codechef AUG17 T2 Chef and Mover

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Chef and Mover Problem Code: CHEFMOVR

Chef‘s dog Snuffles has so many things to play with! This time around, Snuffles has an array A containing N integers: A1, A2, ..., AN.

Bad news: Snuffles only loves to play with an array in which all the elements are equal.

Good news: We have a mover of size D!

A mover of size D is a tool which helps to change arrays. Chef can pick two existing elements Ai and Aj from the array, such that i + D = j and subtract 1 from one of these elements, and add 1 to the other element. In effect, a single operation of the mover, moves a value of 1 from one of the elements to the other.

Chef wants to find the minimum number of times she needs to use the mover of size D to make all the elements of the array A equal. Help her find this out.

Input

  • The first line of the input contains an integer T, denoting the number of test cases. The description of T test cases follows.
  • The first line of each test case contains two integers N and D, denoting the number of elements in the array and the size of the mover.
  • The second line of each testcase contains N space-separated integers: A1, A2, ..., AN, denoting the initial elements of the array.

Output

  • For each test case, output a single line containing the minimum number of uses or -1 if it is impossible to do what Snuffles wants.

Constraints

  • 1 ≤ T ≤ 10
  • 2 ≤ N ≤ 105
  • 1 ≤ D < N
  • 1 ≤ Ai ≤ 109

Subtasks

  • Subtask 1 (30 points) : N ≤ 103
  • Subtask 2 (70 points) : Original constraints

Example

Input:
3
5 2
1 6 5 0 3
3 1
0 3 0
4 2
3 4 3 5

Output:
5
2
-1

Explanation

Testcase 1:

Here is a possible sequence of usages of the mover:

  • Move 1 from A3 to A1
  • Move 1 from A3 to A1
  • Move 1 from A2 to A4
  • Move 1 from A2 to A4
  • Move 1 from A2 to A4

At the end, the array becomes (3, 3, 3, 3, 3), which Snuffles likes. And you cannot achieve this in fewer moves. Hence the answer is 5.

Testcase 2:

Here is a possible sequence of usages of the mover:

  • Move 1 from A2 to A1
  • Move 1 from A2 to A3

At the end, the array becomes (1, 1, 1), which Snuffles likes. And you cannot achieve this in fewer moves. Hence the answer is 2.

Testcase 3:

It is impossible to make all the elements equal. Hence the answer is -1.

——————————————————————————————————————

这道题我居然WA了两次QAQ

其实题意就是给你n个数和一个d 相邻距离为d的数字可以进行你+1我-1的操作 求最少的操作次数使得全部的数相等

所以我们一开始就要把所有的数加起来得到sum 如果sum%n!=0 那么肯定不存在这么一个答案 

因为你无论怎么加减 总和都是不变的

然后再判断相邻d的所有数加起来是否为0 不如!=0 说明答案也不存在 这个也很好证明

最后统计答案的时候 我一开始想的是把所有的正数加起来 但是发现不行

比如这样一个例子 d=1时 4 1 1

按上面来算答案应该是2但是答案其实是3

因为你只能相邻交换 所以应该是4给第一个1 2 然后 第一个1给第二个1 1 

答案是3

所以我们统计答案的时候可以像均分纸牌一样 每次拿出第一个数(<=k)

他只能从下一个数拿 而下一个数不可能从这个数再拿回来 所以他只能从下一个拿

这样把值推过去再慢慢统计就好辣

这样这个问题就解决辣

技术分享
#include<cstdio>
#include<cstring>
#include<algorithm>
#define LL long long
using namespace std;
const int inf=0x3f3f3f3f,M=1e6+7;
LL read(){
    LL ans=0,f=1,c=getchar();
    while(c<0||c>9){if(c==-) f=-1; c=getchar();}
    while(c>=0&&c<=9){ans=ans*10+(c-0); c=getchar();}
    return ans*f;
}
LL T,n,k,v[M],sum,ans,x,h;
int main()
{
    T=read();
    while(T--){
        memset(v,0,sizeof(v));
        sum=0; ans=0; 
        n=read(); k=read();
        for(int i=1;i<=n;i++) v[i]=read(),sum+=v[i];
        if(sum%n!=0){printf("-1\n"); continue;}
        sum=sum/n;
        for(int i=1;i<=n;i++) v[i]-=sum;
        for(int i=1;i<=k;i++){
            x=i; h=0;
            while(x<=n){
                h+=v[x];
                if(x+k>n) break;
                x+=k;
            }
            if(h){printf("-1\n"); break;}
        }
        if(h) continue;
        for(int i=1;i<=k;i++){
            x=i;
            while(x<=n){
                ans=ans+abs(v[x]);
                if(x+k>n) break;
                v[x+k]+=v[x]; x+=k;
            }
        }
        printf("%lld\n",ans);
    }
    return 0;
}
View Code

 

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