^= y%=x);9         returny;Ten } One inta[MAXN]; AInlineintINPUT () { -         intx =0, F =1;CharCH =GetChar (); -          while(Ch <'0'||'9'< CH) {if(ch = ='-') F =-1; CH =GetChar ();} the          while('0'<= CH && Ch <='9') {x = (x <<1) + (x <<3) + CH-'0'; CH =GetChar ();} -         returnX *F; - } -  + intMain () { - Qaq N; +N =INPUT (); A          for(intI=1; I<=n; ++i) { ata[I] =INPUT (); -         } -Qaq sum =0 ; -          -Stable_sort (A +1, A + N +1 ) ; -          in          for(intI=1; I<=n; ++i) { -Sum + = (QAQ) a[i] * (4*i-2*n-1 ) ; to         } +Qaq D =GCD (sum, N); -cout << sum/d <<' '<< n/d <<Endl; the         return 0 ;  *}

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2016-10-25 18:07:05

20161022 Noip Simulation Game T2 Problem Solving report