C++ Program to check if two stacks of letters can be emptied or not

Suppose, there are 2n number of letters and each of them has an integer number between 1 to n written on them. There are exactly two letters that have the same number written on them. These letters are arranged into m stacks and stack i has letters stack[i] on it. Our task is to empty all the stacks in the following manner

  • We have to choose any two stacks and remove the top letter from both of them.

  • The letters that we have removed must have the same number on both of them.

If we can empty the m stacks in this manner, we print true or otherwise we return false.

So, if the input is like n = 3, m = 2, stacks = {{2, 1, 3}, {2, 1, 3}}, then the output will be true.

There are two stacks and each of the stacks has letters that have the numbers 2, 1, 3 written on them respectively. So, we can remove from the two stacks and empty them in the given manner.

To solve this, we will follow these steps −

Define one 2D array dp
Define an array tvec
for initialize i := 0, when i < m, update (increase i by 1), do:
   k := size of stacks[i]
   for initialize j := 0, when j < k, update (increase j by 1), do:
      if j < 0, then:
         insert p at the end of dp[stacks[i, j]]
         (increase tvec[p] by 1)
      p := stacks[i, j]
Define an array tp
for initialize i := 1, when i <= n, update (increase i by 1), do:
   Define one queue q
   insert i into q
   while (q is not empty), do:
    if not tp[first element of q] and tvec[first element of q] is same as 0, then:
         for each element next in dp[first element of q], do:
             (decrease tvec[next] by 1)
             insert next into q
         tp[first element of q] := true
   delete first element from q
for initialize i := 1, when i <= n, update (increase i by 1), do:
   if tvec[i] is not equal to 0, then:
return false
return true


Let us see the following implementation to get better understanding −

#include <bits/stdc++.h>
using namespace std;

bool solve(int n, int m, vector<vector<int>> stacks){
   vector<vector<int>> dp(n + 1);
   vector<int> tvec(n + 1);
   for(int i = 0; i < m; i++){
      int k = stacks[i].size();
      int p;
      for(int j = 0; j < k; j++){
         if(j > 0){
         p = stacks[i][j];
   vector<bool> tp(n + 1);
   for(int i = 1; i <= n; i++){
      queue<int> q;
         if(!tp[q.front()] && tvec[q.front()] == 0){
            for(auto next: dp[q.front()]){
   for(int i = 1; i <= n; i++){
      if(tvec[i] != 0){
         return false;
   return true;
int main() {
   int n = 3, m = 2;
   vector<vector<int>> stacks = {{2, 1, 3}, {2, 1, 3}};
   cout<< solve(n, m, stacks);
   return 0;


3, 2, {{2, 1, 3}, {2, 1, 3}}