diff --git a/README.md b/README.md index 3f71fe9be..fc0f24320 100644 --- a/README.md +++ b/README.md @@ -8,6 +8,7 @@ LeetCode | # | Title | Solution | Difficulty | |---| ----- | -------- | ---------- | +|319|[Bulb Switcher](https://leetcode.com/problems/bulb-switcher/) | [C++](./algorithms/cpp/bulbSwitcher/bulbSwitcher.cpp)|Medium| |315|[Count of Smaller Numbers After Self](https://leetcode.com/problems/count-of-smaller-numbers-after-self/) | [C++](./algorithms/cpp/countOfSmallerNumbersAfterSelf/countOfSmallerNumbersAfterSelf.cpp)|Hard| |307|[Range Sum Query - Mutable](https://leetcode.com/problems/range-sum-query-mutable/) | [C++](./algorithms/cpp/rangeSumQuery-Immutable/rangeSumQuery-Mutable/RangeSumQueryMutable.cpp)|Medium| |306|[Additive Number](https://leetcode.com/problems/additive-number/) | [C++](./algorithms/cpp/additiveNumber/AdditiveNumber.cpp)|Medium| diff --git a/algorithms/cpp/bulbSwitcher/bulbSwitcher.cpp b/algorithms/cpp/bulbSwitcher/bulbSwitcher.cpp new file mode 100644 index 000000000..04b046391 --- /dev/null +++ b/algorithms/cpp/bulbSwitcher/bulbSwitcher.cpp @@ -0,0 +1,44 @@ +// Source : https://leetcode.com/problems/bulb-switcher/ +// Author : Calinescu Valentin +// Date : 2015-12-28 + +/*************************************************************************************** + * + * There are n bulbs that are initially off. You first turn on all the bulbs. Then, you + * turn off every second bulb. On the third round, you toggle every third bulb (turning + * on if it's off or turning off if it's on). For the nth round, you only toggle the + * last bulb. Find how many bulbs are on after n rounds. + * + * Example: + * + * Given n = 3. + * + * At first, the three bulbs are [off, off, off]. + * After first round, the three bulbs are [on, on, on]. + * After second round, the three bulbs are [on, off, on]. + * After third round, the three bulbs are [on, off, off]. + * + * So you should return 1, because there is only one bulb is on. + * + ***************************************************************************************/ + /* + * Solution 1 - O(1) + * ========= + * + * We notice that for every light bulb on position i there will be one toggle for every + * one of its divisors, given that you toggle all of the multiples of one number. The + * total number of toggles is irrelevant, because there are only 2 possible positions(on, + * off). We quickly find that 2 toggles cancel each other so given that the start position + * is always off a light bulb will be in if it has been toggled an odd number of times. + * The only integers with an odd number of divisors are perfect squares(because the square + * root only appears once, not like the other divisors that form pairs). The problem comes + * down to finding the number of perfect squares <= n. That number is the integer part of + * the square root of n. + * + */ +class Solution { +public: + int bulbSwitch(int n) { + return (int)sqrt(n); + } +};