data-structure-typed/test/utils/big-o.ts

import { AnyFunction } from '../types';
import { isDebugTest } from '../config';

const isDebug = isDebugTest;
const orderReducedBy = 1; // reduction of bigO's order compared to the baseline bigO

export const magnitude = {
  CONSTANT: Math.pow(10, 9),
  LOG_N: Math.pow(10, 8 - orderReducedBy),
  LINEAR: Math.pow(10, 7 - orderReducedBy),
  N_LOG_N: Math.pow(10, 4 - orderReducedBy),
  SQUARED: Math.pow(10, 3 - orderReducedBy),
  CUBED: Math.pow(10, 2 - orderReducedBy),
  FACTORIAL: 20 - orderReducedBy,
  THOUSAND: 1000,
  TEN_THOUSAND: 10000,
  HUNDRED_THOUSAND: 100000,
  MILLION: 1000000,
  TEN_MILLION: 10000000,
  BILLION: 100000000
};

export const bigO = {
  CONSTANT: magnitude.CONSTANT / 100000,
  LOG_N: Math.log2(magnitude.LOG_N) / 1000,
  LINEAR: magnitude.LINEAR / 1000,
  N_LOG_N: (magnitude.N_LOG_N * Math.log2(magnitude.LOG_N)) / 1000,
  SQUARED: Math.pow(magnitude.SQUARED, 2) / 1000,
  CUBED: Math.pow(magnitude.SQUARED, 3) / 1000,
  FACTORIAL: 10000
};

function findPotentialN(input: any): number {
  let longestArray: any[] = [];
  let mostProperties: { [key: string]: any } = {};

  function recurse(obj: any) {
    if (Array.isArray(obj)) {
      if (obj.length > longestArray.length) {
        longestArray = obj;
      }
    } else if (typeof obj === 'object' && obj !== null) {
      const keys = Object.keys(obj);
      if (keys.length > Object.keys(mostProperties).length) {
        mostProperties = obj;
      }
      keys.forEach(key => {
        recurse(obj[key]);
      });
    }
  }

  if (Array.isArray(input)) {
    input.forEach(item => {
      recurse(item);
    });
  } else {
    recurse(input);
  }

  // return [longestArray, mostProperties] : [any[], { [key: string]: any }];
  return Math.max(longestArray.length, Object.keys(mostProperties).length);
}

function linearRegression(x: number[], y: number[]) {
  const n = x.length;

  const sumX = x.reduce((acc, value) => acc + value, 0);
  const sumY = y.reduce((acc, value) => acc + value, 0);

  const sumXSquared = x.reduce((acc, value) => acc + value ** 2, 0);
  const sumXY = x.reduce((acc, value, i) => acc + value * y[i], 0);

  const slope = (n * sumXY - sumX * sumY) / (n * sumXSquared - sumX ** 2);
  const intercept = (sumY - slope * sumX) / n;

  const yHat = x.map(value => slope * value + intercept);

  const totalVariation = y.map((value, i) => (value - yHat[i]) ** 2).reduce((acc, value) => acc + value, 0);
  const explainedVariation = y.map(value => (value - sumY / n) ** 2).reduce((acc, value) => acc + value, 0);

  const rSquared = 1 - totalVariation / explainedVariation;

  return { slope, intercept, rSquared };
}

function estimateBigO(runtimes: number[], dataSizes: number[]): string {
  // Make sure the input runtimes and data sizes have the same length
  if (runtimes.length !== dataSizes.length) {
    return 'Lengths of input arrays do not match';
  }

  // Create an array to store the computational complexity of each data point
  const complexities: string[] = [];

  // Traverse different possible complexities
  const complexitiesToCheck: string[] = [
    'O(1)', // constant time complexity
    'O(log n)', // Logarithmic time complexity
    'O(n)', // linear time complexity
    'O(n log n)', // linear logarithmic time complexity
    'O(n^2)' // squared time complexity
  ];

  for (const complexity of complexitiesToCheck) {
    // Calculate data points for fitting
    const fittedData: number[] = dataSizes.map(size => {
      if (complexity === 'O(1)') {
        return 1; // constant time complexity
      } else if (complexity === 'O(log n)') {
        return Math.log(size);
      } else if (complexity === 'O(n)') {
        return size;
      } else if (complexity === 'O(n log n)') {
        return size * Math.log(size);
      } else if (complexity === 'O(n^2)') {
        return size ** 2;
      } else {
        return size ** 10;
      }
    });

    // Fit the data points using linear regression analysis
    const regressionResult = linearRegression(fittedData, runtimes);

    // Check the R-squared value of the fit. It is usually considered a valid fit if it is greater than 0.9.
    if (regressionResult.rSquared >= 0.9) {
      complexities.push(complexity);
    }
  }

  // If there is no valid fitting result, return "cannot estimate", otherwise return the estimated time complexity
  if (complexities.length === 0) {
    return 'Unable to estimate';
  } else {
    return complexities.join(' or ');
  }
}

const methodLogs: Map<string, [number, number][]> = new Map();

export function logBigOMetricsWrap<F extends AnyFunction>(fn: F, args: Parameters<F>, fnName: string) {
  const startTime = performance.now();
  const result = fn(args);
  const endTime = performance.now();
  const runTime = endTime - startTime;
  const methodName = `${fnName}`;
  if (!methodLogs.has(methodName)) {
    methodLogs.set(methodName, []);
  }

  const methodLog = methodLogs.get(methodName);

  const maxDataSize = args.length === 1 && typeof args[0] === 'number' ? args[0] : findPotentialN(args);
  if (methodLog) {
    methodLog.push([runTime, maxDataSize]);

    if (methodLog.length >= 20) {
      isDebug && console.log('triggered', methodName, methodLog);
      const bigO = estimateBigO(
        methodLog.map(([runTime]) => runTime),
        methodLog.map(([runTime]) => runTime)
      );
      isDebug && console.log(`Estimated Big O: ${bigO}`);
      methodLogs.delete(methodName);
    }
  }

  return result;
}

export function logBigOMetrics(target: any, propertyKey: string, descriptor: PropertyDescriptor) {
  const originalMethod = descriptor.value;

  descriptor.value = function (...args: any[]) {
    const startTime = performance.now();
    const result = originalMethod.apply(this, args);
    const endTime = performance.now();
    const runTime = endTime - startTime;

    const methodName = `${target.constructor.name}.${propertyKey}`;
    if (!methodLogs.has(methodName)) {
      methodLogs.set(methodName, []);
    }

    const methodLog = methodLogs.get(methodName);

    const maxDataSize = args.length === 1 && typeof args[0] === 'number' ? args[0] : findPotentialN(args);
    if (methodLog) {
      methodLog.push([runTime, maxDataSize]);

      if (methodLog.length >= 20) {
        isDebug && console.log('triggered', methodName, methodLog);
        const bigO = estimateBigO(
          methodLog.map(([runTime]) => runTime),
          methodLog.map(([runTime]) => runTime)
        );
        isDebug && console.log(`Estimated Big O: ${bigO}`);
        methodLogs.delete(methodName);
      }
    }

    return result;
  };

  return descriptor;
}