Moving Stones Until Consecutive II

Introduction

On an infinite number line, the position of the i-th stone is given by stones[i]. Call a stone an endpoint stone if it has the smallest or largest position.

Each turn, you pick up an endpoint stone and move it to an unoccupied position so that it is no longer an endpoint stone.

In particular, if the stones are at say, stones = [1,2,5], you cannot move the endpoint stone at position 5, since moving it to any position (such as 0, or 3) will still keep that stone as an endpoint stone.

The game ends when you cannot make any more moves, ie. the stones are in consecutive positions.

When the game ends, what is the minimum and maximum number of moves that you could have made? Return the answer as an length 2 array: answer = [minimum_moves, maximum_moves]

Example 1:

Input: [7,4,9]
Output: [1,2]
Explanation:
We can move 4 -> 8 for one move to finish the game.
Or, we can move 9 -> 5, 4 -> 6 for two moves to finish the game.

Example 2:

Input: [6,5,4,3,10]
Output: [2,3]
We can move 3 -> 8 then 10 -> 7 to finish the game.
Or, we can move 3 -> 7, 4 -> 8, 5 -> 9 to finish the game.
Notice we cannot move 10 -> 2 to finish the game, because that would be an illegal move.

Example 3:

Input: [100,101,104,102,103]
Output: [0,0]

Note:

3 <= stones.length <= 10^4
1 <= stones[i] <= 10^9
stones[i] have distinct values.

Solution

Golang:

func numMovesStonesII(stones []int) []int {
    sort.Ints(stones)
    k := 0
    n := len(stones)
    j := 0
    for i, stone := range stones {
        for stone-stones[j] > n-1 {
          j++
        }
        k = max(k, i-j+1)
    }
    mx := max(stones[n-2]-stones[0]-n+2, stones[n-1]-stones[1]-n+2);
    if stones[n-1]-stones[0] > n && (stones[n-2]-stones[0]==n-2 || stones[n-1]-stones[1]==n-2) {
        k--;
    }
    return []int{n-k, mx}
}

func max(a, b int) int {
    if a > b {
        return a
    } else {
        return b
    }
}

Explanation

We need to sort stones before use, then we need to find max distance between stones greater than range n-1, because finally we need to end up with sequence of stones where dimension between them would be n-1. Max distance if the max distance between two pairs of stones, first and one before last or second stone and last one. Plus additional corner case check.