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    <p>Ok, here's what you need to do.. </p> <p>You need to maintain some <code>data structure</code> containing information of each element you insert regarding, what was the <code>minimum</code> and <code>second minimum</code> value at the time when you inserted that element.. </p> <p>So, you want to have information like this: - </p> <p><strong>For each Element pushed -></strong> </p> <ul> <li>minimum value after insertion</li> <li>minimum value before insertion</li> </ul> <p>This information will be needed when you <code>pop</code> that element from stack.. So, you would know that, whether you are <code>popping</code> minimum value or not.. If yes, then you can replace the current <code>minimum</code> value with the <code>minimum value</code> before pushing this element.. If not, then there will be no change in <code>minimum</code> value at that time.. </p> <p><strong>For E.g: -</strong> </p> <p>Suppose currently you have following element in stack: - </p> <pre><code>[3, 5, 7, 9, 2, 4] </code></pre> <ul> <li><p>And you push a <strong>value 8</strong>.. Then you have two values to maintain.. (minimum value before 8 in pushed, i.e. 2, and miminum value after 8 is inserted, i.e. 2): -</p> <pre><code>min_value_before_push = min(stack) push 8 min_value_after_push = min(stack) </code></pre></li> <li><p>And if you push a <strong>value 1</strong>, then <code>minimum_before_insertion</code> is 2, and <code>minimum_after_insertion</code> is 1: -</p> <pre><code>min_value_before_push = 2 min_value_after_push = 1 </code></pre></li> </ul> <p>Now your stack is :- </p> <pre><code>[1, 8, 3, 5, 7, 9, 2, 4] </code></pre> <p>Now, if you <strong><code>pop</code></strong>, You will see that for <strong><code>value 1</code></strong>: - </p> <pre><code> min_value_before_push = 2 min_value_after_push = 1 </code></pre> <p>So, popping will alter the minimum value, So, you change the current minimum value with the <code>minimum_value_before_push</code> of 1.. So, again your minimum is 2..</p> <p>Your current stack becomes : - </p> <pre><code>[8, 3, 5, 7, 9, 2, 4] </code></pre> <p><strong>Now, let's check whether this algorithm works for <code>duplicate</code> element : -</strong> </p> <p>Suppose you want to push a <code>value 2</code> again..</p> <pre><code>min_value_before_push = 2 min_value_after_push = 2 </code></pre> <p>Then you go on and <code>pop</code>, you see that for <code>value 2</code>, <code>min_value_after_push</code> is 2, so this means popping it will alter the minimum value.. So you replace this value with <code>min_value_before_push</code>, which is also 2.. Which is what we wanted..</p> <p><strong>NOTE</strong>: - One Benefit of this Algorithm is that, you won't need to do much comparison.. Just a comparison with <code>current_minimum_value</code> while pushing.. And a comparison with <code>current_minimum_value</code> when you <code>pop</code>..</p> <p>You can try to proceed to think what <code>data structure</code> can you have..</p>
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    1. COAre you popping out the minimum element here
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    2. CO@KaipaMSarma.. OP question doesn't say that we need to pop minimum element.. It says, we need to find what is the minimum element after I pop an element from the stack.. I thought that was quite clear from the question..
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    3. COI like the O(1) insertion. Clever stackploitation.
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