文心一言 VS 讯飞星火 VS chatgpt （380）-- 算法导论24.4 12题

package main

import(
"fmt"
"math"
)

const(
    INF = math.MaxInt32
)

// BellmanFord 解决差分约束系统问题
func BellmanFord(n int, edges [][]int, weights [][]float64)([]int,bool){
// 初始化距离数组，dist[i] 表示从源点到 i 的最短距离
    dist :=make([]int, n+1)
for i :=range dist {
        dist[i]= INF
}
    dist[0]=0// 源点到自身的距离为 0

// Bellman-Ford 算法
for i :=0; i < n; i++{
for _, edge :=range edges {
            u, v := edge[0], edge[1]
            w :=float64(weights[u-1][v-1])
if dist[u]!= INF && dist[u]+int(math.Round(w))< dist[v]{
                dist[v]= dist[u]+int(math.Round(w))
}
}
}

// 检查负权环
for _, edge :=range edges {
        u, v := edge[0], edge[1]
        w :=float64(weights[u-1][v-1])
if dist[u]!= INF && dist[u]+int(math.Round(w))< dist[v]{
returnnil,false// 存在负权环，无解
}
}

// 检查是否为整数解
for _, d :=range dist[1:]{
iffloat64(d)!= math.Round(float64(d)){
returnnil,false// 不是整数解
}
}

return dist[1:],true// 返回从源点到各个节点的最短路径（去掉源点自身）
}

func main(){
// 示例：假设 A 是一个 3x3 矩阵，b 是一个长度为 3 的向量
    A :=[][]float64{
{1,-1,0},
{0,1,2},
{-1,0,1},
}
    b :=[]float64{4,3,2}

    n :=len(b)
    edges :=make([][]int,0)
    weights :=make([][]float64, n)
for i :=range weights {
        weights[i]=make([]float64, n)
}

// 构建图和权重
for i :=0; i < n; i++{
for j :=0; j < n; j++{
if A[i][j]>0{
                edges =append(edges,[]int{i +1, j +1})
                weights[i][j]= b[i]/ A[i][j]
}elseif A[i][j]<0{
                edges =append(edges,[]int{j +1, i +1})
                weights[j][i]=-b[i]/ A[i][j]
}
}
}

// 添加超级源点
for i :=1; i <= n; i++{
        edges =append(edges,[]int{0, i})
        weights[0][i-1]=0.0
}

// 调用 BellmanFord 算法
    result, ok :=BellmanFord(n, edges, weights)
if!ok {
        fmt.Println("无解")
}else{
        fmt.Println("解:", result)
}
}

package main

import(
"fmt"
"math"
)

// Constraint represents a single constraint in the form of Ax <= b
typeConstraintstruct{
    A []float64
    B float64
}

// Node represents a node in the branch and bound tree
typeNodestruct{
    level    int
    bound    float64
    solution []float64
}

// SolveDifferenceConstraints solves the difference constraint system using branch and bound
func SolveDifferenceConstraints(constraints []Constraint, integerVars []int)([]float64,bool){
    n :=len(constraints[0].A)// Number of variables
    root :=&Node{
        level:0,
        bound:    math.Inf(1),// Positive infinity
        solution:make([]float64, n),
}

var bestSolution []float64
    bestBound := math.Inf(1)

    queue :=[]*Node{root}

forlen(queue)>0{
        node := queue[0]
        queue = queue[1:]

if node.level == n {
if node.bound < bestBound {
                bestBound = node.bound
                bestSolution =make([]float64, n)
copy(bestSolution, node.solution)
}
continue
}

if node.bound >= bestBound {
continue
}

        isInteger :=false
for _, i :=range integerVars {
if i == node.level {
                isInteger =true
break
}
}

if isInteger {
// Integer variable case
            leftChild :=&Node{
                level:    node.level +1,
                bound:    math.Inf(1),
                solution:make([]float64, n),
}
copy(leftChild.solution, node.solution)
            leftChild.solution[node.level]= math.Floor(node.solution[node.level])

            rightChild :=&Node{
                level:    node.level +1,
                bound:    math.Inf(1),
                solution:make([]float64, n),
}
copy(rightChild.solution, node.solution)
            rightChild.solution[node.level]= math.Ceil(node.solution[node.level])

            queue =append(queue, leftChild, rightChild)
}else{
// Continuous variable case
            child :=&Node{
                level:    node.level +1,
                bound:    math.Inf(1),
                solution:make([]float64, n),
}
copy(child.solution, node.solution)

            queue =append(queue, child)
}
}

return bestSolution, bestBound != math.Inf(1)
}

func main(){
    constraints :=[]Constraint{
{A:[]float64{1,-1}, B:2},
{A:[]float64{-1,1}, B:0},
}

    integerVars :=[]int{0}// x0 is an integer variable

    solution, found :=SolveDifferenceConstraints(constraints, integerVars)
if found {
        fmt.Println("Solution found:", solution)
}else{
        fmt.Println("No solution exists")
}
}

package main

import(
"fmt"
"github.com/optimization-tools/go-mip"
)

func solveMILP(A [][]float64, b []float64, integerIndices []int)(*mip.Model,error){
// 创建一个新的MIP模型
    model := mip.NewModel()

// 添加变量
    n :=len(A[0])
    vars :=make([]*mip.Var, n)
for i :=0; i < n; i++{
if contains(integerIndices, i){
// 整数变量
            vars[i]= model.AddVar(0, mip.Infinity,0, mip.Int)
}else{
// 连续变量
            vars[i]= model.AddVar(0, mip.Infinity,0, mip.Continuous)
}
}

// 添加约束
    m :=len(A)
for i :=0; i < m; i++{
        expr := mip.NewLinExpr()
for j :=0; j < n; j++{
            expr.AddTerm(A[i][j], vars[j])
}
        model.AddConstr(expr, mip.LE, b[i])
}

// 设置目标函数（这里假设没有目标函数，只是求解可行性问题）
    model.SetObjective(mip.NewLinExpr(), mip.Minimize)

// 求解
    err := model.Optimize()
if err !=nil{
returnnil, err
}

return model,nil
}

func contains(slice []int, val int)bool{
for _, item :=range slice {
if item == val {
returntrue
}
}
returnfalse
}

func main(){
// 示例数据
    A :=[][]float64{
{1,-1,0},
{0,1,-1},
{1,0,-1},
}
    b :=[]float64{1,2,3}
    integerIndices :=[]int{0,2}// 假设第0和第2个变量是整数

    model, err := solveMILP(A, b, integerIndices)
if err !=nil{
        fmt.Println("Error solving MILP:", err)
return
}

// 输出结果
    fmt.Println("Solution:")
for i, var_ :=range model.Vars(){
        fmt.Printf("x[%d] = %f\n", i, var_.X())
}
}

package main

import(
"fmt"
"math"
)

// Edge represents a directed edge in the graph with a weight.
typeEdgestruct{
from, to, weight int
}

// BellmanFord function to find shortest path in a graph with possible negative weights
func BellmanFord(edges []Edge, vertexCount, source int)([]float64,error){
    distances :=make([]float64, vertexCount)
for i :=range distances {
        distances[i]= math.MaxFloat64// Initialize distances to infinity
}
    distances[source]=0// Distance to source is 0

// Relax edges repeatedly
for i :=0; i < vertexCount-1; i++{
for _, edge :=range edges {
if distances[edge.from]!= math.MaxFloat64&& distances[edge.from]+float64(edge.weight)< distances[edge.to]{
                distances[edge.to]= distances[edge.from]+float64(edge.weight)
}
}
}

// Check for negative-weight cycles
for _, edge :=range edges {
if distances[edge.from]!= math.MaxFloat64&& distances[edge.from]+float64(edge.weight)< distances[edge.to]{
returnnil, fmt.Errorf("negative weight cycle detected")
}
}

return distances,nil
}

// SolveDiffConstraintSystem solves Ax ≤ b using Bellman-Ford
func SolveDiffConstraintSystem(A [][]int, b []int)([]int,error){
    vertexCount :=len(A)
var edges []Edge

// Create edges based on the constraints
for i :=0; i < vertexCount; i++{
for j :=0; j < vertexCount; j++{
if A[i][j]!=0{
                edges =append(edges,Edge{from: i, to: j, weight:-A[i][j]})
}
}
}

// Add edges for the inequalities b[i]
for i :=0; i < vertexCount; i++{
        edges =append(edges,Edge{from: i, to: vertexCount -1, weight: b[i]})
}

    distances, err :=BellmanFord(edges, vertexCount+1, vertexCount-1)
if err !=nil{
returnnil, err
}

// The resulting distances can be adjusted for the integer constraints

return distances[:vertexCount],nil// Return the result excluding the last vertex
}

func main(){
    A :=[][]int{
{0,1,1},// x_1 - x_0 <= 1
{-1,0,2},// x_2 - x_1 <= 2
{3,-1,0},// x_0 - x_2 <= 3
}
    b :=[]int{1,2,3}

    result, err :=SolveDiffConstraintSystem(A, b)
if err !=nil{
        fmt.Println("Error:", err)
return
}

    fmt.Println("Result:", result)
}

package main

import(
"fmt"
"gonum.org/v1/gonum/mat"
)

func main(){
// 定义矩阵A和向量b
    A := mat.NewDense(3,3,[]float64{1,1,1,1,2,1,1,1,3})
    b :=[]float64{10,20,30}

// 定义变量的界限
    varLB :=[]float64{0,0,0}// 下界
    varUB :=[]float64{100,100,100}// 上界

// 调用外部求解器（这里只是示例，实际需要调用CPLEX等）
    solveLP(A, b, varLB, varUB)

// 检查是否有非整数解，并进行分支定界
    checkForIntegerSolution()
}

func solveLP(A *mat.Dense, b, varLB, varUB []float64){
// 这里应该是调用LP求解器的代码
// 例如，使用CPLEX的Go接口
    fmt.Println("Solving LP...")
}

func checkForIntegerSolution(){
// 检查解是否为整数，如果不是，则进行分支
    fmt.Println("Checking for integer solution...")
}

package main

import(
"fmt"
"math"
)

typeEdgestruct{
    to     int
    weight float64
}

func BellmanFord(edges [][]Edge, source int, n int)([]float64,bool){
    dist :=make([]float64, n)
for i :=range dist {
        dist[i]= math.Inf(1)
}
    dist[source]=0

for i :=0; i < n-1; i++{
for u :=0; u < n; u++{
for _, edge :=range edges[u]{
                v := edge.to
if dist[u]+edge.weight < dist[v]{
                    dist[v]= dist[u]+ edge.weight
}
}
}
}

// Check for negative-weight cycles
for u :=0; u < n; u++{
for _, edge :=range edges[u]{
            v := edge.to
if dist[u]+edge.weight < dist[v]{
returnnil,false// Negative cycle detected
}
}
}

return dist,true
}

func solveDifferentialConstraints(A [][]float64, b []float64, integerIndices []int)([]float64,bool){
    n :=len(b)
    edges :=make([][]Edge, n)

for i :=0; i < n; i++{
for j :=0; j < n; j++{
if A[i][j]!=0{
                weight := b[i]/ A[i][j]
                edges[j]=append(edges[j],Edge{to: i, weight: weight})
}
}
}

// Add a source node connected to all integer variables with weight 0
    source := n
    edges =append(edges,make([]Edge, n))
for _, idx :=range integerIndices {
        edges[source]=append(edges[source],Edge{to: idx, weight:0})
}

    dist, ok :=BellmanFord(edges, source, n+1)
if!ok {
returnnil,false// Negative cycle detected
}

    result :=make([]float64, n)
for i :=0; i < n; i++{
        result[i]= dist[i]
}

return result,true
}

func main(){
    A :=[][]float64{
{0,1,0},
{-1,0,1},
{0,-1,0},
}
    b :=[]float64{3,3,0}
    integerIndices :=[]int{0}

    result, ok := solveDifferentialConstraints(A, b, integerIndices)
if ok {
        fmt.Println("Solution:", result)
}else{
        fmt.Println("No solution exists")
}
}