Answer Big O Notation Exercises

Notes/Exercise/Questions/Exercise-04.md

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-**Write a function that accepts an array of strings and return a new array that only contains the strings that start with the character 'd'. Use Big O Notation to describe the time complexity of the function.**
+**Write a function that accepts an array of strings and return a new array that only contains the strings that start with the character 'd'. Use Big O Notation to describe the time complexity of the function.**

Notes/Exercise/Solutions/Solution-01.md

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+**Use Big O Notation to describe the time complexity of the following function that determines whether a given yaer is a leap year:**
+
+```js
+
+function isLeapYear(year){
+  return (year % 100 === 0) ? (year % 400 === 0) : (year % 4 === 0);
+}
+
+````
+
+The time complexity for  `isLeapYear` is: `O(1)`. Regardless of the input the algorithm will still go through the same number of operations during operation.

Notes/Exercise/Solutions/Solution-02.md

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+**Use Big O Notation to describe the time complexity of the following function that sums up all the numbers from a given array:**
+
+```js
+
+const sumOfArray = (array) => {
+  let sum = 0;
+
+  for(let i = 0; i < array.length; i++){
+    sum += array[i];
+  }
+  return sum;
+}
+
+```
+
+The time complexity for  `sumOfArray` is: `O(n)`. The number of operations that will be used in the for loop will increase as the input increases.

Notes/Exercise/Solutions/Solution-03.md

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+**Imagine you have a chessboard and put a single grain of rice on one square. On the second square, you put 2 grains of rice, since that is double the amount of rice on the previous square. On the third square, you put 4 grains and on the fourth square you put 8 grains. The pattern continues like that.**
+
+**Write a function calculates which square you will need to place a certain number of rice grains. For example, for 16 grains, the function will return 5. Use Big O Notation to describe the time complexity of that function.**

Notes/Exercise/Solutions/Solution-04.md

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+**Write a function that accepts an array of strings and return a new array that only contains the strings that start with the character 'd'. Use Big O Notation to describe the time complexity of the function.**
+
+```js
+const returnString = (arr) => {
+        return arr.filter(string => string.toLowerCase().startsWith('d'));
+}
+```
+The above function will have a time complexity of `O(n)`. This is because the filteration operations will increase as the input increases.

Notes/Exercise/Solutions/Solution-05.md

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+**The following function calculates the median from an ordered array. Describe its time complexity in terms of Big O Notation:**
+
+```js
+
+const median (array) => {
+  const middle = Math.floor(array.length / 2);
+
+  if(array.length % 2 === 0) {
+    return (array[middle - 1] + array[middle]) / 2;
+  }
+  return array[middle];
+}
+
+```
+
+The time complexity for  `median` is: `O(1)`. Regardless of the length of the input array accessing the middle elements will take constant time.