Sort the given stack elements based on their modulo with K

Given a stack of integers and an integer K, the task is to sort the elements of the given stack using another stack in the increasing order of their modulo with K. If two numbers have the same remainder then the smaller number should come first.


Input: stack = {10, 3, 2, 6, 12}, K = 4
Output: 12 2 6 10 3
{12, 2, 6, 10, 3} is the required sorted order as the modulo
of these elements with K = 4 is {2, 3, 2, 2, 0}

Input: stack = {3, 4, 5, 10, 11, 1}, K = 3
Output: 3 1 4 10 5 11

Approach: An approach to sort the elements of the stack using another temporary stack has been discussed in this article, the same approach can be used here to sort the elements based on their modulo with K, the only difference is that when the elements being compared give the same modulo value then they will be compared based on their values.

Below is the implementation of the above approach:





// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Function to sort the stack using
// another stack based on the
// values of elements modulo k
void sortStack(stack<int>& input, int k)
    stack<int> tmpStack;
    while (!input.empty()) {
        // Pop out the first element
        int tmp =;
        // While temporary stack is not empty
        while (!tmpStack.empty()) {
            int tmpStackMod = % k;
            int tmpMod = tmp % k;
            // The top of the stack modulo k is
            // greater than (temp & k) or if they
            // are equal then compare the values
            if ((tmpStackMod > tmpMod)
                || (tmpStackMod == tmpMod
                    && > tmp)) {
                // Pop from temporary stack and push
                // it to the input stack
        // Push temp in tempory of stack
    // Push all the elements in the original
    // stack to get the ascending order
    while (!tmpStack.empty()) {
    // Print the sorted elements
    while (!input.empty()) {
        cout << << " ";
// Driver code
int main()
    stack<int> input;
    int k = 4;
    sortStack(input, k);
    return 0;



12 2 6 10 3

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