最短路径(弗洛伊德算法)

1.定义概述

Floyd-Warshall算法（Floyd-Warshall algorithm）是解决任意两点间的最短路径的一种算法，可以正确处理有向图或负权的最短路径问题，同时也被用于计算有向图的传递闭包。

2.实例演示

/**
* 弗洛伊德算法求最短路径
* @author sunbufu
*
*/
public class ShortestPathFloyd {
/**无穷大*/
final static int INF = Integer.MAX_VALUE;

public static void main(String[] args) {
int[] points = { 1, 2, 3, 4, 5, 6 };
int[][] weights = {
//               1    2    3    4    5    6
{0,   7,   9,   INF, INF, 14   },//1
{7,   0,   10,  15,  INF, INF  },//2
{9,   10,  0,   11,  INF, 2    },//3
{INF, 15,  11,  0,   6,   INF  },//4
{INF, INF, INF, 6,   0,   9    },//5
{14,  INF, 2,   INF, 9,   0    } //6
};
int[][] previousPoint = {
//               1    2    3    4    5    6
{1,   2,   3,   4,   5,   6    },//1
{1,   2,   3,   4,   5,   6    },//2
{1,   2,   3,   4,   5,   6    },//3
{1,   2,   3,   4,   5,   6    },//4
{1,   2,   3,   4,   5,   6    },//5
{1,   2,   3,   4,   5,   6    } //6
};
floyd(points, weights, previousPoint);
}

private static void floyd(int[] points, int[][] weights, int[][] previousPoint) {
int pointsNumber = points.length;
for(int k = 0; k < pointsNumber; k ++){
for(int i = 0; i < pointsNumber; i ++){
for(int j = 0; j < pointsNumber; j ++){
if(weights[i][k] != INF && weights[k][j] != INF && (weights[i][k] + weights[k][j]) < weights[i][j]){
weights[i][j] = weights[i][k] + weights[k][j];
previousPoint[i][j] = k;
}
}
}
}
System.out.println(weights);
}
}

3.总结

简洁的解决了最短路径问题，但是时间复杂度为

O(n^3)

。