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+/**%0A * Starting in the top left corner of a 22 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.%0A * %3Cp%3E%0A * How many such routes are there through a 2020 grid?%0A *%0A * @author david.clutter@ca.com%0A */%0Apublic class Problem0015 %7B%0A%0A    private static final int GRID_SIZE = 20;%0A%0A    // Dynamic Backtrack%0A    public static void main(final String%5B%5D args) %7B%0A        final long%5B%5D%5B%5D grid = new long%5BGRID_SIZE + 1%5D%5BGRID_SIZE + 1%5D;%0A        for (int i = GRID_SIZE; i %3E= 0; --i) %7B%0A            for (int j = GRID_SIZE; j %3E= 0; --j) %7B%0A                if (i == GRID_SIZE %7C%7C j == GRID_SIZE) %7B%0A                    grid%5Bi%5D%5Bj%5D = 1;%0A                %7D else %7B%0A                    grid%5Bi%5D%5Bj%5D = grid%5Bi + 1%5D%5Bj%5D + grid%5Bi%5D%5Bj + 1%5D;%0A                %7D%0A            %7D%0A        %7D%0A        grid%5BGRID_SIZE%5D%5BGRID_SIZE%5D = 0;%0A        System.out.print(grid%5B0%5D%5B0%5D);%0A    %7D%0A%7D

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