Java short O(mn) time, O(n) space

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    public int uniquePaths(int m, int n) {
            int[] paths = new int[n];
            Arrays.fill(paths, 1);
            for(int i=0; i<m-1; i++)
                for(int j=1; j<n; j++)
                    paths[j] = paths[j] + paths[j-1];
            return paths[n-1];

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