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‎CH11/Checkpoints

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#11.1
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lst = [
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[0,0,0,0],
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[0,0,0,0],
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[0,0,0,0]
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]
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#11.2
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Yes
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#11.3
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[[2, 1, 1], [1, 1, 1], [1, 1, 1]]
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#11.4
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[[[1, 1, 1]], [[1, 1, 1]], [[1, 1, 1]]]
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[3, [[1, 1, 1]], [[1, 1, 1]]]
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#11.5
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[[1, 2, 3], [4, 5], [6, 7, 8, 9]]
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#11.6
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00
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01
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11
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12
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#11.7
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0001
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0001
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1112
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1112

‎CH11/EX11.1.py

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# 11.1 (Sum elements column by column) Write a function that returns the sum of all the
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# elements in a specified column in a matrix using the following header:
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# def sumColumn(m, columnIndex):
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# Write a test program that reads a 3*4 matrix and displays the sum of each column.
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def sumColumn(m, columnIndex):
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sum = 0
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for row in range(len(m)):
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sum += m[row][columnIndex]
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return sum
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m = []
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for i in range(3):
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row = input("Enter a 3-by-4 matrix row for row " + str(i)+": ").split()
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m.append([float(x) for x in row])
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for i in range(4):
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s = sumColumn(m, i)
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print("Sum of the elements for column", i, 'is', s)

‎CH11/EX11.10.py

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# 11.10 (Largest rows and columns) Write a program that randomly fills in 0s and 1s into
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# a 4*4 matrix, prints the matrix, and finds the rows and columns with the most
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# 1s.
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import random
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def count_ones(lst):
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count = 0
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current_count = count
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indx = []
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for row in range(len(lst)):
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for col in lst[row]:
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if col == 1:
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current_count += 1
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if current_count > count:
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indx.clear()
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count = current_count
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indx.append(row)
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elif current_count == count:
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indx.append(row)
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current_count = 0
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return indx
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lst = []
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for i in range(4):
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lst.append([])
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for j in range(4):
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lst[i].append(random.randint(0, 1))
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for r in lst:
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for c in r:
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print(c, end=" ")
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print()
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print("The largest row index:", count_ones(lst))
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# transose matrix
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lst = [[row[i] for row in lst] for i in range(len(lst[0]))]
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print("The largest column index:", count_ones(lst))

‎CH11/EX11.11.py

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# 11.11 (Game: nine heads and tails) Nine coins are placed in a matrix with some
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# face up and some face down. You can represent the state of the coins with the values
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# 0 (heads) and 1 (tails). Here are some examples:
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# 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0
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# 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1
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# 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0
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# Each state can also be represented using a binary number. For example, the preceding
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# matrices correspond to the numbers:
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# 000010000 101001100 110100001 101110100 100111110
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# There are a total of 512 possibilities. So, you can use the decimal numbers 0, 1, 2,
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# 3, ..., and 511 to represent all states of the matrix. Write a program that prompts
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# the user to enter a number between 0 and 511 and displays the corresponding
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# 3 * 3 matrix with the characters H and T.
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# The user entered 7, which corresponds to 000000111. Since 0 stands for H and 1 for T, the output is correct.
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def dec_to_bin(num):
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bin = []
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while num > 0:
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bin.append(num % 2)
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num = num // 2
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while len(bin) < 9:
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bin.append(0)
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bin.reverse()
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return bin
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def print_matrix(mat):
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for i in range(len(mat)):
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if mat[i] == 0:
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print('H', end=' ')
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else:
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print('T', end=' ')
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if (i + 1) % 3 == 0:
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print()
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num = int(input("Enter a number between 0 and 511: "))
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mat = dec_to_bin(num)
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print_matrix(mat)

‎CH11/EX11.12.py

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# 11.12 (Financial application: compute tax) Rewrite Listing 4.7, ComputeTax.py, using
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# lists. For each filing status, there are six tax rates. Each rate is applied to a certain
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# amount of taxable income. For example, from the taxable income of 400,000ドル for
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# a single filer, 8,350ドル is taxed at 10%, (33,950 – 8,350) at 15%, (82,250 – 33,950)
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# at 25%, (171,550 – 82,250) at 28%, (372,950 – 171,550) at 33%, and (400,000 –
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# 372,950) at 35%. The six rates are the same for all filing statuses, which can be
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# represented in the following list:
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# rates = [0.10, 0.15, 0.25, 0.28, 0.33, 0.35]
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# The brackets for each rate for all the filing statuses can be represented in a twodimensional
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# list as follows:
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# brackets = [
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# [8350, 33950, 82250, 171550, 372950], # Single filer
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# [16700, 67900, 137050, 208850, 372950], # Married jointly
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# [8350, 33950, 68525, 104425, 186475], # Married separately
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# [11950, 45500, 117450, 190200, 372950] # Head of household
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# ]
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# Suppose the taxable income is 400,000ドル for single filers. The tax can be computed
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# as follows:
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# tax = brackets[0][0] * rates[0] +
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# (brackets[0][1] – brackets[0][0]) * rates[1] +
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# (brackets[0][2] – brackets[0][1]) * rates[2] +
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# (brackets[0][3] – brackets[0][2]) * rates[3] +
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# (brackets[0][4] – brackets[0][3]) * rates[4] +
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# (400000 – brackets[0][4]) * rates[5]
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def main():
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status = eval(input("(0-single filer, 1-married jointly,\n" +
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"2-married separately, 3-head of household)\n" +
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"Enter the filing status: "))
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# Prompt the user to enter taxable income
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income = eval(input("Enter the taxable income: "))
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# Compute and display the result
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print("Tax is", format(computeTax(status, income), "7.2f"))
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def computeTax(status, income):
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rates = [0.10, 0.15, 0.25, 0.28, 0.33, 0.35]
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brackets = [
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[8350, 33950, 82250, 171550, 372950], # Single filer
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[16700, 67900, 137050, 20885, 372950], # Married jointly
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[8350, 33950, 68525, 104425, 186475], # Married separately
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[11950, 45500, 117450, 190200, 372950] # Head of household
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]
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tax = 0 # Tax to be computed
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# Compute tax in the first bracket
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if income <= brackets[status][0]:
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return income * rates[0] # Done
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else:
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tax = brackets[status][0] * rates[0]
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# Compute tax in the 2nd, 3rd, 4th, and 5th brackets, if needed
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for i in range(1, len(brackets[0])):
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if income > brackets[status][i]:
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tax += (brackets[status][i] - brackets[status][i - 1]) * rates[i]
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else:
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tax += (income - brackets[status][i - 1]) * rates[i]
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return tax # Done
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# Compute tax in the last (i.e., 6th) bracket
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return tax + (income - brackets[status][4]) * rates[5]
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main()

‎CH11/EX11.13.py

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# 11.13 (Locate the largest element) Write the following function that returns the location
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# of the largest element in a two-dimensional list:
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# def locateLargest(a):
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# The return value is a one-dimensional list that contains two elements. These
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# two elements indicate the row and column indexes of the largest element in the
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# two-dimensional list. Write a test program that prompts the user to enter a two dimensional
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# list and displays the location of the largest element in the list.
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def locateLargest(a):
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max_indx_row = 0
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max_indx_col = 0
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for i in range(len(a)):
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for j in range(len(a[i])):
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if a[i][j] > a[max_indx_row][max_indx_col]:
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max_indx_row = i
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max_indx_col = j
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return max_indx_row, max_indx_col
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rows = int(input("Enter the number of rows in the list: "))
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matrix = []
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for i in range(rows):
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r = input("Enter a row: ").split()
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r = [float(x) for x in r]
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matrix.append(r)
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row, col = locateLargest(matrix)
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print("The location of the largest element is at (" + str(row) + "," + str(col) + ")")

‎CH11/EX11.14.py

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# 11.14 (Explore matrix) Write a program that prompts the user to enter the length of a
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# square matrix, randomly fills in 0s and 1s into the matrix, prints the matrix, and
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# finds the rows, columns, and major diagonal with all 0s or all 1s.
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import random
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def print_matrix(mat):
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for i in mat:
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for j in i:
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print(j, end='')
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print()
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def find_in_row(mat, x):
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indx = []
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for row in mat:
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if sum(row) == x * len(row):
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indx.append(mat.index(row))
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if len(indx) == 0:
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return None
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return indx
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def find_in_diagonal(mat, x):
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indx = []
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for i in range(len(mat)):
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if mat[i][i] != x:
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return None
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for i in range(len(mat)-1, 0, -1):
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if mat[i][i] != x:
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return None
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return True
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size = int(input("Enter the size for the matrix: "))
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mat = []
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for r in range(size):
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mat.append([0] * size)
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for c in range(size):
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mat[r][c] = random.randint(0, 1)
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print_matrix(mat)
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a = find_in_row(mat, 0)
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b = find_in_row(mat, 1)
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if a is None and b is None:
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print("No same numbers in a row")
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else:
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if a is not None:
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print("All 0s on row ", end='')
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for i in a:
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print(i, end=' ')
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print()
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if b is not None:
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print("All 1s on row ", end='')
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for i in b:
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print(i, end=' ')
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print()
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# transpose matrix
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mat_traspose = [[row[i] for row in mat] for i in range(len(mat[0]))]
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a = find_in_row(mat_traspose, 0)
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b = find_in_row(mat_traspose, 1)
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if a is None and b is None:
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print("No same numbers in a column")
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else:
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if a is not None:
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print("All 0s on column ", end='')
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for i in a:
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print(i, end=' ')
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print()
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if b is not None:
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print("All 1s on column ", end='')
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for i in b:
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print(i, end=' ')
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print()
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c = find_in_diagonal(mat, 0)
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d = find_in_diagonal(mat, 1)
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if c is None and d is None:
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print("No same numbers in the major diagonal")
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else:
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if c is not None:
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print("All 0s on the diagonal")
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elif d is not None:
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print("All 1s on the diagonal")
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print()

‎CH11/EX11.15.py

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# 11.15 (Geometry: same line?) Exercise 6.19 gives a function for testing whether three
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# points are on the same line. Write the following function to test whether all the
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# points in the points list are on the same line:
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# def sameLine(points):
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# Write a program that prompts the user to enter five points and displays whether
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# they are on the same line.
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def sameLine(points):
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x0 = points[0]
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y0 = points[1]
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x4 = points[-2]
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y4 = points[-1]
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for i in range(2, len(points) - 1, 2):
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x = points[i]
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y = points[i + 1]
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d = (x - x0) * (y4 - y0) - (x4 - x0) * (y - y0)
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if d != 0:
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return False
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return True
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points = input("Enter five points: ").split()
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points = [eval(x) for x in points]
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if sameLine(points):
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print("The five points are on the same line")
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else:
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print("The five points are not on the same line")

‎CH11/EX11.16.py

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# 11.16 (Sort a list of points on y-coordinates) Write the following function to sort a list
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# of points on their y-coordinates. Each point is a list of two values for x- and ycoordinates.
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# # Returns a new list of points sorted on the y-coordinates
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# def sort(points):
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# For example, the points [[4, 2], [1, 7], [4, 5], [1, 2], [1, 1], [4, 1]] will be sorted
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# to [[1, 1], [4, 1], [1, 2], [4, 2], [4, 5], [1, 7]]. Write a test program that displays
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# the sorted result for points [[4, 34], [1, 7.5], [4, 8.5], [1, -4.5], [1, 4.5],
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# [4, 6.6]] using print(list).
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# Returns a new list of points sorted on the y-coordinates
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def sort(points): # insertion sort
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for i in range(1, len(points)):
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current = points[i]
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j = i - 1
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while j >= 0 and current[1] < points[j][1]:
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points[j + 1] = points[j]
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j -= 1
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points[j + 1] = current
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points = [[4, 34], [1, 7.5], [4, 8.5], [1, -4.5], [1, 4.5], [4, 6.6]]
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sort(points)
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print(points)

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