347 lines
10 KiB
Rust
347 lines
10 KiB
Rust
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/* OpenTally: Open-source election vote counting
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* Copyright © 2021 Lee Yingtong Li (RunasSudo)
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU Affero General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Affero General Public License for more details.
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*
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* You should have received a copy of the GNU Affero General Public License
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* along with this program. If not, see <https://www.gnu.org/licenses/>.
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*/
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use ndarray::{Array, Dimension, IxDyn};
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use std::fmt;
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use std::ops;
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#[derive(Debug)]
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enum ConstraintError {
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NoConformantResult,
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}
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#[derive(Clone)]
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struct ConstraintMatrixCell {
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elected: usize,
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min: usize,
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max: usize,
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cands: usize,
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}
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struct ConstraintMatrix(Array<ConstraintMatrixCell, IxDyn>);
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impl ConstraintMatrix {
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pub fn new(constraints: &mut [usize]) -> Self {
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// Add 1 to dimensions for totals cells
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for c in constraints.iter_mut() {
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*c += 1;
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}
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return Self(Array::from_elem(
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IxDyn(constraints),
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ConstraintMatrixCell {
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elected: 0,
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min: 0,
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max: 0,
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cands: 0,
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}
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));
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}
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pub fn init(&mut self) {
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let indices: Vec<IxDyn> = ndarray::indices(self.0.shape()).into_iter().collect();
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// Compute candidate totals
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self.recount_cands();
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// Initialise max for grand total cell
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let idx = IxDyn(&vec![0; self.0.ndim()][..]);
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self.0[&idx].max = self.0[&idx].cands;
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// Initialise max for inner cells (>=2 zeroes)
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for idx in indices.iter() {
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if (0..idx.ndim()).fold(0, |acc, d| if idx[d] != 0 { acc + 1 } else { acc }) < 2 {
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continue;
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}
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self.0[idx].max = self.0[idx].cands;
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}
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// NB: Bounds on min, max, etc. will be further refined in initial step() calls
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}
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pub fn recount_cands(&mut self) {
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let shape = Vec::from(self.0.shape());
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let indices: Vec<IxDyn> = ndarray::indices(self.0.shape()).into_iter().collect();
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// Compute cands/elected totals
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for nzeroes in 1..self.0.ndim()+1 {
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for idx in indices.iter() {
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// First compute totals cells with 1 zero, then 2 zeroes, ... then grand total (all zeroes)
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if (0..idx.ndim()).fold(0, |acc, d| if idx[d] == 0 { acc + 1 } else { acc }) != nzeroes {
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continue;
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}
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self.0[idx].cands = 0;
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self.0[idx].elected = 0;
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// The axis along which to sum - if multiple, just pick the first, as these should agree
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let zero_axis = (0..idx.ndim()).filter(|d| idx[*d] == 0).next().unwrap();
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// Traverse along the axis and sum the candidates
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let mut idx2 = idx.clone();
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for coord in 1..shape[zero_axis] {
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idx2[zero_axis] = coord;
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self.0[idx].cands += self.0[&idx2].cands;
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self.0[idx].elected += self.0[&idx2].elected;
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}
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}
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}
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}
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pub fn step(&mut self) -> Result<bool, ConstraintError> {
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let shape = Vec::from(self.0.shape());
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let indices: Vec<IxDyn> = ndarray::indices(self.0.shape()).into_iter().collect();
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for idx in indices.iter() {
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let cell = &mut self.0[idx];
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// Rule 1: Ensure elected < min < max < cands
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if cell.min < cell.elected {
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cell.min = cell.elected;
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return Ok(false);
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}
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if cell.max > cell.cands {
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cell.max = cell.cands;
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return Ok(false);
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}
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if cell.min > cell.max {
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return Err(ConstraintError::NoConformantResult);
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}
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let nzeroes = (0..idx.ndim()).fold(0, |acc, d| if idx[d] == 0 { acc + 1 } else { acc });
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// Rule 2/3: Ensure min/max is possible in inner cells
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if nzeroes == 0 {
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for axis in 0..self.0.ndim() {
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let mut idx2 = idx.clone();
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// What is the min/max number of candidates that can be elected from other cells in this axis?
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let (other_max, other_min) = (1..shape[axis]).fold((0, 0), |(acc_max, acc_min), coord| {
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if coord == idx[axis] {
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return (acc_max, acc_min);
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}
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idx2[axis] = coord;
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return (acc_max + self.0[&idx2].max, acc_min + self.0[&idx2].min);
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});
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// What is the min/max number of candidates that can be elected along this axis?
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idx2[axis] = 0;
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let axis_max = self.0[&idx2].max;
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let axis_min = self.0[&idx2].min;
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// How many must be elected from this cell?
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let this_max = (axis_max as i32) - (other_min as i32);
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let this_min = (axis_min as i32) - (other_max as i32);
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if this_max < (self.0[idx].max as i32) {
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self.0[idx].max = this_max as usize;
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return Ok(false);
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}
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if this_min > (self.0[idx].min as i32) {
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self.0[idx].min = this_min as usize;
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return Ok(false);
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}
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}
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}
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// Rule 4/5: Ensure min/max is possible in totals cells
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if nzeroes > 0 {
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for axis in 0..self.0.ndim() {
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if idx[axis] != 0 {
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continue;
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}
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// What is the total min/max along this axis?
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let mut idx2 = idx.clone();
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let (axis_max, axis_min) = (1..shape[axis]).fold((0, 0), |(acc_max, acc_min), coord| {
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idx2[axis] = coord;
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return (acc_max + self.0[&idx2].max, acc_min + self.0[&idx2].min);
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});
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if axis_max < self.0[idx].max {
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self.0[idx].max = axis_max;
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return Ok(false);
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}
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if axis_min > self.0[idx].min {
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self.0[idx].min = axis_min;
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return Ok(false);
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}
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}
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}
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}
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return Ok(true);
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}
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}
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impl fmt::Display for ConstraintMatrix {
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fn fmt(&self, f: &mut fmt::Formatter<'_>) -> std::fmt::Result {
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let shape = self.0.shape();
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let mut result = String::new();
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// TODO: ≠2 dimensions
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for y in 0..shape[1] {
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result.push_str("+");
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for _ in 0..shape[0] {
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result.push_str(if y == 1 { "=============+" } else { "-------------+" });
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}
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result.push_str("\n");
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result.push_str("|");
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for x in 0..shape[0] {
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result.push_str(&format!(" Elected: {:2}", self[&[x, y]].elected));
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result.push_str(if x == 0 { " ‖" } else { " |" });
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}
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result.push_str("\n");
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result.push_str("|");
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for x in 0..shape[0] {
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result.push_str(&format!(" Min: {:2}", self[&[x, y]].min));
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result.push_str(if x == 0 { " ‖" } else { " |" });
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}
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result.push_str("\n");
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result.push_str("|");
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for x in 0..shape[0] {
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result.push_str(&format!(" Max: {:2}", self[&[x, y]].max));
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result.push_str(if x == 0 { " ‖" } else { " |" });
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}
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result.push_str("\n");
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result.push_str("|");
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for x in 0..shape[0] {
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result.push_str(&format!(" Cands: {:2}", self[&[x, y]].cands));
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result.push_str(if x == 0 { " ‖" } else { " |" });
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}
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result.push_str("\n");
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}
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result.push_str("+");
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for _ in 0..shape[0] {
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result.push_str("-------------+");
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}
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result.push_str("\n");
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return f.write_str(&result);
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}
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}
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impl ops::Index<&[usize]> for ConstraintMatrix {
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type Output = ConstraintMatrixCell;
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fn index(&self, index: &[usize]) -> &Self::Output { &self.0[index] }
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}
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impl ops::IndexMut<&[usize]> for ConstraintMatrix {
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fn index_mut(&mut self, index: &[usize]) -> &mut Self::Output { &mut self.0[index] }
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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fn assert_cell(cm: &ConstraintMatrix, idx: &[usize], elected: usize, min: usize, max: usize, cands: usize) {
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assert_eq!(cm[idx].elected, elected, "Failed to validate elected at {:?}", idx);
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assert_eq!(cm[idx].min, min, "Failed to validate min at {:?}", idx);
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assert_eq!(cm[idx].max, max, "Failed to validate min at {:?}", idx);
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assert_eq!(cm[idx].cands, cands, "Failed to validate cands at {:?}", idx);
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}
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#[test]
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fn cm_otten() {
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let mut cm = ConstraintMatrix::new(&mut [3, 2]);
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// Totals
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let c = &mut cm[&[0, 1]]; c.min = 7; c.max = 7;
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let c = &mut cm[&[0, 2]]; c.min = 7; c.max = 7;
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let c = &mut cm[&[1, 0]]; c.min = 7; c.max = 7;
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let c = &mut cm[&[2, 0]]; c.min = 6; c.max = 6;
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let c = &mut cm[&[3, 0]]; c.min = 1; c.max = 1;
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// Candidates
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let c = &mut cm[&[1, 1]]; c.cands = 4;
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let c = &mut cm[&[2, 1]]; c.cands = 11;
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let c = &mut cm[&[3, 1]]; c.cands = 2;
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let c = &mut cm[&[1, 2]]; c.cands = 7;
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let c = &mut cm[&[2, 2]]; c.cands = 3;
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let c = &mut cm[&[3, 2]]; c.cands = 1;
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// Init
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cm.init();
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while !cm.step().expect("No conformant result") {}
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println!("{}", cm);
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assert_cell(&cm, &[1, 1], 0, 0, 4, 4);
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assert_cell(&cm, &[2, 1], 0, 3, 6, 11);
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assert_cell(&cm, &[3, 1], 0, 0, 1, 2);
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assert_cell(&cm, &[0, 1], 0, 7, 7, 17);
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assert_cell(&cm, &[1, 2], 0, 3, 7, 7);
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assert_cell(&cm, &[2, 2], 0, 0, 3, 3);
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assert_cell(&cm, &[3, 2], 0, 0, 1, 1);
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assert_cell(&cm, &[0, 2], 0, 7, 7, 11);
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assert_cell(&cm, &[1, 0], 0, 7, 7, 11);
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assert_cell(&cm, &[2, 0], 0, 6, 6, 14);
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assert_cell(&cm, &[3, 0], 0, 1, 1, 3);
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assert_cell(&cm, &[0, 0], 0, 14, 14, 28);
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// Election of Welsh man
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cm[&[3, 1]].elected += 1;
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cm.recount_cands();
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while !cm.step().expect("No conformant result") {}
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println!("{}", cm);
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assert_cell(&cm, &[1, 1], 0, 0, 3, 4);
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assert_cell(&cm, &[2, 1], 0, 3, 6, 11);
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assert_cell(&cm, &[3, 1], 1, 1, 1, 2);
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assert_cell(&cm, &[0, 1], 1, 7, 7, 17); // Error in Otten paper
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assert_cell(&cm, &[1, 2], 0, 4, 7, 7);
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assert_cell(&cm, &[2, 2], 0, 0, 3, 3);
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assert_cell(&cm, &[3, 2], 0, 0, 0, 1);
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assert_cell(&cm, &[0, 2], 0, 7, 7, 11);
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assert_cell(&cm, &[1, 0], 0, 7, 7, 11);
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assert_cell(&cm, &[2, 0], 0, 6, 6, 14);
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assert_cell(&cm, &[3, 0], 1, 1, 1, 3);
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assert_cell(&cm, &[0, 0], 1, 14, 14, 28);
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// Remaining Welsh man, Welsh woman doomed
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cm[&[3, 1]].cands -= 1;
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cm[&[3, 2]].cands -= 1;
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// Election of 2 English men, 2 English women
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// Exclusion of 1 Scottish woman
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cm[&[1, 1]].elected += 2;
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cm[&[1, 2]].elected += 2;
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cm[&[2, 2]].cands -= 1;
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cm.recount_cands();
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while !cm.step().expect("No conformant result") {}
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println!("{}", cm);
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assert_cell(&cm, &[1, 1], 2, 2, 2, 4);
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assert_cell(&cm, &[2, 1], 0, 4, 4, 11);
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assert_cell(&cm, &[3, 1], 1, 1, 1, 1);
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assert_cell(&cm, &[0, 1], 3, 7, 7, 16); // Error in Otten paper
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assert_cell(&cm, &[1, 2], 2, 5, 5, 7);
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assert_cell(&cm, &[2, 2], 0, 2, 2, 2);
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assert_cell(&cm, &[3, 2], 0, 0, 0, 0);
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assert_cell(&cm, &[0, 2], 2, 7, 7, 9);
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assert_cell(&cm, &[1, 0], 4, 7, 7, 11);
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assert_cell(&cm, &[2, 0], 0, 6, 6, 13);
|
||
|
|
assert_cell(&cm, &[3, 0], 1, 1, 1, 1);
|
||
|
|
assert_cell(&cm, &[0, 0], 5, 14, 14, 25);
|
||
|
|
}
|
||
|
|
}
|