알고리즘 Jailbreak문제 도저히 모르겠습니다. 고수님 알려주세요

#include <stdio.h>
#include <vector>
#include <string.h>
#include <algorithm>
#include <queue>
using namespace std;
#define mp make_pair
#define INF 987654321
 
int t, n, m, map[105][105], ans;
int tx[4] = { 0,0,1,-1 };
int ty[4] = { 1,-1,0,0 };
vector<pair<int, int > > v;
priority_queue<pair<int, pair<int, int> > > qq;
void init() {
	char a[102];
	while (!qq.empty()) qq.pop();
	ans = INF;
	v.clear();
	memset(map, -1, sizeof(map));
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; i++) {
		scanf("%s", a);
		for (int j = 1; j <= m; j++) {
			if (a[j - 1] == '*') map[i][j] = -1;
			if (a[j - 1] == '.') map[i][j] = 0;
			if (a[j - 1] == '#') map[i][j] = 1;
			if (a[j - 1] == '$') v.push_back(mp(i, j)), map[i][j] = 0;
			//if ((i == 1 || j == 1 || i == n || j == m) && (map[i][j] != -1)) s.push_back(mp(i, j));
		}
	}
}
 
void bfs() {
	int vis[105][105][2] = { 0, };
	priority_queue<pair<pair<int, int>, pair<int, int> > > q;
	//거리 타입 좌표xy
	q.push(mp(mp(0, 1), mp(v[0].first, v[0].second)));
	q.push(mp(mp(0, 2), mp(v[1].first, v[1].second)));
	vis[v[0].first][v[0].second][0] = 1;
	vis[v[0].first][v[0].second][1] = 0;
	vis[v[1].first][v[1].second][0] = 2;
	vis[v[1].first][v[1].second][1] = 0;
	while (!q.empty()) {
		int cx = q.top().second.first;
		int cy = q.top().second.second;
		int dis = -q.top().first.first;
		int type = q.top().first.second;
		vis[cx][cy][0] = type;
		vis[cx][cy][1] = dis;
		q.pop();
		for (int i = 0; i < 4; i++) {
			int nx = cx + tx[i];
			int ny = cy + ty[i];
			int ndis = dis;
			if (vis[nx][ny][0] != 0 && vis[nx][ny][0] != type){
				qq.push(mp(-(dis + vis[nx][ny][1]), mp(nx, ny)));
				continue;
			}
			if (vis[nx][ny][0] != 0 || map[nx][ny] == -1) continue;
			if (map[nx][ny] == 1) ndis++;
			vis[nx][ny][0] = type;
			vis[nx][ny][1] = ndis;
			q.push(mp(mp(-ndis, type), mp(nx, ny)));
		}
	}
	return;
}
int bfs2(int x, int y) {
	priority_queue<pair<int, pair<int, int> >  > q;
	q.push(mp(0, mp(x, y)));
 
	int visit[105][105] = { 0, };
	while (!q.empty()) {
		int cx = q.top().second.first;
		int cy = q.top().second.second;
		int dis = -q.top().first;
		if (cx == 1 || cy == 1 || cx == n || cy == m) return dis;
		q.pop();
		for (int i = 0; i < 4; i++) {
			int nx = cx + tx[i];
			int ny = cy + ty[i];
			int ndis = dis;
			if (map[nx][ny] == -1 || visit[nx][ny] == 1) continue;
			visit[nx][ny] = 1;
			if (map[nx][ny] > 0) ndis++;
			//if (nx == 1 || ny == 1 || nx == n || ny == m) return ndis;
			q.push(mp(-ndis, mp(nx, ny)));
		}
	}
	return INF;
}
 
int bfs3() {
	int visit[105][105] = { 0, };
	while (!qq.empty()) {
		int cx = qq.top().second.first;
		int cy = qq.top().second.second;
		int dis = -qq.top().first;
		if (cx == 1 || cy == 1 || cx == n || cy == m) return dis;
		qq.pop();
		for (int i = 0; i < 4; i++) {
			int nx = cx + tx[i];
			int ny = cy + ty[i];
			int ndis = dis;
			if (map[nx][ny] == -1 || visit[nx][ny] == 1) continue;
			visit[nx][ny] = 1;
			if (map[nx][ny] > 0) ndis++;
			//if (nx == 1 || ny == 1 || nx == n || ny == m) return ndis;
			qq.push(mp(-ndis, mp(nx, ny)));
		}
	}
	return INF;
}
 
int main() {
	scanf("%d", &t);
	while (t--) {
		init();
		bfs();
		printf("%d\n", min(bfs2(v[0].first, v[0].second) + bfs2(v[1].first, v[1].second), bfs3()));
	}
}