Broken Calculator

Description

On a broken calculator that has a number showing on its display, we can perform two operations:

• Double: Multiply the number on the display by 2, or;
• Decrement: Subtract 1 from the number on the display.

Initially, the calculator is displaying the number X.

Return the minimum number of operations needed to display the number Y.

 

Example 1:

Input: X = 2, Y = 3
Output: 2
Explanation: Use double operation and then decrement operation {2 -> 4 -> 3}.

Example 2:

Input: X = 5, Y = 8
Output: 2
Explanation: Use decrement and then double {5 -> 4 -> 8}.

Example 3:

Input: X = 3, Y = 10
Output: 3
Explanation:  Use double, decrement and double {3 -> 6 -> 5 -> 10}.

Example 4:

Input: X = 1024, Y = 1
Output: 1023
Explanation: Use decrement operations 1023 times.

 

Note:

1. 1 <= X <= 10^9
2. 1 <= Y <= 10^9

Solution(javascript)

/*
 * @lc app=leetcode id=991 lang=javascript
 *
 * [991] Broken Calculator
 */

// @lc code=start
/** DP top-down 不可以
 * @param {number} X
 * @param {number} Y
 * @return {number}
 */
const brokenCalc = function (X, Y) {
  let result = 0
  while (Y > X) {
    if (Y % 2 === 0) {
      Y /= 2
    } else {
      Y += 1
    }
    result += 1
  }
  return result + X - Y
}