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Codeforces 11B Jumping Jack(数学)

2019年04月13日 ⁄ 综合 ⁄ 共 1073字 ⁄ 字号 评论关闭

B. Jumping Jack
time limit per test

1 second

memory limit per test

64 megabytes

input

standard input

output

standard output

Jack is working on his jumping skills recently. Currently he's located at point zero of the number line. He would like to get to the point x.
In order to train, he has decided that he'll first jump by only one unit, and each subsequent jump will be exactly one longer than the previous one. He can go either left or right with each jump. He wonders how many jumps he needs to reach x.

Input

The input data consists of only one integer x ( - 109 ≤ x ≤ 109).

Output

Output the minimal number of jumps that Jack requires to reach x.

Sample test(s)
input
2
output
3
input
6
output
3
input
0
output
0


题意:

Jack在数轴上跳。他第i次跳可以往左或往右跳i个单位。现在问你他最少花多少步跳到点x。

思路:

可以不管x正负把x变成正数。这样是等效的。然后他最快的跳法当然是往一个方向一直跳。如果这样恰好能到x。这样肯定是步数最小的解。如果不能恰好跳到。我们设按这种方法跳第一个比x大的位置为y。如果y-x是偶数的话。我们还是可以达到最优步数。就是先将第(y-x)/2步往左跳。其它不变。那么恰好也能到x。如果为奇数。变成下一个偶数就行了。为什么可以这样呢。因为不管怎样。x=(±1)+(±2)+(±3)+.......(±n)。所以要想跳到必须奇偶性一致。比y小一定不行、所以只有在y右边找了。

详细见代码:

#include<bits/stdc++.h>
int main()
{
    int tp,x,ans;
    while(~scanf("%d",&x))
    {
        x=x<0?-x:x,ans=ceil((-1+sqrt(1+8.0*x))/2),tp=ans*(ans+1)/2-x;
        while(tp&1) ans++,tp+=ans;
        printf("%d\n",ans);
    }
    return 0;
}


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