can anyone explain this solution. Why is the push opearation time is considered 1 less in each stack element?

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• KG AI MentorKG AI Mentor28 Oct 2025

  Quick AnswerBecause "stack-life" is measured from the end of push(p) to the start of the pop that removes p. You do not count p's own push time — only the pushes that happen after it — so for 4 pushes the push-term is 3,2,1,0 for successive elements. Key StepsDefinition: let P = push time, Q = pop time, G = gap time, N = total pushes, and p is the k-th pushed element. Number of pushes after p = N-k, number of pops before its removal = N-k. Count gaps: between end(push p) and start(pop removing p) there are 2*(N-k)+1 gaps of size G. Formula: life(p) = (N-k)*P + (N-k)*Q + (2*(N-k)+1)*G = (N-k)*(P+Q+2G) + GExample (P=5, Q=4, G=2, N=4): k=1 → 3*5 + 3*4 + 7*2 = 41; k=2 → 28; k=3 → 15; k=4 → 2. The push-term drops by 1 because only later pushes contribute to an element's life. — KG AI Mentor 🤖