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# 311.Sparse-Matrix-Multiplication

## 311. Sparse Matrix Multiplication

## 题目地址

<https://leetcode.com/problems/sparse-matrix-multiplication/>

## 题目描述

```
Given two sparse matrices A and B, return the result of AB.

You may assume that A's column number is equal to B's row number.

Example:

Input:

A = [
  [ 1, 0, 0],
  [-1, 0, 3]
]

B = [
  [ 7, 0, 0 ],
  [ 0, 0, 0 ],
  [ 0, 0, 1 ]
]

Output:

     |  1 0 0 |   | 7 0 0 |   |  7 0 0 |
AB = | -1 0 3 | x | 0 0 0 | = | -7 0 3 |
                  | 0 0 1 |
```

## 代码

### Approach #1

```java
class Solution {
  public int[][] multiply(int[][] A, int[][] B) {
        int m = A.length, n = A[0].length;
    int nB = B[0].length;
    int[][] C = new int[m][nB];

    for (int i = 0; i < m; i++) {
      for (int k = 0; k < n; k++) {
        if (A[i][k] != 0) {
          for (int j = 0; j < nB; j++) {
            if (B[k][j] != 0) C[i][j] += A[i][k] * B[k][j];
          }
        }
      }
    }

    return C;
  }
}
```

```java
class Solution {
  public int[][] multiply(int[][] A, int[][] B) {
    int m = A.length, n = A[0].length, nB = B[0].length;
    int[][] C = new int[m][nB];

    for (int i = 0; i < m; i++) {
      for (int j = 0; j < nB; j++) {
          for (int k = 0; k < n; k++) {
            C[i][j] += A[i][k] * B[k][j];
          }
      }
    }
    return C;  
  }
}
```