# C++ program to find out the maximum value of i

Suppose, we have a permutation of integers 'seq' and an array of integer pairs 'pairs' of size m that contains integers 0 to n - 1. Now, we perform the following operation on seq as many times as possible so that seq[i] = i (0 ≤ i < n) is maximized.

• We have to choose an integer j where 0 <= j < m, and then swap seq[first value of pair[j]] and seq[second value of pair[j]]

We have to find out the maximum value of i so that seq[i] = i after performing the operation multiple times.

So, if the input is like n = 4, m = 2, seq = {0, 3, 2, 1}, pairs = {{0, 1}, {2, 3}}, then the output will be 2.

The maximum possible value is 2.

To solve this, we will follow these steps −

N := 100
Define an array tp of size: N.
Define arrays vtmp, vis of size N.
Define a function dfs(), this will take j, k,
tp[j] := k
insert j at the end of vtmp[k]
for each value b in vis[j], do:
if tp[b] is not equal to 0, then:
dfs(b, k)
res := 0
for initialize i := 0, when i < n, update (increase i by 1), do:
if seq[i] is same as i, then:
(increase res by 1)
for initialize i := 0, when i < m, update (increase i by 1), do:
a := first value of pairs[i]
b := second value of pairs[i]
insert b at the end of vis[a]
insert a at the end of vis[b]
idx := 1
for initialize i := 0, when i < n, update (increase i by 1), do:
if tp[i] is same as 0, then:
dfs(i, idx)
for each element j in vtmp[idx], do:
if tp[seq[j]] is same as idx and seq[j] is not equal to j, then:
(increase res by 1)
(increase idx by 1)
print(res)

## Example

Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;
const int INF = 1e9;
#define N 100
int tp[N];
vector<int> vtmp[N], vis[N];
void dfs(int j, int k){
tp[j] = k;
vtmp[k].push_back(j);
for(auto b : vis[j]) {
if(tp[b] != 0)
continue;
dfs(b, k);
}
}
void solve(int n, int m, int seq[], vector<pair<int, int>> pairs) {
int res = 0;
for(int i = 0; i < n; i++){
if(seq[i] == i)
res++;
}
for(int i = 0; i < m; i++){
int a = pairs[i].first;
int b = pairs[i].second;
vis[a].push_back(b);
vis[b].push_back(a);
}
int idx = 1;
for(int i = 0; i < n; i++) {
if(tp[i] == 0) {
dfs(i, idx);
for(auto j: vtmp[idx]){
if(tp[seq[j]] == idx && seq[j] != j)
res++;
}
idx++;
}
}
cout<< res;
}
int main() {
int n = 4, m = 2, seq[] = {0, 3, 2, 1};
vector<pair<int,int>> pairs = {{0, 1}, {2, 3}};
solve(n, m, seq, pairs);
return 0;
}

## Input

4, 2, {0, 3, 2, 1}, {{0, 1}, {2, 3}}

## Output

2