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Problem · Math

Particle Moves to Target

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● Easy

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Problem statement

A particle starts at integer coordinate (startX, startY) and must reach (targetX, targetY) on an unbounded grid. You may use these operations any nonnegative number of times:

PROTON: move one cell right, from (x, y) to (x + 1, y).
NEUTRON: move one cell down, from (x, y) to (x, y - 1).
ALPHA: move two cells up and two cells left, from (x, y) to (x - 2, y + 2).

Return a three-element integer array [protons, neutrons, alphas] whose operations reach the target using the minimum possible total number of operations. The result is ordered as PROTON, NEUTRON, ALPHA.

Function

particleMoves(startX: int, startY: int, targetX: int, targetY: int) → int[]

Examples

Example 1

startX = 0startY = 0targetX = 3targetY = -2return = [3,2,0]

Three PROTON operations add 3 to x, and two NEUTRON operations subtract 2 from y. No ALPHA operation is needed.

Example 2

startX = 4startY = -3targetX = -2targetY = 5return = [2,0,4]

Four ALPHA operations change the position by (-8, 8), and two PROTON operations restore x by 2. The net change is (-6, 8).

Example 3

startX = -5startY = 7targetX = -8targetY = 0return = [1,11,2]

Two ALPHA operations contribute (-4, 4). One PROTON and eleven NEUTRON operations then produce the required net change (-3, -7).

Constraints

-10^6 <= startX, startY, targetX, targetY <= 10^6.
Movement occurs on an unbounded integer grid.
A minimum-operation solution always exists and every returned count fits a signed 32-bit integer.