This paper presents an efficient and accurate algorithm for integrating the basins of attraction of a smooth function defined on a general discrete grid, with application to Bader charge partitioning in electron charge density. The method computes the fraction of each grid volume that belongs to a basin (Bader volume) and serves as a weight for the discrete integration of functions over the Bader volume. It is robust, computationally efficient with linear computational effort, accurate, and has quadratic convergence. The algorithm is straightforward to extend to non-uniform grids and can be used to identify basins of attraction of fixed points and integrate functions over the basins. The algorithm is based on the evolution of trajectories in space following the gradient of charge density. It derives an expression for the fraction of space neighboring each grid point that flows to its neighbors. This fraction is used to compute the fraction of each grid volume that belongs to a basin and as a weight for the discrete integration of functions over the Bader volume. The algorithm is derived by considering the probability flux of trajectories and the evolution of probability distribution over time. The weight for each grid point is determined by the fraction of points in its Voronoi cell whose trajectory ends in the basin. The algorithm is efficient, requiring overall effort that scales linearly with the number of grid points, and is more accurate than other grid-based algorithms. The algorithm is tested on various systems, including Gaussian densities, TiO₂ bulk, and NaCl crystal. The results show that the weight method has better error scaling—quadratic in the grid spacing—and improved computational efficiency compared to the near-grid method. The weight method also converges faster and has smaller absolute error. The algorithm is applicable to both uniform and non-uniform grids and is computationally efficient, making it suitable for large systems. The results demonstrate that the weight method provides more accurate Bader charge integration with fewer grid points than the near-grid method.This paper presents an efficient and accurate algorithm for integrating the basins of attraction of a smooth function defined on a general discrete grid, with application to Bader charge partitioning in electron charge density. The method computes the fraction of each grid volume that belongs to a basin (Bader volume) and serves as a weight for the discrete integration of functions over the Bader volume. It is robust, computationally efficient with linear computational effort, accurate, and has quadratic convergence. The algorithm is straightforward to extend to non-uniform grids and can be used to identify basins of attraction of fixed points and integrate functions over the basins. The algorithm is based on the evolution of trajectories in space following the gradient of charge density. It derives an expression for the fraction of space neighboring each grid point that flows to its neighbors. This fraction is used to compute the fraction of each grid volume that belongs to a basin and as a weight for the discrete integration of functions over the Bader volume. The algorithm is derived by considering the probability flux of trajectories and the evolution of probability distribution over time. The weight for each grid point is determined by the fraction of points in its Voronoi cell whose trajectory ends in the basin. The algorithm is efficient, requiring overall effort that scales linearly with the number of grid points, and is more accurate than other grid-based algorithms. The algorithm is tested on various systems, including Gaussian densities, TiO₂ bulk, and NaCl crystal. The results show that the weight method has better error scaling—quadratic in the grid spacing—and improved computational efficiency compared to the near-grid method. The weight method also converges faster and has smaller absolute error. The algorithm is applicable to both uniform and non-uniform grids and is computationally efficient, making it suitable for large systems. The results demonstrate that the weight method provides more accurate Bader charge integration with fewer grid points than the near-grid method.