Reset the Magic Counter to 1

Medium

Find the minimum number of operations to reduce X to 1 using /3, /2, -1 with dynamic programming.

📊 Complexity

Type	Value
Best	O(X)
Average	O(X)
Worst	O(X)
Space	O(X)

🏷️ Tags

DP1D TableOptimization

📋 Problem

Reset the Magic Counter to 1

A toy shop has a curious magic counter. Its screen shows an integer X, and there are only three buttons: • 🟦 "÷3" button: usable only when the number is a multiple of 3; divides it by 3. • 🟩 "÷2" button: usable only when the number is even; divides it by 2. • 🟥 "−1" button: subtracts 1 from the number. Reduce the screen to 1 to win candy. But you only win if you pressed the buttons the fewest possible times. Find the minimum number of button clicks to turn X into 1.

1/15

🎯Reach 1 with Fewest Clicks

Turn the counter number X into 1! • Start X = 10 • Buttons: ÷3 (if multiple of 3), ÷2 (if even), −1 Goal: Minimize the button clicks! Define dp[i] as "min clicks to turn i into 1" and fill from small numbers upward.

Reset the Magic Counter to 1

Medium

Reset the Magic Counter to 1

Find the minimum number of operations to reduce X to 1 using /3, /2, -1 with dynamic programming.

📊 Complexity

Type	Value
Best	O(X)
Average	O(X)
Worst	O(X)
Space	O(X)

🎯Reach 1 with Fewest Clicks