B. Soldier and Badges
time limit per test3 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
Colonel has n badges. He wants to give one badge to every of his n soldiers. Each badge has a coolness factor, which shows how much it’s owner reached. Coolness factor can be increased by one for the cost of one coin.
For every pair of soldiers one of them should get a badge with strictly higher factor than the second one. Exact values of their factors aren’t important, they just need to have distinct factors.
Colonel knows, which soldier is supposed to get which badge initially, but there is a problem. Some of badges may have the same factor of coolness. Help him and calculate how much money has to be paid for making all badges have different factors of coolness.
Input
First line of input consists of one integer n (1 ≤ n ≤ 3000).
Next line consists of n integers ai (1 ≤ ai ≤ n), which stand for coolness factor of each badge.
Output
Output single integer — minimum amount of coins the colonel has to pay.
Examples
input
4
1 3 1 4
output
1
input
5
1 2 3 2 5
output
2
Note
In first sample test we can increase factor of first badge by 1.
In second sample test we can increase factors of the second and the third badge by 1.
題解：對序列進行排序，因爲數字只能增大或不變，爲保證每個數都不一樣，那麼後一個一定要比前一個大，把每個數最少的增加量累加起來就是結果。
#include<iostream>
#include<algorithm>
using namespace std;
int main()
{
int a[3010];
int n;
cin >> n;
for (int i = 0; i < n; i++)
cin >> a[i];
sort(a, a + n);
int sumcoin = 0;
int coin; //coin爲當前需要花費的最少金幣個數
for (int i = 1; i < n; i++)
{
if (a[i-1] < a[i])
coin = 0;
else
{
coin = a[i-1] - a[i] + 1;
a[i] += coin;
}
sumcoin += coin;
}
cout << sumcoin << endl;
return 0;
}