Description

Given an array of n * m matrix, and a moving matrix window (size k * k), move the window from top left to bottom right at each iteration, find the maximum sum inside the window at each moving.

Return 0 if the answer does not exist.

Example

Example 1:

Input:[[1,5,3],[3,2,1],[4,1,9]],k=2
Output:13
Explanation:
At first the window is at the start of the matrix like this [
[|1, 5|, 3],
[|3, 2|, 1],
[4, 1, 9],
]
,get the sum 11;
then the window move one step forward. [
[1, |5, 3|],
[3, |2, 1|],
[4, 1, 9],
]
,get the sum 11;
then the window move one step forward again. [
[1, 5, 3],
[|3, 2|, 1],
[|4, 1|, 9],
]
,get the sum 10;
then the window move one step forward again. [
[1, 5, 3],
[3, |2, 1|],
[4, |1, 9|],
]
,get the sum 13;
SO finally, get the maximum from all the sum which is 13.

Example 2:

Input:[[10],k=1
Output:10
Explanation:
sliding window size is 1*1,and return 10.

Challenge

O(n^2) time.

思路:

考点:

  • 二维前缀和

题解:

  • sum[i][j]存储左上角坐标为(0,0),右下角坐标为(i,j)的子矩阵的和。
  • sum[i][j] = matrix[i - 1][j - 1] + sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1];递推求值即可,两部分相加,减去重复计算部分。
  • int value = sum[i][j] - sum[i - k][j] -sum[i][j - k] + sum[i - k][j - k];可求得一个k * k大小子矩阵的和。
    public class Solution {
    /**
    * @param matrix: an integer array of n * m matrix
    * @param k: An integer
    * @return: the maximum number
    */
    public int maxSlidingMatrix(int[][] matrix, int k) {
    // Write your code here
    int n = matrix.length;
    if (n == 0 || n < k)
    return 0;
    int m = matrix[0].length;
    if (m == 0 || m < k)
    return 0; int[][] sum = new int[n + 1][m + 1];
    for (int i = 0; i <= n; ++i) sum[i][0] = 0;
    for (int i = 0; i <= m; ++i) sum[0][i] = 0; for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= m; ++j)
    sum[i][j] = matrix[i - 1][j - 1] +
    sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1]; int max_value = Integer.MIN_VALUE;
    for (int i = k; i <= n; ++i)
    for (int j = k; j <= m; ++j) {
    int value = sum[i][j] - sum[i - k][j] -
    sum[i][j - k] + sum[i - k][j - k]; if (value > max_value)
    max_value = value;
    }
    return max_value;
    }
    }

      

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