从和来重建矩阵

1 回答

• 1

  是 . 你拥有的是system of linear equations，每行一个，每列一个; m * n个变量和m n个方程 .

  如何计算（和表示）解决此类系统的解决方案集取决于您的环境 .

  EDIT: 我明白了 . 有关此问题的大型实例，请参阅integer programming .

  但如果矩阵和行/列总和很小，则可以通过backtracking找到所有解 . 非常高级的伪代码：

  function SOLVE(partially filled M) {
  
      if (M has no empty entries) {
  
          M is a solution
  
      } else {
  
          ij <- one empty position of M
          // in practice, try picking one that reduces the number of
          // iterations of the following loop
  
          for (each possible value v of M[ij], subject to the constraints) {
              M' <- a copy of M
              M'[ij] = v
              SOLVE(M')
      }
  }
  
  
  M0 <- an empty Matrix of correct size
  
  SOLVE(M0)
  

  回复于 2024-04-29T17:30:28+08:00