A15570 | Least Prefix Sum
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题目描述
Baltic, a famous chess player who is also a mathematician, has an array $a_1,a_2, \ldots, a_n$ , and he can perform the following operation several (possibly $0$ ) times:
- Choose some index $i$ ( $1 \leq i \leq n$ );
- multiply $a_i$ with $-1$ , that is, set $a_i := -a_i$ .
Baltic's favorite number is $m$ , and he wants $a_1 + a_2 + \cdots + a_m$ to be the smallest of all non-empty prefix sums. More formally, for each $k = 1,2,\ldots, n$ it should hold that $$$$a_1 + a_2 + \cdots + a_k \geq a_1 + a_2 + \cdots + a_m. $$ </p><p>Please note that multiple smallest prefix sums may exist and that it is only required that $a\_1 + a\_2 + \\cdots + a\_m$ is one of them.</p><p>Help Baltic find the minimum number of operations required to make $a\_1 + a\_2 + \\cdots + a\_m$$$ the least of all prefix sums. It can be shown that a valid sequence of operations always exists.
- Choose some index $i$ ( $1 \leq i \leq n$ );
- multiply $a_i$ with $-1$ , that is, set $a_i := -a_i$ .
Baltic's favorite number is $m$ , and he wants $a_1 + a_2 + \cdots + a_m$ to be the smallest of all non-empty prefix sums. More formally, for each $k = 1,2,\ldots, n$ it should hold that $$$$a_1 + a_2 + \cdots + a_k \geq a_1 + a_2 + \cdots + a_m. $$ </p><p>Please note that multiple smallest prefix sums may exist and that it is only required that $a\_1 + a\_2 + \\cdots + a\_m$ is one of them.</p><p>Help Baltic find the minimum number of operations required to make $a\_1 + a\_2 + \\cdots + a\_m$$$ the least of all prefix sums. It can be shown that a valid sequence of operations always exists.
输入格式
Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \leq t \leq 10\,000$ ). The description of the test cases follows.
The first line of each test case contains two integers $n$ and $m$ ( $1 \leq m \leq n \leq 2\cdot 10^5$ ) — the size of Baltic's array and his favorite number.
The second line contains $n$ integers $a_1,a_2, \ldots, a_n$ ( $-10^9 \leq a_i \leq 10^9$ ) — the array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$ .
The first line of each test case contains two integers $n$ and $m$ ( $1 \leq m \leq n \leq 2\cdot 10^5$ ) — the size of Baltic's array and his favorite number.
The second line contains $n$ integers $a_1,a_2, \ldots, a_n$ ( $-10^9 \leq a_i \leq 10^9$ ) — the array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$ .
输出格式
For each test case, print a single integer — the minimum number of required operations.
输入输出样例
输入 #1
6 4 3 -1 -2 -3 -4 4 3 1 2 3 4 1 1 1 5 5 -2 3 -5 1 -20 5 2 -2 3 -5 -5 -20 10 4 345875723 -48 384678321 -375635768 -35867853 -35863586 -358683842 -81725678 38576 -357865873
输出 #1
1 1 0 0 3 4
In the first example, we perform the operation $a_4 := -a_4$ . The array becomes $[-1,-2,-3,4]$ and the prefix sums, $[a_1, \ a_1+a_2, \ a_1+a_2+a_3, \ a_1+a_2+a_3+a_4]$ , are equal to $[-1,-3,-6,-2]$ . Thus $a_1 + a_2 + a_3=-6$ is the smallest of all prefix sums.
In the second example, we perform the operation $a_3 := -a_3$ . The array becomes $[1,2,-3,4]$ with prefix sums equal to $[1,3,0,4]$ .
In the third and fourth examples, $a_1 + a_2 + \cdots + a_m$ is already the smallest of the prefix sums — no operation needs to be performed.
In the fifth example, a valid sequence of operations is:
- $a_3 := -a_3$ ,
- $a_2 := -a_2$ ,
- $a_5 := -a_5$ .
The array becomes $[-2,-3,5,-5,20]$ and its prefix sums are $[-2,-5,0,-5,15]$ . Note that $a_1+a_2=-5$ and $a_1+a_2+a_3+a_4=-5$ are both the smallest of the prefix sums (and this is a valid solution).
In the second example, we perform the operation $a_3 := -a_3$ . The array becomes $[1,2,-3,4]$ with prefix sums equal to $[1,3,0,4]$ .
In the third and fourth examples, $a_1 + a_2 + \cdots + a_m$ is already the smallest of the prefix sums — no operation needs to be performed.
In the fifth example, a valid sequence of operations is:
- $a_3 := -a_3$ ,
- $a_2 := -a_2$ ,
- $a_5 := -a_5$ .
The array becomes $[-2,-3,5,-5,20]$ and its prefix sums are $[-2,-5,0,-5,15]$ . Note that $a_1+a_2=-5$ and $a_1+a_2+a_3+a_4=-5$ are both the smallest of the prefix sums (and this is a valid solution).
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评测结果：Accepted