Go: package main

import (
	"container/heap"
	"fmt"
	"runtime"
)

type Node struct {
	NowPosition          int
	DiscountTicketTCount int
	Amount               int
}

type PriorityQueueNode []*Node

func (pq PriorityQueueNode) Len() int {
	return len(pq)
}

func (pq PriorityQueueNode) Less(i, j int) bool {
	return pq[i].Amount < pq[j].Amount
}

func (pq PriorityQueueNode) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
}

func (pq *PriorityQueueNode) Push(node interface{}) {
	*pq = append(*pq, node.(*Node))
}

func (pq *PriorityQueueNode) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	*pq = old[0 : n-1]
	return item
}

type Point struct {
	NextPoint int
	Fee       int
}

type Memo struct {
	NowPoint             int
	DiscountTicketTCount int
}

func main() {
	var c, n, m, s, d int
	var a, b, f int

	for {
		fmt.Scan(&c, &n, &m, &s, &d)
		if c == 0 && n == 0 && m == 0 && s == 0 && d == 0 {
			break
		}
		s--
		d--
		pointMap := make([][]Point, n)
		for i := 0; i < n; i++ {
			pointMap[i] = make([]Point, 0, n)
		}
		for i := 0; i < m; i++ {
			fmt.Scan(&a, &b, &f)
			a--
			b--
			pointMap[a] = append(pointMap[a], Point{NextPoint: b, Fee: f})
			pointMap[b] = append(pointMap[b], Point{NextPoint: a, Fee: f})
		}
		pq := make(PriorityQueueNode, 0, m)
		start := Node{NowPosition: s, DiscountTicketTCount: c, Amount: 0}
		heap.Push(&pq, &start)
		memo := make(map[Memo]int)
		for len(pq) != 0 {
			now := heap.Pop(&pq).(*Node)
			if now.NowPosition == d {
				fmt.Println(now.Amount)
				break
			}
			memo[Memo{NowPoint: now.NowPosition, DiscountTicketTCount: now.DiscountTicketTCount}] = now.Amount
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
					memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
					heap.Push(&pq, next)
				}
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
						memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
						heap.Push(&pq, next)
					}
				}
			}
		}
		runtime.GC()
	}
}

C++: #include <iostream>
#include <vector>
#include <stack>
#include <queue>
#include <algorithm>
#include <string>
#include <bitset>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <string.h>

#define X first
#define Y second
#define MP make_pair
typedef long long ll;
using namespace std;

int mindis[101], pre[101];
bool used[101];
int eCost[101][101];

int getPathSum(int c, int p, int g){
	vector<int> edge;
	edge.push_back(eCost[p][g]);
		
	int to = p;
	for(int from = pre[to]; from != 0; from = pre[from]){
		edge.push_back(eCost[from][to]);
		to = from;
	}

	sort(edge.begin(), edge.end());

	int idx = edge.size()-1;
	for(int i = 0; i < c; i++){
		edge[idx--] /= 2;
		if(idx < 0) break;
	}
	
	int ans = 0;
	for(int i = 0; i < edge.size(); i++){
		ans += edge[i];
	}

	return ans;
}

int main(){
	int c, n, m, s, d;
	while(cin >> c >> n >> m >> s >> d){
		if(c == 0 && n == 0 && m == 0 && s == 0 && d == 0) break;

		fill(mindis, mindis+101, 1<<30);
		fill(pre, pre+101, 0);
		fill(used, used+101, false);
		for(int i = 0; i < 101; i++) fill(eCost[i], eCost[i]+101, 1<<30);

		for(int i = 0; i < m; i++){
			int a, b, cost;
			cin >> a >> b >> cost;
			eCost[a][b] = cost;
			eCost[b][a] = cost;
		}

		mindis[s] = 0;
		vector<int> goals;

		//最短経路(ダイクストラ)
		while(true){
			int v = -1;
			for(int i = 1; i <= n; i++){
				if(!used[i] && (v == -1 || mindis[v] > mindis[i])) v = i;
			}

			if(v == d) break;
			used[v] = true;

			for(int i = 1; i <= n; i++){
				if(mindis[i] > mindis[v]+eCost[v][i]){
					if(i == d){
						//次がゴールならここでチケットを適用した総和を出して最終的な結果にする
						//それをgoalsに格納していく
						goals.push_back(getPathSum(c, v, i));
					}else{
						mindis[i] = mindis[v]+eCost[v][i];
						pre[i] = v;
					}
				}
			}
		}

		int minc = 100000000;
		for(int i = 0; i < goals.size(); i++){
			if(minc > goals[i]) minc = goals[i];
		}

		cout << minc << endl;
	}
	return 0;
}

C++: #include <iostream>
#include <queue>
#include <functional>
#include <map>
#include <utility>
#include <vector>
using namespace std;

typedef pair<int, int> P;
typedef pair<P, int> State;

const int N = 100, INF = 1e8;

int edge[N][N];

int dijkstra(int n, int s, int d, int c){
	priority_queue<State, vector<State>, greater<State> > q;
	vector<int> visited(n, INF);
	q.push(make_pair(make_pair(0, s), c));
	while(!q.empty()){
		int c = q.top().first.first;
		int curr = q.top().first.second;
		int dc = q.top().second;
		q.pop();
		visited[curr]  = c;
		if(curr == d) return c;
        if(c > visited[curr]) continue;
		for(int i(0);i < n;++i){
			if(edge[curr][i] != INF){
				int nc = c + edge[curr][i];
				int next = i;
                q.push(make_pair(make_pair(nc, next), dc));
				nc = c + edge[curr][i] / 2;
				if(dc > 0){
					q.push(make_pair(make_pair(nc, next), dc - 1));
				}
			}
		}
	}
	return -1;
}

int main(){
	int c, n, m, s, d, a, b, f;
	while(cin >> c >> n >> m >> s >> d, c && n && m && s && d){
		for(int i(0);i < N;++i){
			for(int j(0);j < N;++j){
				edge[i][j] = INF;
			}
		}
		--s;
		--d;
		for(int i(0);i < m;++i){
			cin >> a >> b >> f;
			--a;
			--b;
			edge[a][b] = edge[b][a] = f;
		}
        cout << dijkstra(n, s, d, c) << endl;
	}
}

C++: #include <cstdio>
#include <queue>
#include <algorithm>

#define rep(i, n) for(int i = 0; i < (n); ++i)

using namespace std;

const int inf = 2e7;

typedef pair<int, int> P;

struct E{
	E(int t, int c) :
		t(t), c(c)
	{}

	int t, c;
};

int c, n, m, s, t;
vector<E> g[1100];
int d[1100];

int index(int i, int j){
	return i * (c + 1) + j;
}

int main(){
	while(1){
		scanf("%d%d%d%d%d", &c, &n, &m, &s, &t);
		--s;
		--t;
		if(c == 0){
			break;
		}
		rep(i, m){
			int a, b, k;
			scanf("%d%d%d", &a, &b, &k);
			--a;
			--b;
			rep(j, c + 1){
				g[index(a, j)].push_back(E(index(b, j), k));
				g[index(b, j)].push_back(E(index(a, j), k));
			}
			rep(j, c){
				g[index(a, j + 1)].push_back(E(index(b, j), k / 2));
				g[index(b, j + 1)].push_back(E(index(a, j), k / 2));
			}
		}

		fill_n(d, n * (c + 1), inf);

		priority_queue<P, vector<P>, greater<P> > q;
		d[index(s, c)] = 0;
		q.push(P(0, index(s, c)));
		while(!q.empty()){
			P v = q.top();
			q.pop();
			if(v.first > d[v.second]){
				continue;
			}
			rep(i, g[v.second].size()){
				E e = g[v.second][i];
				if(d[e.t] > v.first + e.c){
					d[e.t] = v.first + e.c;
					q.push(P(d[e.t], e.t));
				}
			}
		}

		printf("%d\n", *min_element(d + index(t, 0), d + index(t + 1, 0)));

		rep(i, n * (c + 1)){
			g[i].clear();
		}
	}
	return 0;
}