Microbiologists estimating the number of bacteria in a sample that contains
bacteria that do not grow well on solid media may use a statistical technique
called the most probable number (MPN) method. Each of five tubes of nutrient
medium receives 10 ml of the sample. A second set of five tubes receives
1 ml of sample per tube, and in each of a third set of five tubes, only 0.1 ml of
sample is placed. Each tube in which bacterial growth is observed is recorded
as a positive, and the numbers for the three groups are combined to create a
triplet such as 5-2-1, which means that all five tubes receiving 10 ml of sample
show bacterial growth, only two tubes in the 1-ml group show growth, and
only one of the 0.1-ml group is positive. A microbiologist would use this combination-
of-positives triplet as an index to a table like the table below to determine
that the most probable number of bacteria per 100 ml of the sample is
Table of Bacterial Concentrations for Most Probable Number Method
Combination of Positives MPN Index/100 ml 95 percent Confi dence Limits
Lower Upper
4-2-0 22 9 56
4-2-1 26 12 65
4-3-0 27 12 67
4-3-1 33 15 77
4-4-0 34 16 80
5-0-0 23 9 86
5-0-1 30 10 110
5-0-2 40 20 140
5-1-0 30 10 120
5-1-1 50 20 150
5-1-2 60 30 180
5-2-0 50 20 170
5-2-1 70 30 210
5-2-2 90 40 250
5-3-0 80 30 250
5-3-1 110 40 300
5-3-2 140 60 360
70, and 95 percent of the samples yielding this triplet contain between 30 and
210 bacteria per 100 ml.
Define a structure type to represent one row of the MPN table. The
structure will include one string component for the combination-of-positives
triplet and three integer components in which to store the associated most
probable number and the lower and upper bounds of the 95 percent confidence
range. Write a program to implement the following algorithm for generating
explanations of combination-of-positives triplets.
a. Load the MPN table from a file into an array of structures called
mpn_table .
b. Repeatedly get from the user a combination-of-positives triplet, search
for it in the combination-of-positives components of mpn_table , and then
generate a message such as:
For 5-2-1, MPN = 70; 95% of samples contain between 30 and
210 bacteria/ml.
c. Define and call the following functions.
load_Mpn_Table —Takes as parameters the name of the input fi le, the
mpn_table array and its maximum size. Function opens the fi le, fi lls
the mpn_table array, and closes the fi le. Then it returns the actual
array size as the function result. If the fi le contains too much data, the
function should store as much data as will fi t, display an error message
indicating that some data has been ignored, and return the array’s
maximum size as its actual size.
search —Takes as parameters the mpn_table array, its actual size, and a
target string representing a combination-of-positives triplet. Returns
the subscript of the structure whose combination-of-positives component
matches the target or 1 if not found.
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mujhe mujhe nahin aate hai
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