Stone Game II
Alex and Lee continue their games with piles of stones. There are a number of piles arranged in a row, and each pile has a positive integer number of stones piles[i]. The objective of the game is to end with the most stones.
Alex and Lee take turns, with Alex starting first. Initially, M = 1.
On each player’s turn, that player can take all the stones in the first X remaining piles, where 1 <= X <= 2M. Then, we set M = max(M, X).
The game continues until all the stones have been taken.
Assuming Alex and Lee play optimally, return the maximum number of stones Alex can get.
Example
Input: piles = [2,7,9,4,4]
Output: 10
Explanation: If Alex takes one pile at the beginning, Lee takes two piles, then Alex takes 2 piles again. Alex can get 2 + 4 + 4 = 10 piles in total. If Alex takes two piles at the beginning, then Lee can take all three piles left. In this case, Alex get 2 + 7 = 9 piles in total. So we return 10 since it’s larger.
Solution
func stoneGameII(piles []int) int {
n := len(piles)
mem := [101][33]int{}
for i:=n-2;i>=0;i-- {
piles[i] += piles[i+1]
}
var dp func(int, int)int
dp = func(index, m int)int{
if index + 2*m>=n {
return piles[index]
}
if mem[index][m]>0 {
return mem[index][m]
}
ret := 0
for x:=1;x<=2*m;x++ {
ret = max(ret, piles[index]-dp(index+x, max(x, m)))
}
mem[index][m] = ret
return ret
}
return dp(0,1)
}
func max(a, b int)int {
if a>b{
return a
}
return b
}