Syntax error Program to find valid matrix given row and column sums in Python

Program to find valid matrix given row and column sums in Python

Suppose we have two arrays rowSum and colSum with non-negative values where rowSum[i] has the sum of the elements in the ith row and colSum[j] has the sum of the elements in the jth column of a 2D matrix. We have to find any matrix with non-negative values of size (rowSum size x colSum size) that satisfies the given rowSum and colSum values.

So, if the input is like rowSum = [13,14,12] colSum = [9,13,17], then the output will be

9 4 0
0 9 5
0 0 12

To solve this, we will follow these steps −

  • matrix := create empty matrix
  • visited := a new set
  • Define a function minimum() . This will take r,c
  • min_total := infinity
  • type := blank string
  • for i in range 0 to size of r - 1, do
    • if r[i] < min_total, then
      • index := i
      • type := 'row'
      • min_total := r[i]
  • for i in range 0 to size of c - 1, do
    • if c[i] < min_total, then
      • min_total := c[i]
      • type := 'col'
      • index := i
  • if type is same as 'row', then
    • r[index] := infinity
    • for i in range 0 to size of c - 1, do
      • if c[i] is not same as infinity and c[i] >= min_total, then
        • c[i] := c[i] - min_total
        • matrix[index, i] := min_total
        • come out from loop
  • if type is same as 'col', then
    • c[index] := infinity
    • for i in range 0 to size of r - 1, do
      • if r[i] is not same as infinity and r[i] >= min_total, then
        • r[i] := r[i] - min_total
        • matrix[i, index] := min_total
        • come out from loop
  • insert pair (index,type) into visited
  • From the main method do the following −
  • while size of visited is not same as size of r +len(c) , do
  • minimum(r, c)
  • return matrix

Example

Let us see the following implementation to get better understanding −

def solve(r, c):
   matrix = [[0]*len(c) for _ in range(len(r))]
   visited = set()

   def minimum(r,c):
      min_total = float('inf')
   
      type = ''
      for i in range(len(r)):
         if(r[i] < min_total):
            index = i
            type = 'row'
            min_total = r[i]

      for i in range(len(c)):
         if(c[i] < min_total):
            min_total = c[i]
            type = 'col'
            index = i

      if(type == 'row'):
         r[index] = float('inf')

         for i in range(len(c)):
            if(c[i] != float('inf') and c[i] >= min_total):
               c[i] -= min_total
               matrix[index][i] = min_total
               break

      if(type == 'col'):
         c[index] = float('inf')
         for i in range(len(r)):
            if(r[i] != float('inf') and r[i] >= min_total):
               r[i] -= min_total
               matrix[i][index] = min_total
               break

      visited.add((index,type))

   while len(visited) != len(r)+len(c):
      minimum(r,c)

   return matrix

rowSum = [13,14,12]
colSum = [9,13,17]
print(solve(rowSum, colSum))

Input

[13,14,12], [9,13,17]

Output

[[9, 4, 0], [0, 9, 5], [0, 0, 12]]
Updated on: 2021-10-04T13:15:42+05:30

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