Max Sum of Max-K-sub-sequence----单调队列

ぐ巨炮叔叔 提交于 2019-11-26 14:06:23

至于题是哪来的,老师BB出来的

至于怎么BB的,请自己联想

我csdn的博客

Max Sum of Max-K-sub-sequence

Given a circle sequence A[1],A[2],A[3]......A[n]. Circle sequence means the left neighbour of A[1] is A[n] , and the right neighbour of A[n] is A[1].
Now your job is to calculate the max sum of a Max-K-sub-sequence. Max-K-sub-sequence means a continuous non-empty sub-sequence which length not exceed K.

Input

The first line of the input contains an integer T(1<=T<=100) which means the number of test cases.
Then T lines follow, each line starts with two integers N , K(1<=N<=100000 , 1<=K<=N), then N integers followed(all the integers are between -1000 and 1000).

Output

For each test case, you should output a line contains three integers, the Max Sum in the sequence, the start position of the sub-sequence, the end position of the sub-sequence. If there are more than one result, output the minimum start position, if still more than one , output the minimum length of them.

Sample Input

4
6 3
6 -1 2 -6 5 -5
6 4
6 -1 2 -6 5 -5
6 3
-1 2 -6 5 -5 6
6 6
-1 -1 -1 -1 -1 -1

Sample Output

7 1 3
7 1 3
7 6 2
-1 1 1

题意自己百度

这道题,可以这样做

解释都在注释和下面
`

由于是一个圈
1 2 3 4 5
显然1的左边还有5
那么我们就把问题分为两类
第一类:
    就是一个没有跨过了n的序列
第二类:
    一个跨过了n的序列`

第一类

题意可转换为
有一序列
在其中找一个长度不超过k的子序列使其和最大
有多个子序列满足条件的按题意输出
就用。。。

第二类

在整个序列中找一子序列,使其总和最小且长度大于等于n - k
ans = ALL - 子序列总和

是不是很简单( ⊙ o ⊙ )啊!

#include <cstdio>
#include <climits>
const int MAXN = 100001;
class MYOWN
{
    public:
        int val,it;
        MYOWN()
        {
            val = 0;
            it = 0;
        }
};
int main()
{
    int T;
    scanf("%d",&T);
    //多组数据
    while(T--)
    {
        int i,n,k,head,tail,ALL = 0;
        /*
        显然head记录队头,tail记录队尾
        ALL方便第二种
        */
        int num[MAXN] = {},sum[MAXN] = {};
        int ans = -1001,l,r;
        MYOWN q[MAXN];
        scanf("%d%d",&n,&k);
        for(i = 1;i <= n;i++)
        {
            scanf("%d",&num[i]);
            sum[i] = sum[i - 1] + num[i];
            ALL += num[i];
        }
        head = 1;tail = 1;
        for(i = 1;i <= n;i++)
        {
            while(q[head].it < i - k&&head <= tail)
                head++;
            int delta = sum[i] - q[head].val;
            if(delta > ans)
            {
                ans = delta;
                l = q[head].it + 1;
                r = i;
            }
            while(sum[i] <= q[tail].val&&tail >= head)
                tail--;
            tail++;
            q[tail].val = sum[i];
            q[tail].it = i;
        }
        //第一类,单调队列嘛
        k = n - k;
        q[0].val = -1001;
        for(i = 1;i <= n;i++)
        {
            if(sum[i] <= q[i - 1].val)
            {
                q[i].it = q[i - 1].it;
                q[i].val = q[i - 1].val;
            } else {
                q[i].val = sum[i];
                q[i].it = i;
            }   
        }
        //第二类,根本不需要单调队列!!用用动规思想记录下
        //q[i].val 记录从一到i的sum[i]的最大值
        //q[i].it记录q[i].val第一次出现的下标(题目要求的多个答案的输出要求)
        for(i = k + 1;i < n;i++)
        {
            int delta = ALL - sum[i] + q[q[i - k].it].val;
            if(delta > ans)
            {
                ans = delta;
                l = i + 1;
                r = q[i - k].it;
            }
        }
        printf("%d %d %d\n",ans,l,r);
    }
    return 0;
}
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