TSP-dp(状态压缩)

• TSP-DP
  直接上js代码

//js代码
//D 为二维数组(nxn矩阵)
function TSP(D) { //起点为0
    const INF = 65535 //定义的最大值
    var n= D.length // n的个数
    var i, j, k, min, tmp;
    var b = 1 << (n - 1); // 点集状态总数
    var dp = {}  // 记录状态
    var bridge = {} //记录中间节点
    for (i = 0; i < n; i++) { //初始化dp与bridge
        dp[i] = {}
        bridge[i] = {}
        for (j = 0; j < b; j++)
		{
			dp[i][j] = -1;
			bridge[i][j] = -1;
		}
    } 
    for (i = 0; i < n; i++) { //初始化 dp的第0列
        dp[i][0] = D[i][0]
    }
    //init end

    //遍历二维数组即遍历dp
    for (i = 1; i < b - 1; i++) {
        for (j = 1; j < n; j++) {
            if ((1 << (j - 1) & i) == 0) { 
                //点j未访问
                min = INF
                for (k = 1; k < n; k++) { //遍历点集
                    if (1 << (k - 1) & i) { 
                        //点k在集合中

                        // 松弛操作
                        tmp = D[j][k] + dp[k][i - (1 << (k - 1))]
                        if (tmp < min) { 
                            min = tmp
                            dp[j][i] = min
                            bridge[j][i] = k
                        }
                    }
                }
            }
        }
    }
    //处理最后一列
    min = INF
    for(k=1;k<n;k++) {
        // 松弛操作
        tmp = D[0][k] + dp[k][b-1-(1<<(k-1))] //b-1-(1<<(k-1)) :  去掉k节点
        if( tmp < min) {
            min = tmp
            dp[0][b-1] = min
            bridge[0][b-1] = k
        }
    }
    var mincost = dp[0][b-1]
    var path = [0]
    for(i=b-1,j=0;i>0;) {
        j = bridge[j][i] // 下一个节点
        i = i-( 1<<(j-1))
        path.push(j)
    }
    path.push(0)
    //返回值说明 path为路径, mincost为最短花费
    return [path, mincost]
    
}

//测试数据
var m = [
    [0, 7, 6, 10, 13],
    [7, 0, 7, 10, 10],
    [6, 7, 0, 5, 9],
    [10, 10, 5, 0, 6],
    [13, 10, 9, 6, 0]
]

var res = TSP(m)
console.log("最短路径 : ",res[0])
console.log("最少花费 : ",res[1])