POJ 1701

  1 /*
  2 Every tenant went up N floors would make the dissatisfied degree rise N * a + 0.5 * N * (N - 1) degrees,
  3 every tenant went down N floors would make the dissatisfied degree rise N * b + 0.5 * N * (N - 1) degrees.
  4
  5   △= Dp+1 – Dp
  6 = ∑1=<i<=p Ki*(b+p-i)) - ∑p<i<=n Ki*(a+i-p-1)
  7 =  ∑1=<i<=n Ki * i +(b+p)*∑1=<i<=p Ki   -     (a-p-1)∑p<i<=n Ki
  8 */
  9
 10 #include <iostream>
 11 #define MAXN  10001
 12 using namespace std;
 13
 14 __int64 _m[MAXN+1];
 15 int k[MAXN+1];
 16 __int64 p_2[MAXN+1];
 17 __int64 p_3[MAXN+1];
 18 int k_1[MAXN];
 19 int k_2[MAXN];
 20
 21
 22 int main()
 23 {
 24     //freopen("acm.acm","r",stdin);
 25     int test;
 26     int n;
 27     int i;
 28     int j;
 29     int  p_1;
 30     int a;
 31     int b;
 32     scanf("%d",&test);
 33     while(test --)
 34     {
 35         scanf("%d",&n);
 36         scanf("%d",&a);
 37         scanf("%d",&b);
 38
 39         for(i = 1; i <= n; ++ i)
 40         {
 41             scanf("%d",&k[i]);
 42         }
 43
 44         for(i = 1; i <= n; ++ i)
 45         {
 46             k_1[i] = k_2[i] = k[i];
 47         }
 48
 49         for(i = n-1; i >=1; -- i)
 50         {
 51             k_2[i] += k_2[i+1];
 52         }
 53
 54         for(i = 2; i <= n; ++i)
 55         {
 56             k_1[i] += k_1[i-1];
 57         }
 58
 59         p_1 = 0;
 60         for(i = 1; i <= n; ++ i)
 61         {
 62             p_1 += k[i]*i;
 63         }
 64
 65         for(i = 1; i <= n; ++ i)
 66         {
 67             p_2[i] = (b + i)*k_1[i];
 68         }
 69
 70         for(i = 1; i <= n; ++ i)
 71         {
 72             k_2[i] -= k[i];
 73         }
 74
 75
 76         copy(k_2,k_2+n+1,p_3);
 77
 78         for(i = 1; i <= n; ++ i)
 79         {
 80             p_3[i] *= (a-i-1);
 81         }
 82         _m[1] = 0;
 83         for(i = 2; i <= n; ++ i)
 84         {
 85             _m[1] += (i-1)*a+((i-1)*(i-2)/2);
 86         }
 87
 88         for(i = 2; i <= n; ++ i)
 89         {
 90             _m[i] = _m[i-1] - p_1 + p_2[i-1] - p_3[i-1];
 91         }
 92
 93         __int64 min = 999999999999999;
 94
 95         int place;
 96
 97         for(i = 1; i <= n; ++ i)
 98         {
 99             if(_m[i] < min)
100             {
101                 min = _m[i];
102                 place = i;
103             }
104         }
105         cout<<place<<endl;
106     }
107 }