Matrix Restoration

Solution

Let grid be before, and prefix_sum be after.

Prefix Sum

From prefix_sum[i][j] = prefix_sum[i][j-1] + prefix_sum[i-1][j] + grid[i][j] - prefix_sum[i-1][j-1], after moving terms we get:
grid[i][j] = prefix_sum[i][j] - prefix_sum[i][j-1] - prefix_sum[i-1][j] + prefix_sum[i-1][j-1]

def matrixRestoration(self, n, m, prefix_sum):
    """
    @param n: the row of the matrix
    @param m: the column of the matrix
    @param after: the matrix
    @return: restore the matrix
    """
    grid = [[0 for _ in range(m)] for _ in range(n)]
    for i in range(n):
        for j in range(m):
            grid[i][j] = prefix_sum[i][j]
            if i > 0:
                grid[i][j] -= prefix_sum[i-1][j]
            if j > 0:
                grid[i][j] -= prefix_sum[i][j-1]
            if i > 0 and j > 0:
                grid[i][j] += prefix_sum[i-1][j-1]
    return grid