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... + a[i]`\n- Update one element: `a[i] += delta`\n\nWith a naïve implementation, only one of the operations can be made to have constant time\ncomplexity while the other one has to be linear. With Fenwick tree, both take only `O(log(N))`.\n\nThis crate is `no_std` and has no (non-dev) dependencies.\n\n[wiki]: https://en.wikipedia.org/wiki/Fenwick_tree\n\n# Examples\n\nUse the `array` module for operations on a 1D Fenwick tree:\n\n```rust\nuse fenwick::array::{update, prefix_sum};\n\nlet fw = \u0026mut [0i32; 10]; // backing array of Fenwick tree (NOT original array!)\nassert_eq!(prefix_sum(fw, 0), 0);\nassert_eq!(prefix_sum(fw, 9), 0);\nupdate(fw, 0, 3); // original array: [3, 0, 0, 0, 0, 0, 0, 0, 0, 0]\nassert_eq!(prefix_sum(fw, 0), 3);\nassert_eq!(prefix_sum(fw, 9), 3);\nupdate(fw, 5, 9); // original array: [3, 0, 0, 0, 0, 9, 0, 0, 0, 0]\nassert_eq!(prefix_sum(fw, 4), 3);\nassert_eq!(prefix_sum(fw, 5), 12);\nassert_eq!(prefix_sum(fw, 6), 12);\nupdate(fw, 4, -5); // original array: [3, 0, 0, 0, -5, 9, 0, 0, 0, 0]\nassert_eq!(prefix_sum(fw, 4), -2);\nassert_eq!(prefix_sum(fw, 5), 7);\nupdate(fw, 0, -2); // original array: [1, 0, 0, 0, -5, 9, 0, 0, 0, 0]\nassert_eq!(prefix_sum(fw, 4), -4);\nassert_eq!(prefix_sum(fw, 5), 5);\n```\n\nUse the `index` module to implement multidimensional Fenwick trees:\n\n```rust\nuse fenwick::index::zero_based::{down, up};\nconst MAX: usize = 1000;\n\nfn update(i: usize, j: usize, k: usize, delta: i32) {\n    for ii in up(i, MAX) {\n        for jj in up(j, MAX) {\n            for kk in up(k, MAX) {\n                /* increment 3D array at [ii, jj, kk] by delta */\n            }\n        }\n    }\n}\n\nfn prefix_sum(i: usize, j: usize, k: usize) -\u003e i32 {\n    let mut sum = 0i32;\n    for ii in down(i) {\n        for jj in down(j) {\n            for kk in down(k) {\n                /* increment sum by 3D array at [ii, jj, kk] */\n            }\n        }\n    }\n    sum\n}\n```\n\n# References\n\n* [Original Paper](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.8917)\n* [Tutorial on Topcoder](https://www.topcoder.com/community/data-science/data-science-tutorials/binary-indexed-trees/)\n\n","funding_links":[],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsummivox%2Ffenwick.rs","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fsummivox%2Ffenwick.rs","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsummivox%2Ffenwick.rs/lists"}