3 0 10 5 -5 -5 -5
10.000000000000000000000000000000000000000000000000 The final distance from the origin can be $10$ if we use the engines in one of the following three ways: * Use Engine $1$ to move to $(0, 10)$. * Use Engine $2$ to move to $(5, -5)$, and then use Engine $3$ to move to $(0, -10)$. * Use Engine $3$ to move to $(-5, -5)$, and then use Engine $2$ to move to $(0, -10)$. The distance cannot be greater than $10$, so the maximum possible distance is $10$.
5 1 1 1 0 0 1 -1 0 0 -1
2.828427124746190097603377448419396157139343750753
The maximum possible final distance is $2 \sqrt{2} = 2.82842...$. One of the ways to achieve it is:
* Use Engine $1$ to move to $(1, 1)$, and then use Engine $2$ to move to $(2, 1)$, and finally use Engine $3$ to move to $(2, 2)$.5 1 1 2 2 3 3 4 4 5 5
21.213203435596425732025330863145471178545078130654
If we use all the engines in the order $1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 5$, we will end up at $(15, 15)$, with the distance $15 \sqrt{2} = 21.2132...$ from the origin.3 0 0 0 1 1 0
1.414213562373095048801688724209698078569671875376 There can be useless engines with $(x_i, y_i) = (0, 0)$.
1 90447 91000
128303.000000000000000000000000000000000000000000000000 Note that there can be only one engine.
2 96000 -72000 -72000 54000
120000.000000000000000000000000000000000000000000000000 There can be only two engines, too.
10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
148.660687473185055226120082139313966514489855137208
{
"problem": {
"name": "Engines",
"description": {
"content": "E869120 is initially standing at the origin $(0, 0)$ in a two-dimensional plane. He has $N$ engines, which can be used as follows: * When E869120 uses the $i$\\-th engine, his $X$\\- and $Y$\\-coordin",
"description_type": "Markdown"
},
"platform": "AtCoder",
"limit": {
"time_limit": 2000,
"memory_limit": 262144
},
"difficulty": "None",
"is_remote": true,
"is_sync": true,
"sync_url": null,
"sign": "abc139_f"
},
"statements": [
{
"statement_type": "Markdown",
"content": "E869120 is initially standing at the origin $(0, 0)$ in a two-dimensional plane.\nHe has $N$ engines, which can be used as follows:\n\n* When E869120 uses the $i$\\-th engine, his $X$\\- and $Y$\\-coordin...",
"is_translate": false,
"language": "English"
}
]
}