# 991. Broken Calculator

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`

``````class Solution {
public:
int brokenCalc(int X, int Y) {
int res = 0;
while (Y > X) {
Y = (Y % 2 == 0) ? Y / 2 : Y + 1;
++res;
}
return res + X - Y;
}
};
``````

``````class Solution {
public:
int brokenCalc(int X, int Y) {
if (X >= Y) return X - Y;
return (Y % 2 == 0) ? (1 + brokenCalc(X, Y / 2)) : (1 + brokenCalc(X, Y + 1));
}
};
``````

Github 同步地址:

https://github.com/grandyang/leetcode/issues/991

2 Keys Keyboard

https://leetcode.com/problems/broken-calculator/

https://leetcode.com/problems/broken-calculator/discuss/234484/JavaC%2B%2BPython-Change-Y-to-X-in-1-Line

https://leetcode.com/problems/broken-calculator/discuss/236565/Detailed-Proof-Of-Correctness-Greedy-Algorithm

LeetCode All in One 题目讲解汇总(持续更新中…)

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