# Longest Mod Path

### Problem Statement :

```n the middle of a nightmare, Maxine suddenly finds herself in a mysterious room with the following items:

A piece of paper with the word score and the integer  written on it.
A map of the castle where the room is located.
There are  rooms uniquely labeled from  to .
There are  bidirectional corridors connecting pairs of rooms. The value of score changes every time she travels up or down a corridor, and this value differs depending on her direction of travel along the corridor. Each corridor can be traveled any number of times in either direction.
Every room is reachable from every other room.
Maxine is located in the room labeled .
The exit is located in the room labeled . Once this room is reached, score is reduced modulo  and Maxine can (but is not required to) exit that level!
Assume some corridor  (where ) is associated with an integer, , and connects rooms  and . Then:

Traveling corridor  from room  to room  increases score by .
Traveling corridor  from room  to room  decreases score by .
There are  levels to Maxine's nightmare castle, and each one has a different set of values for , , and . Given the above information, help Maxine by finding and printing her maximum possible score for each level. Only you can help her wake up from this nightmare!

Note: Recall that the result of a modulo operation is always non-negative. For example, .

Input Format

The first line contains a single integer, , denoting the number of rooms.
Each of the  subsequent lines describes a corridor in the form of three space-separated integers denoting the respective values for , , and .
The next line contains a single integer, , denoting the number of queries.
Each of the  subsequent lines describes a level in the form of three space-separated integers denoting its respective , , and  values.

Constraints

,
For each level:

The room layout is the same```

### Solution :

```                            ```Solution in C :

In C++ :

#include <cstdio>
#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <string>
#include <set>
#include <map>
#include <ctime>
#include <cstring>
#include <cassert>
#include <bitset>
#include <sstream>
#include <queue>

#define pb push_back
#define mp make_pair
#define fs first
#define sc second
#define sz(a) ((int) (a).size())
#define eprintf(...) fprintf(stderr, __VA_ARGS__)

using namespace std;

typedef long long int64;
typedef long double ldb;

const long double eps = 1e-9;
const int inf = (1 << 30) - 1;
const long long inf64 = ((long long)1 << 62) - 1;
const long double pi = acos(-1);

template <class T> T sqr (T x) {return x * x;}
template <class T> T abs (T x) {return x < 0 ? -x : x;}

const int MAXN = 120 * 1000;

vector <pair <int, int> > adj[MAXN];
long long a[MAXN];
bool used[MAXN];
long long cycle = 0;

void dfs(int v, long long num) {
a[v] = num;
used[v] = true;
for (int i = 0; i < sz(adj[v]); ++i) {
if (!used[u]) {
} else if (a[v] + adj[v][i].sc - a[u] != 0) {
cycle = a[v] + adj[v][i].sc - a[u];
}
}
}

int gcd(int a, int b) {
return (a == 0 ? b : gcd(b % a, a));
}

int main () {
//  ios_base::sync_with_stdio(0);
// freopen("input.txt", "rt", stdin);
//  freopen("output.txt", "wt", stdout);

int n;
scanf("%d", &n);
for (int i = 0; i < n; ++i) {
int v1, v2, c;
scanf("%d%d%d", &v1, &v2, &c);
v1--, v2--;
}

dfs(0, 0);

int q;
scanf("%d", &q);
for (int i = 0; i < q; ++i) {
int s, e, m;
scanf("%d%d%d", &s, &e, &m);
s--, e--;

int val = ((a[e] - a[s]) % m + m) % m;
int cycle_val = (cycle % m  + m) % m;

// cerr << val << " " << cycle_val << " " << m << endl;

int d = gcd(cycle_val, m);

// cerr << d << endl;

int res = (val % d) + m - d;
printf("%d\n", res);
}

return 0;
}

In C :

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define HASH_SIZE 123455
#define INF 1000000007
typedef struct _node{
int x;
int y;
int w;
struct _node *next;
} node;
typedef struct _lnode{
int x;
int w;
struct _lnode *next;
} lnode;
void insert_edge(int x,int y,int w);
void dfs0(int x,int y);
void dfs1(int x);
void get_loop(int x,int y);
long long CC(long long n, long long d);
void insert(int x,int y,int w);
int search(int x,int y);
lnode *table[100000]={0};
node *hash[HASH_SIZE]={0};
int loop[100000]={0},trace[100000]={0},point[100000];
int first_point,breakp=0,cycle_found=0;
long long cycle=0,dis[100000]={0},cycle_save;

int main(){
int N,a,b,x,S,E,M,Q,MOD,DIS,GCD,ans,i;
scanf("%d",&N);
for(i=0;i<N;i++){
scanf("%d%d%d",&a,&b,&x);
insert_edge(a-1,b-1,x);
if(a>b)
Q=search(b-1,a-1);
else
Q=search(a-1,b-1);
if(Q==INF)
if(a>b)
insert(b-1,a-1,-x);
else
insert(a-1,b-1,x);
else{
if(a>b)
cycle=x+Q;
else
cycle=x-Q;
cycle_found=1;
cycle_save=cycle;
}
}
dfs0(0,-1);
if(!loop[0])
point[0]=first_point;
memset(trace,0,sizeof(trace));
dfs1(0);
if(cycle_found)
cycle=cycle_save;
scanf("%d",&Q);
while(Q--){
scanf("%d%d%d",&S,&E,&M);
MOD=(cycle%M+M)%M;
DIS=((dis[E-1]-dis[S-1])%M+M)%M;
if(!MOD)
ans=DIS;
else{
GCD=CC(MOD,M);
ans=(M-1-DIS)/GCD*GCD+DIS;
}
printf("%d\n",ans);
}
return 0;
}
void insert_edge(int x,int y,int w){
lnode *t=malloc(sizeof(lnode));
t->x=y;
t->w=w;
t->next=table[x];
table[x]=t;
t=malloc(sizeof(lnode));
t->x=x;
t->w=-w;
t->next=table[y];
table[y]=t;
return;
}
void dfs0(int x,int y){
lnode *p;
trace[x]=1;
for(p=table[x];p;p=p->next)
if(!trace[p->x]){
dis[p->x]=dis[x]+p->w;
dfs0(p->x,x);
}
else if(p->x!=y && !loop[p->x]){
first_point=p->x;
get_loop(p->x,-1);
cycle+=p->w;
}
return;
}
void dfs1(int x){
lnode *p;
trace[x]=1;
if(loop[x])
point[x]=x;
for(p=table[x];p;p=p->next)
if(!trace[p->x]){
if(!loop[p->x])
point[p->x]=point[x];
dfs1(p->x);
}
return;
}
void get_loop(int x,int y){
lnode *p;
loop[x]=1;
for(p=table[x];p && !breakp;p=p->next)
if(trace[p->x] && !loop[p->x]){
cycle+=p->w;
get_loop(p->x,x);
if(!breakp)
cycle-=p->w;
}
else if(p->x==first_point && p->x!=y){
breakp=1;
break;
}
return;
}
long long CC(long long n, long long d){
while( 1 )
{
n = n % d;
if( n == 0 )
return d;
d = d % n;
if( d == 0 )
return n;
}
}
void insert(int x,int y,int w){
int bucket=(x*100000LL+y)%HASH_SIZE;
node *t;
t=(node*)malloc(sizeof(node));
t->x=x;
t->y=y;
t->w=w;
t->next=hash[bucket];
hash[bucket]=t;
return;
}
int search(int x,int y){
int bucket=(x*100000LL+y)%HASH_SIZE;
node *t=hash[bucket];
while(t){
if(t->x==x && t->y==y)
return t->w;
t=t->next;
}
return INF;
}

In Python3 :

from fractions import gcd

n=int(input())
adjlst = [[] for i in range(n)]
for j in range(0,n):
arr=list(map(int,input().split()))
a=arr[0]-1
b=arr[1]-1
c=arr[2]

dist = [None]*n
parents = [set() for i in range(n)]
dist[0] = 0
stack = [0]
while stack:
i = stack.pop()
if j in parents[i]: continue
dist1 = dist[i] + c
if dist[j] is None:
dist[j] = dist1
stack.append(j)
else:
cycle = abs(dist[j] - dist1)
q=int(input())
for j in range(0,q):

arr1=list(map(int,input().split()))
s=arr1[0]
e=arr1[1]
m=arr1[2]
a = gcd(cycle, m)
print (m - a + (dist[e-1] - dist[s-1]) % a)```
```

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