矩阵最优路径
Given an NxM (N rows and M columns) integer matrix with non-negative values (0..MAX_INT inclusive). What is the maximum sum from going top left (0, 0) to bottom right (N-1, M-1) ? The condition is that when you're at point (p, q), you can only move to either right (p, q+1) or down (p+1, q).
Expected time complexity O(N*M)
Expected space complexity O(N+M)
about space complexity, need elaborate on it.
package com.zhuyu_deng.test;
public class Test
{
private static int findOptPath(int[][] a)
{
int d[][] = new int[a.length][a[0].length];
int m = a.length;
int n = a[0].length;
d[0][0] = a[0][0];
for (int i = 1; i < m; ++i)
d[i][0] = d[i - 1][0] + a[i][0];
for (int j = 1; j < n; ++j)
d[0][j] = d[0][j - 1] + a[0][j];
for (int i = 1; i < m; ++i)
{
for (int j = 1; j < n; ++j)
{
if (d[i-1][j] > d[i][j-1])
d[i][j] = a[i][j] + d[i-1][j];
else
d[i][j] = a[i][j] + d[i][j-1];
}
}
for (int i = 0; i < m; ++i)
{
for (int j = 0; j < n; ++j)
System.out.print(a[i][j] + " ");
System.out.println();
}
System.out.println();
for (int i = 0; i < m; ++i)
{
for (int j = 0; j < n; ++j)
System.out.print(d[i][j] + " ");
System.out.println();
}
return d[m - 1][n - 1];
}
public static void main(String args[])
{
// int[] a = {-2,11,-4,13,-5,-2};
int[][] b = { { 0, -2, -7, 0 }, { 9, 2, -6, 2 }, { -4, 1, -4, 1 },
{ -1, 8, 0, -2 } };
int [][] matrix =
{ {2,3,4,1},
{1,1,3,9},
{2,2,3,1},
{2,2,3,1}
};
System.out.println(findOptPath(matrix));
}
}