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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: Ignore following part, skip to the next iteration 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
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