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How to solve the big numbers matrix problem in Python

Srivasthavi Mannepula

Given a two-dimensional integer matrix, return the total number of integers whose value is the largest in its row and column.

Step 1

Understanding the problem

  • We need to find the maximum element in each row and see if it’s also the maximum in its column.
  • Return the count for the number of times this condition is satisfied.
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  • 3 is the maximum element in row 0, but it’s not the maximum in its column-(column 1).

  • 6 is the largest/maximum element in row 1 and column 1.

  • Similarly, 7 is the largest element in row 2 and column 2.

Therefore, since 6 and 7 are the maximum elements that satisfy the condition, we return 2.

Step 2

Finding the maximum element in the row

  • Using the for loop we find the maximum element in each row and append each element into a list.

Ex:

|1|33|2|

|4|66|5|

|1|5|77|

Here, 3, 6, and 7 are going to be appended to list1.

 m=[[1, 3, 2], [4, 6, 5], [1, 5, 7]]
 r=len(m)
 c=len(m[0])
 l=[]
 for i in range(r): 
     max=0
     for j in range(c): 
         if m[i][j] > max:
             max = m[i][j]
     l.append(max)

Step 3

Verifying the maximum element in its respective column

  • In order to find the maximum element in the previous maximum element’s respective column, we will to transpose the matrix.
  • Then, repeat step 2 to find the max element.

Ex: transpose method

| 1 | 4 | 1 |

| 3 | 6 | 5 |

| 2 | 5 | 7 |

matrix2 = (Transpose of matrix1)

We can take transpose using the zip method.

m=[[1, 3, 2], [4, 6, 5], [1, 5, 7]]
m2 = list(zip(*m))
  • Repeat step 2 with the transposed matrix:

Ex:

| 1 | 44 | 1 |

| 3 | 66| 5 |

| 2 | 5 | 77 |

Here, 4, 6, and 7 will be appended to list2:

 m=[[1, 3, 2], [4, 6, 5], [1, 5, 7]]
 r=len(m)
 c=len(m[0])
 m2 = list(zip(*m))
 l2=[]
 for i in range(r): 
     max=0
     for j in range(c): 
         if m[i][j] > max: 
             max = m[i][j]
     l2.append(max)

Step 4

Count the elements that satisfy the condition

  • Using the for and if conditions, we compare the element in list1 and list2, from steps 2 and 3, to see if they match.
  • If they do match, we append them to a list.

EX:

LIST1=[3,6,7]

LIST2=[4,6,7]

Therefore, since 6 and 7 are the same, we append those two elements to list3:

m=[[1, 3, 2], [4, 6, 5], [1, 5, 7]]
r=len(m)
c=len(m[0])
l=[]
for i in range(r): 
    max=0
    for j in range(c): 
        if m[i][j] > max:
            max = m[i][j]
    l.append(max)
m2 = list(zip(*m))
l2=[]
for i in range(r): 
    max=0
    for j in range(c): 
        if m[i][j] > max: 
            max = m[i][j]
    l2.append(max)
a=[]
for r in range(len(m)):
    for c in range(len(m2)):
        b = m[r][c]
        if (l[r], l2[c]) == (b, b):
            a.append(b)

Step-5:

Output:

  • We return the length of list three.

EX:

List3 = [6,7]

Therefore, the length is 2.

Hence, the output is 2.

m=[[1, 3, 2], [4, 6, 5], [1, 5, 7]]
r=len(m)
c=len(m[0])
l=[]
for i in range(r): 
    max=0
    for j in range(c): 
        if m[i][j] > max:
            max = m[i][j]
    l.append(max)
m2 = list(zip(*m))
l2=[]
for i in range(r): 
    max=0
    for j in range(c): 
        if m[i][j] > max: 
            max = m[i][j]
    l2.append(max)
a=[]
for r in range(len(m)):
    for c in range(len(m2)):
        b = m[r][c]
        if (l[r], l2[c]) == (b, b):
            a.append(b)
print(len(a))

Complete code

m=[[1, 3, 2], [4, 6, 5], [1, 5, 7]]
r=len(m)
c=len(m[0])
l=[]
for i in range(r): 
    max=0
    for j in range(c): 
        if m[i][j] > max:
            max = m[i][j]
    l.append(max)
m2 = list(zip(*m))
l2=[]
for i in range(r): 
    max=0
    for j in range(c): 
        if m[i][j] > max: 
            max = m[i][j]
    l2.append(max)
a=[]
for r in range(len(m)):
    for c in range(len(m2)):
        b = m[r][c]
        if (l[r], l2[c]) == (b, b):
            a.append(b)
print(len(a))

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