Permutation p is an ordered set of integers p1, p2, ..., pn, consisting of n distinct positive integers, each of them doesn't exceed n. We'll denote the i-th element of permutation p as pi. We'll call number n the size or the length of permutation p1, p2, ..., pn.
You have a sequence of integers a1, a2, ..., an. In one move, you are allowed to decrease or increase any number by one. Count the minimum number of moves, needed to build a permutation from this sequence.
The first line contains integer n (1 ≤ n ≤ 3·105) — the size of the sought permutation. The second line contains n integers a1, a2, ..., an ( - 109 ≤ ai ≤ 109).
Print a single number — the minimum number of moves.
Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
2 3 0
2
3 -1 -1 2
6
In the first sample you should decrease the first number by one and then increase the second number by one. The resulting permutation is (2, 1).
In the second sample you need 6 moves to build permutation (1, 3, 2).
思路:对于若a[i]满足0<a[i]<=n,则标记tag[a[i]]=1,否则tag[a[i]]=1.对于集合A={a[i]|a[i]<=0 || a[i]>n},进行不降序排列,集合B=[1,n]-{a[i]|0<a[i]<=n}也不降序排列,A中元素转化为B中位置对应相同的元素。
AC Code:
1 #include <iostream> 2 #include <fstream> 3 #include <string> 4 #include <set> 5 #include <map> 6 #include <vector> 7 #include <stack> 8 #include <queue> 9 #include <cmath> 10 #include <cstdio> 11 #include <cstring> 12 #include <algorithm> 13 #include <utility> 14 using namespace std; 15 #define ll long long 16 #define cti const int 17 #define ctll const long long 18 #define dg(i) cout << '*' << i << endl; 19 20 int p[300002], pi; 21 bool tag[300002]; 22 23 int main() 24 { 25 int n, x; 26 ll cnt; 27 while(scanf("%d", &n) != EOF) 28 { 29 memset(tag, false, sizeof(tag)); 30 pi = 0; 31 for(int i = 0; i < n; i++) 32 { 33 scanf("%d", &x); 34 if(x < 1 || x > n || tag[x]) p[pi++] = x; 35 else tag[x] = true; 36 } 37 sort(p, p + pi); 38 cnt = 0; 39 for(int i = 0, j = 1; i < pi; i++, j++) 40 { 41 while(tag[j]) j++; 42 cnt += (ll)abs(p[i] - j); 43 } 44 printf("%I64d\n", cnt); 45 } 46 return 0; 47 }