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A Fenwick tree or binary indexed tree is a data structure that can efficiently update elements and calculate prefix sums in a table of numbers .. tree. Tree ( data structure ). This structure was proposed by Peter Fenwick in 1994 to improve the efficiency of arithmetic coding compression algorithms .. Peter Fenwick. Peter Fenwick ( computer scientist ). arithmetic coding. arithmetic coding. compression algorithms. Data compression. When compared with a flat array of numbers , the Fenwick tree achieves a much better balance between two operations  : element update and prefix sum calculation .. prefix sum. prefix sum. tree. Tree ( data structure ). In a flat array of numbers , you can either store the elements , or the prefix sums .. In the first case , computing prefix sums requires linear time ; in the second case , updating the array elements requires linear time -LRB- in both cases , the other operation can be performed in constant time -RRB- .. Fenwick trees allow both operations to be performed in time .. This is achieved by representing the numbers as a tree , where the value of each node is the sum of the numbers in that subtree .. tree. Tree ( data structure ). The tree structure allows operations to be performed using only node accesses .. tree. Tree ( data structure )