2017. Grid Game - Explanation

class Solution:
    def gridGame(self, grid: List[List[int]]) -> int:
        cols = len(grid[0])
        res = float('inf')

        top1 = 0
        for i in range(cols):
            top1 += grid[0][i]
            bottom1 = 0
            for j in range(i, cols):
                bottom1 += grid[1][j]

            top2 = robot2 = 0
            for j in range(cols):
                if j > i:
                    top2 += grid[0][j]

                bottom2 = 0
                for k in range(j, i):
                    bottom2 += grid[1][k]
                robot2 = max(robot2, top2 + bottom2)

            res = min(res, robot2)

        return res

class Solution:
    def gridGame(self, grid: List[List[int]]) -> int:
        N = len(grid[0])
        preRow1, preRow2 = grid[0].copy(), grid[1].copy()

        for i in range(1, N):
            preRow1[i] += preRow1[i - 1]
            preRow2[i] += preRow2[i - 1]

        res = float("inf")
        for i in range(N):
            top = preRow1[-1] - preRow1[i]
            bottom = preRow2[i - 1] if i > 0 else 0
            secondRobot = max(top, bottom)
            res = min(res, secondRobot)
        return res

class Solution:
    def gridGame(self, grid: List[List[int]]) -> int:
        res = float("inf")
        topSum = sum(grid[0])
        bottomSum = 0

        for i in range(len(grid[0])):
            topSum -= grid[0][i]
            res = min(res, max(topSum, bottomSum))
            bottomSum += grid[1][i]

        return res