Step by Step solution about How to resolve the algorithm Statistics/Basic step by step in the Go programming language

First code: Sample data analysis

This Go program demonstrates how to perform statistical analysis on a sample of data. It takes an integer value n as input, generates n random floating-point numbers, and then calculates the mean (average), standard deviation, and a histogram of the data. Here is a breakdown of the code:

1. main() function:

   • Calls the sample() function three times with different values of n to analyze samples of size 100, 1000, and 10000.

2. sample() function:

   • Generates a slice of n random floating-point numbers.
   • Computes the sum and sum of squares of the data.
   • Calculates the mean (m) and standard deviation (math.Sqrt(ssq/float64(n)-m*m)).
   • Creates a histogram (h) with 10 bins, where each bin represents a range of 0.1 (e.g., bin 0 is 0-0.1, bin 1 is 0.1-0.2, etc.).
   • The histogram is represented as a series of asterisks (*), with the number of asterisks in a bin proportional to the count of data points in that bin.

Second code: Big sample data analysis using MapReduce

This Go program demonstrates how to parallelize statistical analysis using the MapReduce pattern for a very large dataset (10 million elements). The main idea is to divide the dataset into smaller chunks, process them in parallel, and then combine the results to obtain the final statistics. Here is a breakdown of the code:

1. main() function:

   • Calls the bigSample() function with n set to 10 million.

2. bigSample() function:

   • Computes the sum, sum of squares, and histogram by invoking the reduce() function with start and end values representing the range of data to process.

3. reduce() function:

   • If n is less than a predefined threshold (threshold is set to 1 million), it calls getSegment() to fetch the data and computeSegment() to calculate the sum, sum of squares, and histogram for that segment.
   • If n exceeds the threshold, it recursively divides the task into two subproblems (reducing the size of n) and combines the results from the subproblems.

4. getSegment() function:

   • Fetches a segment of the data (slice of floating-point numbers) based on the given range.

5. computeSegment() function:

   • Computes the sum, sum of squares, and histogram for a segment of the data.

The MapReduce approach allows us to process large datasets in parallel, reducing the overall computation time and making it feasible to analyze massive amounts of data efficiently.

package main

import (
    "fmt"
    "math"
    "math/rand"
    "strings"
)

func main() {
    sample(100)
    sample(1000)
    sample(10000)
}

func sample(n int) {
    // generate data
    d := make([]float64, n)
    for i := range d {
        d[i] = rand.Float64()
    }
    // show mean, standard deviation
    var sum, ssq float64
    for _, s := range d {
        sum += s
        ssq += s * s
    }
    fmt.Println(n, "numbers")
    m := sum / float64(n)
    fmt.Println("Mean:  ", m)
    fmt.Println("Stddev:", math.Sqrt(ssq/float64(n)-m*m))
    // show histogram
    h := make([]int, 10)
    for _, s := range d {
        h[int(s*10)]++
    }
    for _, c := range h {
        fmt.Println(strings.Repeat("*", c*205/int(n)))
    }
    fmt.Println()
}


package main

import (
    "fmt"
    "math"
    "math/rand"
    "strings"
)

func main() {
    bigSample(1e7)
}

func bigSample(n int64) {
    sum, ssq, h := reduce(0, n)
    // compute final statistics and output as above
    fmt.Println(n, "numbers")
    m := sum / float64(n)
    fmt.Println("Mean:  ", m)
    fmt.Println("Stddev:", math.Sqrt(ssq/float64(n)-m*m))
    for _, c := range h {
        fmt.Println(strings.Repeat("*", c*205/int(n)))
    }
    fmt.Println()
}

const threshold = 1e6

func reduce(start, end int64) (sum, ssq float64, h []int) {
    n := end - start
    if n < threshold {
        d := getSegment(start, end)
        return computeSegment(d)
    }
    // map to two sub problems
    half := (start + end) / 2
    sum1, ssq1, h1 := reduce(start, half)
    sum2, ssq2, h2 := reduce(half, end)
    // combine results
    for i, c := range h2 {
        h1[i] += c
    }
    return sum1 + sum2, ssq1 + ssq2, h1
}

func getSegment(start, end int64) []float64 {
    d := make([]float64, end-start)
    for i := range d {
        d[i] = rand.Float64()
    }
    return d
}

func computeSegment(d []float64) (sum, ssq float64, h []int) {
    for _, s := range d {
        sum += s
        ssq += s * s
    }
    h = make([]int, 10)
    for _, s := range d {
        h[int(s*10)]++
    }
    return
}