88 lines
2.5 KiB
C++
88 lines
2.5 KiB
C++
// Source : https://leetcode.com/problems/bulb-switcher-ii/
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// Author : Hao Chen
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// Date : 2021-03-29
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/*****************************************************************************************************
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*
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* There is a room with n lights which are turned on initially and 4 buttons on the wall. After
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* performing exactly m unknown operations towards buttons, you need to return how many different
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* kinds of status of the n lights could be.
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*
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* Suppose n lights are labeled as number [1, 2, 3 ..., n], function of these 4 buttons are given
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* below:
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*
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* Flip all the lights.
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* Flip lights with even numbers.
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* Flip lights with odd numbers.
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* Flip lights with (3k + 1) numbers, k = 0, 1, 2, ...
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*
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* Example 1:
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*
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* Input: n = 1, m = 1.
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* Output: 2
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* Explanation: Status can be: [on], [off]
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*
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* Example 2:
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*
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* Input: n = 2, m = 1.
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* Output: 3
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* Explanation: Status can be: [on, off], [off, on], [off, off]
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*
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* Example 3:
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*
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* Input: n = 3, m = 1.
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* Output: 4
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* Explanation: Status can be: [off, on, off], [on, off, on], [off, off, off], [off, on, on].
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*
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* Note: n and m both fit in range [0, 1000].
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******************************************************************************************************/
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/*
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We have 4 operations:
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1) Flip all the lights.
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2) Flip lights with even numbers.
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3) Flip lights with odd numbers.
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4) Flip lights with (3k + 1) numbers, k = 0, 1, 2, ...
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if we do 1) + 2), it's same as 3)
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if we do 1) + 3), it's same as 2)
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if we do 2) + 3), it's same as 1)
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if we do 1) + 2) + 3), it's same as do nothing
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So, we can manaully calculate how many different state we could have:
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m = 1, then 1), 2), 3), 4)
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m = 2, then 1)+2), 1)+3), 1)+4), 2)+3), 2)+4), 3)+4) and 1)+1) => inital state
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m = 3, then 1), 2), 3), 4), 1)+4), 2+4), 3)+4), and 1)+2)+3) => inital state
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notice:
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if m == 1, we could only have 4 states at most.
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if m == 2, we could only have 7 states at most. (no the 4) state)
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if m > 2, we could only have 8 states at most. (has the 4) state)
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But for some edge cases, we need to take care specially. For example:
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- m = 0 or n = 0, only 1 state.
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- n = 1, then 2 states.
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- n = 2, then it could have 3(when m=1), or 4 states (whem m>1)
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- n > 2 && m = 1, then it only could have 4 states.
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*/
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class Solution {
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public:
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int flipLights(int n, int m) {
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if (m == 0 || n == 0) return 1;
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if (n == 1) return 2;
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if (n == 2) return m == 1? 3:4;
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if (m == 1) return 4;
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return m==2 ? 7 :8;
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}
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};
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