trips/router/internal/plan/optimize.go

package plan

import "maps/router/internal/route"

// OptimizeResult is the best order of k stops.
type OptimizeResult struct {
	Order      []int // indices into the stops slice
	DetourMin  int
	TotalMin   int
	Exhaustive bool // true when the optimum came from full search
	Feasible   bool // true when TotalMin <= budgetMin (when a budget was given)
	Relaxed    bool // true when we fell back to fewer than k stops
}

// OptimizeStops picks the best ordered subset of k stops minimizing
// SeqCost, subject to TotalMin <= budgetMin when budgetMin > 0.
// m must be the (n+2)-layout matrix for stops.
//
// Selection semantics (k is the user's request, "give me 2 hikes"):
//  1. best feasible exactly-k
//  2. else best feasible with fewer stops (Relaxed)
//  3. else best exactly-k ignoring the budget (Feasible=false)
//
// n <= 10: full enumeration (this is also the ground truth for evals).
// n > 10: greedy best-insertion (exact for k=1).
func OptimizeStops(m route.Matrix, stops []Stop, k, budgetMin int) OptimizeResult {
	n := len(stops)
	if k < 0 || k > n {
		k = n
	}
	if k == 0 {
		return OptimizeResult{Feasible: true, Exhaustive: true}
	}
	if n <= 10 {
		return optimizeExhaustive(m, stops, k, budgetMin)
	}
	return optimizeGreedy(m, stops, k, budgetMin)
}

type cand struct {
	order  []int
	total  int
	detour int
}

func feas(c cand, budgetMin int) bool { return budgetMin <= 0 || c.total <= budgetMin }

func lowerCost(a, b cand) bool {
	if a.total != b.total {
		return a.total < b.total
	}
	return a.detour < b.detour
}

func pickBest(cands []cand, budgetMin, wantSize int) (cand, bool) {
	var best cand
	found := false
	for _, c := range cands {
		if wantSize >= 0 && len(c.order) != wantSize {
			continue
		}
		if !feas(c, budgetMin) {
			continue
		}
		if !found || lowerCost(c, best) {
			best, found = c, true
		}
	}
	return best, found
}

func optimizeExhaustive(m route.Matrix, stops []Stop, k, budgetMin int) OptimizeResult {
	n := len(stops)
	// Enumerate ALL permutations of every subset of size k.
	var all []cand
	var rec func(order []int, used []bool)
	rec = func(order []int, used []bool) {
		if len(order) == k {
			detour, total := SeqCost(m, order, stops)
			if total >= 0 {
				all = append(all, cand{order: append([]int(nil), order...), total: total, detour: detour})
			}
			return
		}
		for i := 0; i < n; i++ {
			if !used[i] {
				used[i] = true
				rec(append(order, i), used)
				used[i] = false
			}
		}
	}
	rec(nil, make([]bool, n))

	// 1. feasible exactly-k
	if c, ok := pickBest(all, budgetMin, k); ok {
		return OptimizeResult{Order: c.order, DetourMin: c.detour, TotalMin: c.total, Exhaustive: true, Feasible: true}
	}
	// 2. feasible with fewer: re-enumerate smaller sizes
	if budgetMin > 0 {
		var less []cand
		var rec2 func(start, size int, order []int, used []bool)
		rec2 = func(start, size int, order []int, used []bool) {
			if len(order) == size {
				detour, total := SeqCost(m, order, stops)
				if total >= 0 && feas(cand{total: total}, budgetMin) {
					less = append(less, cand{order: append([]int(nil), order...), total: total, detour: detour})
				}
				return
			}
			for i := start; i < n; i++ {
				if !used[i] {
					used[i] = true
					rec2(i+1, size, append(order, i), used)
					used[i] = false
				}
			}
		}
		for size := 1; size < k; size++ {
			rec2(0, size, nil, make([]bool, n))
		}
		// best among feasible smaller (larger size preferred on tie? no — just lowest total)
		if c, ok := pickBest(less, budgetMin, -1); ok {
			return OptimizeResult{Order: c.order, DetourMin: c.detour, TotalMin: c.total, Exhaustive: true, Feasible: true, Relaxed: true}
		}
	}
	// 3. best exactly-k ignoring budget
	var bestK cand
	found := false
	for _, c := range all {
		if !found || lowerCost(c, bestK) {
			bestK, found = c, true
		}
	}
	if !found {
		return OptimizeResult{DetourMin: -1, TotalMin: -1, Exhaustive: true}
	}
	return OptimizeResult{Order: bestK.order, DetourMin: bestK.detour, TotalMin: bestK.total, Exhaustive: true, Feasible: budgetMin <= 0}
}

func optimizeGreedy(m route.Matrix, stops []Stop, k, budgetMin int) OptimizeResult {
	n := len(stops)
	order := []int{}
	used := make([]bool, n)
	for len(order) < k {
		_, curTotal := SeqCost(m, order, stops)
		if curTotal < 0 {
			break
		}
		bestTotal := int(^uint(0) >> 1)
		bestStop, bestPos := -1, -1
		for s := 0; s < n; s++ {
			if used[s] {
				continue
			}
			for pos := 0; pos <= len(order); pos++ {
				tri := make([]int, 0, len(order)+1)
				tri = append(tri, order[:pos]...)
				tri = append(tri, s)
				tri = append(tri, order[pos:]...)
				_, total := SeqCost(m, tri, stops)
				if total < 0 {
					continue
				}
				if budgetMin > 0 && total > budgetMin {
					continue
				}
				if total < bestTotal {
					bestTotal = total
					bestStop, bestPos = s, pos
				}
			}
		}
		if bestStop < 0 {
			break
		}
		used[bestStop] = true
		order = append(order[:bestPos], append([]int{bestStop}, order[bestPos:]...)...)
	}
	detour, total := SeqCost(m, order, stops)
	res := OptimizeResult{Order: order, DetourMin: detour, TotalMin: total, Exhaustive: false}
	if len(order) < k {
		res.Relaxed = true
	}
	if total >= 0 {
		res.Feasible = budgetMin <= 0 || total <= budgetMin
	}
	return res
}