From ad9c286ac0091610e2f155df44b6a4235a39dfb6 Mon Sep 17 00:00:00 2001
From: anigonzales <anisgonzales@gmail.com>
Date: Thu, 20 Sep 2018 13:55:25 -0700
Subject: [PATCH 1/8] working on sum

---
 src/recursion.js | 25 ++++++++++++++++++++++++-
 1 file changed, 24 insertions(+), 1 deletion(-)

diff --git a/src/recursion.js b/src/recursion.js
index 12ca0a3d7..7ef64158d 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -4,12 +4,33 @@
 // denoted by n!, is the product of all positive integers less than or equal to n.
 // Example:  5! = 5 x 4 x 3 x 2 x 1 = 120
 // factorial(5);  // 120
-var factorial = function(n) {
+var factorial = function(n, total = 1, i = n) {
+    // base case
+    if(i < 0){
+        return null;
+    }else if(i === 0){
+        return total
+    }
+
+    //changes value of total
+    total *= i;
+
+    // brings i down 1 value (if n = 5 and i = n, then i now = 4)
+    i--;
+
+    //starting with n = 5, then this /v is factorial(4, 20, 4)
+    return factorial(n, total, i);
 };
 
 // 2. Compute the sum of an array of integers.
 // Example:  sum([1, 2, 3, 4, 5, 6]);  // 21
 var sum = function(array) {
+    return array[0];
+    // if(_.contains(array, values < 0)){
+    //     return;
+    // }
+
+
 };
 
 // 3. Sum all numbers in an array containing nested arrays.
@@ -19,6 +40,8 @@ var arraySum = function(array) {
 
 // 4. Check if a number is even.
 var isEven = function(n) {
+    return true;
+
 };
 
 // 5. Sum all integers below a given integer.

From b056097150fdd8addbde317c24f7cfce796a48bc Mon Sep 17 00:00:00 2001
From: anigonzales <anisgonzales@gmail.com>
Date: Fri, 21 Sep 2018 13:59:49 -0700
Subject: [PATCH 2/8]  on range

---
 src/recursion.js | 39 ++++++++++++++++++++++++++++++---------
 1 file changed, 30 insertions(+), 9 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 7ef64158d..e6fa1c0db 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -24,30 +24,51 @@ var factorial = function(n, total = 1, i = n) {
 
 // 2. Compute the sum of an array of integers.
 // Example:  sum([1, 2, 3, 4, 5, 6]);  // 21
-var sum = function(array) {
-    return array[0];
-    // if(_.contains(array, values < 0)){
-    //     return;
-    // }
-
-
+var sum = function(array, total = 0, i = 0) {
+    if(!array.length){
+        return 0
+    }
+    return array[0] + sum(array.slice(1));
 };
 
 // 3. Sum all numbers in an array containing nested arrays.
 // Example: arraySum([1,[2,3],[[4]],5]); // 15
 var arraySum = function(array) {
+
 };
 
 // 4. Check if a number is even.
 var isEven = function(n) {
-    return true;
+    if(n === 0){
+        return true;
+    }
 
+    if(n === -1){
+        return false;
+    }
+    if(n < 0){
+        n *= -1
+    }
+    n = n -2
+    return isEven(n)
 };
 
 // 5. Sum all integers below a given integer.
 // sumBelow(10); // 45
 // sumBelow(7); // 21
-var sumBelow = function(n) {
+var sumBelow = function(n, total = 0) {
+    if(n === 0){
+        return total;
+    }
+    if (n < 0){
+        total += n + 1;
+        n++;
+    }
+    if(n > 0){
+        total += n - 1;
+        n--;
+    }
+    return sumBelow(n, total);
 };
 
 // 6. Get the integers in range (x, y).

From c6b4258fac15194027ed97d8c4d9ffe781f65c1e Mon Sep 17 00:00:00 2001
From: anigonzales <anisgonzales@gmail.com>
Date: Mon, 24 Sep 2018 13:55:43 -0700
Subject: [PATCH 3/8] need to accept neg integers  for exponent

---
 src/recursion.js | 39 ++++++++++++++++++++++++++++++++++++++-
 1 file changed, 38 insertions(+), 1 deletion(-)

diff --git a/src/recursion.js b/src/recursion.js
index e6fa1c0db..afe157ec0 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -73,7 +73,25 @@ var sumBelow = function(n, total = 0) {
 
 // 6. Get the integers in range (x, y).
 // Example:  range(2, 9);  // [3, 4, 5, 6, 7, 8]
-var range = function(x, y) {
+var range = function(x ,y, arr = []) {
+            
+    if(x === y ||  arr[arr.length-1] === y - 1 ||  arr[arr.length-1] === y + 1){
+        return arr;
+     } 
+     if(x + 1 === y || x - 1 === y){
+        return arr;
+     }
+     if ( x < y){
+        arr.push(x + 1);
+        x++;
+        // one less
+     }
+     if (x > y){
+        arr.push(x - 1);
+        x--;
+        // one more
+     }
+    return range(x,y, arr);
 };
 
 // 7. Compute the exponent of a number.
@@ -82,6 +100,23 @@ var range = function(x, y) {
 // Example:  exponent(4,3);  // 64
 // https://www.khanacademy.org/computing/computer-science/algorithms/recursive-algorithms/a/computing-powers-of-a-number
 var exponent = function(base, exp) {
+    // if(exp === 1){
+    //     return base;
+    // }
+    // if(exp === 0){
+    //     return 1; 
+    // }
+    if(exp === 0){
+        return 1;
+    }
+    if(exp < 0){
+        return 0;
+    }
+    if(exp === 1){
+        return base;
+    } else {
+        return base * exponent(base, exp - 1);
+    }
 };
 
 // 8. Determine if a number is a power of two.
@@ -89,6 +124,8 @@ var exponent = function(base, exp) {
 // powerOfTwo(16); // true
 // powerOfTwo(10); // false
 var powerOfTwo = function(n) {
+    //2^n     
+    
 };
 
 // 9. Write a function that accepts a string a reverses it.

From b50ee61d1c87361d86860a51890062d94d53fd66 Mon Sep 17 00:00:00 2001
From: anigonzales <anisgonzales@gmail.com>
Date: Tue, 25 Sep 2018 11:55:03 -0700
Subject: [PATCH 4/8]  finished power of two

---
 src/recursion.js | 16 ++++++++++++++--
 1 file changed, 14 insertions(+), 2 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index afe157ec0..c04db0264 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -110,7 +110,7 @@ var exponent = function(base, exp) {
         return 1;
     }
     if(exp < 0){
-        return 0;
+        return exponent(base, exp + 1)
     }
     if(exp === 1){
         return base;
@@ -125,11 +125,23 @@ var exponent = function(base, exp) {
 // powerOfTwo(10); // false
 var powerOfTwo = function(n) {
     //2^n     
-    
+    if(n <= 0){
+        return false;
+    }else if(n === 1 || n === 0) {
+        return true;
+    }else if(n % 2 === 1){
+        return false;
+    }else{
+        return powerOfTwo(n/2);
+    }
 };
 
 // 9. Write a function that accepts a string a reverses it.
 var reverse = function(string) {
+    if(!string.length){
+        return string;
+    }
+    return string.split("").reverse(string).join("");
 };
 
 // 10. Write a function that determines if a string is a palindrome.

From 425829dc615781602a6990f329804e31fc6d9d91 Mon Sep 17 00:00:00 2001
From: anigonzales <anisgonzales@gmail.com>
Date: Tue, 25 Sep 2018 13:07:31 -0700
Subject: [PATCH 5/8]  on palindrome

---
 src/recursion.js | 45 ++++++++++++++++++++++++++++++++-------------
 1 file changed, 32 insertions(+), 13 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index c04db0264..dd1a2515c 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -77,20 +77,20 @@ var range = function(x ,y, arr = []) {
             
     if(x === y ||  arr[arr.length-1] === y - 1 ||  arr[arr.length-1] === y + 1){
         return arr;
-     } 
-     if(x + 1 === y || x - 1 === y){
+    } 
+    if(x + 1 === y || x - 1 === y){
         return arr;
-     }
-     if ( x < y){
+    }
+    if ( x < y){
         arr.push(x + 1);
         x++;
         // one less
-     }
-     if (x > y){
+    }
+    if (x > y){
         arr.push(x - 1);
         x--;
         // one more
-     }
+    }
     return range(x,y, arr);
 };
 
@@ -110,12 +110,12 @@ var exponent = function(base, exp) {
         return 1;
     }
     if(exp < 0){
-        return exponent(base, exp + 1)
+        return 1 / exponent(base, -exp)
     }
     if(exp === 1){
         return base;
     } else {
-        return base * exponent(base, exp - 1);
+        return base *= exponent(base, exp - 1);
     }
 };
 
@@ -137,15 +137,34 @@ var powerOfTwo = function(n) {
 };
 
 // 9. Write a function that accepts a string a reverses it.
-var reverse = function(string) {
-    if(!string.length){
+var reverse = function (startString, string = "", newString = '', arr = []) {
+    if (startString.length === 0){
         return string;
+    } else if(startString.length > 0){
+        for (let i = startString.length - 1; i >= 0; i--) {
+            arr.push(startString[i]);
+            newString += arr[0];
+            arr.shift();
+        }
     }
-    return string.split("").reverse(string).join("");
+    return (reverse(string, newString ,arr))
 };
 
 // 10. Write a function that determines if a string is a palindrome.
-var palindrome = function(string) {
+var palindrome = function(string, string2= string) {
+    if(string.length === 0){
+        return false;
+    }
+    
+    if(string[0] === string2[string2.length-1]){
+        string.replace(string.charAt(0), "");
+        string2.replace(string2.charAt(string2.length-1), "");
+        return true;
+    }
+
+    
+
+    return palindrome(string, string2);
 };
 
 // 11. Write a function that returns the remainder of x divided by y without using the

From 634849c60e4dbf2ee9900495a4743aed1041b630 Mon Sep 17 00:00:00 2001
From: anigonzales <anisgonzales@gmail.com>
Date: Tue, 25 Sep 2018 13:59:15 -0700
Subject: [PATCH 6/8] merging

---
 src/recursion.js | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/recursion.js b/src/recursion.js
index dd1a2515c..81408a15b 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -178,6 +178,7 @@ var modulo = function(x, y) {
 // 12. Write a function that multiplies two numbers without using the * operator  or
 // JavaScript's Math object.
 var multiply = function(x, y) {
+    
 };
 
 // 13. Write a function that divides two numbers without using the / operator  or

From fde1ae59b402422004ef0eccc82f523e9b470589 Mon Sep 17 00:00:00 2001
From: anigonzales <anisgonzales@gmail.com>
Date: Fri, 28 Sep 2018 14:00:42 -0700
Subject: [PATCH 7/8] finish recursion

---
 src/recursion.js | 167 ++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 142 insertions(+), 25 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 81408a15b..6d9c1b67d 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -151,22 +151,19 @@ var reverse = function (startString, string = "", newString = '', arr = []) {
 };
 
 // 10. Write a function that determines if a string is a palindrome.
-var palindrome = function(string, string2= string) {
-    if(string.length === 0){
-        return false;
-    }
-    
-    if(string[0] === string2[string2.length-1]){
-        string.replace(string.charAt(0), "");
-        string2.replace(string2.charAt(string2.length-1), "");
+var palindrome = function(string) {
+    if (string != string.split("").reverse().join("")){
         return true;
+    }else if(string.length){
+        if (string[0] == string.split("").reverse().join("")[0]) {
+            return palindrome(string.substring(1));
+        }else{
+            return false;
+        }
     }
-
-    
-
-    return palindrome(string, string2);
 };
 
+
 // 11. Write a function that returns the remainder of x divided by y without using the
 // modulo (%) operator.
 // modulo(5,2) // 1
@@ -178,7 +175,13 @@ var modulo = function(x, y) {
 // 12. Write a function that multiplies two numbers without using the * operator  or
 // JavaScript's Math object.
 var multiply = function(x, y) {
-    
+    if (x === 0 || y === 0) {
+        return 0;
+    } else if (y < 0) {
+        return -x + multiply(x, y + 1);
+    } else {
+        return x + multiply(x, y - 1);
+    }
 };
 
 // 13. Write a function that divides two numbers without using the / operator  or
@@ -200,32 +203,80 @@ var gcd = function(x, y) {
 // compareStr('', '') // true
 // compareStr('tomato', 'tomato') // true
 var compareStr = function(str1, str2) {
+    if(str1.length === 0 && str2.length === 0){
+        return true;
+    }
+    if(str1.charAt(0) === str2.charAt(0)){
+        return compareStr(str1.slice(1), str2.slice(1));
+    }
+    
+    
+    if(str1.charAt(0) !== str2.charAt(0)){
+        return false;
+    }
 };
 
 // 16. Write a function that accepts a string and creates an array where each letter
 // occupies an index of the array.
-var createArray = function(str){
+var createArray = function(str, i = 0, arr = []){
+    if(i >= str.length){
+        return arr;
+    }
+    else{
+        arr.push(str[i]);
+    }
+    i++;
+    return createArray(str, i, arr);
 };
 
 // 17. Reverse the order of an array
-var reverseArr = function (array) {
+var reverseArr = function (array, array2 = [], num = 1) {
+    if (num >= array.length + 1){
+        return array2;
+    }else{
+        array2.push(array[array.length - num]);
+    }
+    num++
+    return reverseArr(array, array2, num)
 };
 
 // 18. Create a new array with a given value and length.
 // buildList(0,5) // [0,0,0,0,0]
 // buildList(7,3) // [7,7,7]
-var buildList = function(value, length) {
+var buildList = function(value, length, array = [], i = 0) {
+    if(i >= length){
+        return array;
+    }else {
+        array.push(value);
+    }i++
+    return buildList(value, length, array, i);
 };
 
-// 19. Count the occurence of a value inside a list.
+// 19. Count the occurrence of a value inside a list.
 // countOccurrence([2,7,4,4,1,4], 4) // 3
 // countOccurrence([2,'banana',4,4,1,'banana'], 'banana') // 2
-var countOccurrence = function(array, value) {
+var countOccurrence = function(array, value, i = 0, sum = 0) {
+    if(i >= array.length){
+        return sum; 
+    }
+    if(array[i] === value){
+        sum += 1;
+    }
+    
+    i++;
+    return countOccurrence(array, value, i, sum);
 };
 
 // 20. Write a recursive version of map.
 // rMap([1,2,3], timesTwo); // [2,4,6]
-var rMap = function(array, callback) {
+var rMap = function(array, callback, i = 0, newArray = []) {
+    if(i >= array.length){
+        return newArray;
+    }else{
+        newArray.push(callback(array[i]));
+    }
+    i++;
+    return rMap(array, callback, i, newArray)
 };
 
 // 21. Write a function that counts the number of times a key occurs in an object.
@@ -261,17 +312,42 @@ var fibonacci = function(n) {
 // nthFibo(7); // 13
 // nthFibo(3); // 2
 var nthFibo = function(n) {
+    if (n === 0) {
+        return 0;
+    }
+    if (n === 1) {
+        return 1;
+    }
+    if(n < 0){
+        return null;
+    }
+
+    return nthFibo(n - 1) + nthFibo(n - 2);
 };
 
 // 26. Given an array of words, return a new array containing each word capitalized.
 // var words = ['i', 'am', 'learning', 'recursion'];
 // capitalizedWords(words); // ['I', 'AM', 'LEARNING', 'RECURSION']
-var capitalizeWords = function(input) {
+var capitalizeWords = function(input, i = 0, arr = []) {
+    if(i >= input.length){
+        return arr;
+    }else{
+        arr.push(input[i].toUpperCase());
+    }
+    i++;
+    return capitalizeWords(input,i,arr);
 };
 
 // 27. Given an array of strings, capitalize the first letter of each index.
 // capitalizeFirst(['car', 'poop', 'banana']); // ['Car', 'Poop', 'Banana']
-var capitalizeFirst = function(array) {
+var capitalizeFirst = function(input, i = 0, arr = []) {
+    if(i >= input.length){
+        return arr;
+    }else{
+        arr.push(input[i][0].toUpperCase() + input[i].substring(1));
+    }
+    i++;
+    return capitalizeFirst(input,i,arr);
 };
 
 // 28. Return the sum of all even numbers in an object containing nested objects.
@@ -293,7 +369,22 @@ var flatten = function(arrays) {
 
 // 30. Given a string, return an object containing tallies of each letter.
 // letterTally('potato'); // {'p':1, 'o':2, 't':2, 'a':1}
-var letterTally = function(str, obj) {
+var letterTally = function(str, obj, i = 0) {
+    if(str.length < i){
+        return obj;
+    }
+    if(str.length > i){
+        if(obj[i] === false){
+            // if i is not in obj then add it as a key and a value 1
+            obj.i = "1"
+
+        }else{
+            // if i is in obj then add it as a value of +1
+
+
+        }
+    }
+    return letterTally(str, obj, i);
 };
 
 // 31. Eliminate consecutive duplicates in a list.  If the list contains repeated
@@ -301,7 +392,18 @@ var letterTally = function(str, obj) {
 // elements should not be changed.
 // Example: compress([1, 2, 2, 3, 4, 4, 5, 5, 5]) // [1, 2, 3, 4, 5]
 // Example: compress([1, 2, 2, 3, 4, 4, 2, 5, 5, 5, 4, 4]) // [1, 2, 3, 4, 2, 5, 4]
-var compress = function(list) {
+var compress = function(list, i = 0, arr = []) {
+    if(i >= list.length){
+        return arr;
+    }
+    if(list[i] - 1 === list[i] || list[i] + 1 === list[i]){
+        list.slice(list[i]);
+    }
+    if(arr.indexOf(list[i]) === -1){
+        arr.push(list[i]);
+    }
+    i++;
+    return compress(list, i, arr);
 };
 
 // 32. Augment every element in a list with a new value where each element is an array
@@ -320,8 +422,23 @@ var minimizeZeroes = function(array) {
 // their original sign.  The first number in the index always needs to be positive.
 // alternateSign([2,7,8,3,1,4]) // [2,-7,8,-3,1,-4]
 // alternateSign([-2,-7,8,3,-1,4]) // [2,-7,8,-3,1,-4]
-var alternateSign = function(array) {
-};
+var alternateSign = function(array, i = 0) {
+    if (i >= array.length){
+    array[0] = Math.abs(array[0]);
+        return array;
+    }else if(i % 2 !== 0 && array[i] >= 0){
+        array[i] = array[i]*-1;
+    }else if (i % 2 !== 0 && array[i] < 0){
+        array[i] = array[i];
+    }else if (i % 2 === 0 && array[i] < 0){
+        array[i] = array[i] * -1;
+    }else if (i % 2 === 0 && array[i] >= 0) {
+        array[i] = array[i];
+    }
+
+    i++;
+    return alternateSign(array, i);
+}
 
 // 35. Given a string, return a string with digits converted to their word equivalent.
 // Assume all numbers are single digits (less than 10).

From 6ba4b9644160ffd55fce8adf3cdbea23c0cec49e Mon Sep 17 00:00:00 2001
From: Half Day <halfday@Operations-Mac-mini-6.local>
Date: Fri, 16 Nov 2018 14:32:15 -0600
Subject: [PATCH 8/8] finished

---
 src/recursion.js | 258 +++++++++++++++++++++++++----------------------
 1 file changed, 135 insertions(+), 123 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 6d9c1b67d..993eff36d 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -1,14 +1,14 @@
-// Solve all of the following prompts using recursion.
+/// Solve all of the following prompts using recursion.
 
 // 1. Calculate the factorial of a number.  The factorial of a non-negative integer n,
 // denoted by n!, is the product of all positive integers less than or equal to n.
 // Example:  5! = 5 x 4 x 3 x 2 x 1 = 120
 // factorial(5);  // 120
-var factorial = function(n, total = 1, i = n) {
+var factorial = function (n, total = 1, i = n) {
     // base case
-    if(i < 0){
+    if (i < 0) {
         return null;
-    }else if(i === 0){
+    } else if (i === 0) {
         return total
     }
 
@@ -24,8 +24,8 @@ var factorial = function(n, total = 1, i = n) {
 
 // 2. Compute the sum of an array of integers.
 // Example:  sum([1, 2, 3, 4, 5, 6]);  // 21
-var sum = function(array, total = 0, i = 0) {
-    if(!array.length){
+var sum = function (array, total = 0, i = 0) {
+    if (!array.length) {
         return 0
     }
     return array[0] + sum(array.slice(1));
@@ -33,38 +33,38 @@ var sum = function(array, total = 0, i = 0) {
 
 // 3. Sum all numbers in an array containing nested arrays.
 // Example: arraySum([1,[2,3],[[4]],5]); // 15
-var arraySum = function(array) {
+var arraySum = function (array) {
 
 };
 
 // 4. Check if a number is even.
-var isEven = function(n) {
-    if(n === 0){
+var isEven = function (n) {
+    if (n === 0) {
         return true;
     }
 
-    if(n === -1){
+    if (n === -1) {
         return false;
     }
-    if(n < 0){
+    if (n < 0) {
         n *= -1
     }
-    n = n -2
+    n = n - 2
     return isEven(n)
 };
 
 // 5. Sum all integers below a given integer.
 // sumBelow(10); // 45
 // sumBelow(7); // 21
-var sumBelow = function(n, total = 0) {
-    if(n === 0){
+var sumBelow = function (n, total = 0) {
+    if (n === 0) {
         return total;
     }
-    if (n < 0){
+    if (n < 0) {
         total += n + 1;
         n++;
     }
-    if(n > 0){
+    if (n > 0) {
         total += n - 1;
         n--;
     }
@@ -73,25 +73,25 @@ var sumBelow = function(n, total = 0) {
 
 // 6. Get the integers in range (x, y).
 // Example:  range(2, 9);  // [3, 4, 5, 6, 7, 8]
-var range = function(x ,y, arr = []) {
-            
-    if(x === y ||  arr[arr.length-1] === y - 1 ||  arr[arr.length-1] === y + 1){
+var range = function (x, y, arr = []) {
+
+    if (x === y || arr[arr.length - 1] === y - 1 || arr[arr.length - 1] === y + 1) {
         return arr;
-    } 
-    if(x + 1 === y || x - 1 === y){
+    }
+    if (x + 1 === y || x - 1 === y) {
         return arr;
     }
-    if ( x < y){
+    if (x < y) {
         arr.push(x + 1);
         x++;
         // one less
     }
-    if (x > y){
+    if (x > y) {
         arr.push(x - 1);
         x--;
         // one more
     }
-    return range(x,y, arr);
+    return range(x, y, arr);
 };
 
 // 7. Compute the exponent of a number.
@@ -99,20 +99,20 @@ var range = function(x ,y, arr = []) {
 // 8^2 = 8 x 8 = 64.  Here, 8 is the base and 2 is the exponent.
 // Example:  exponent(4,3);  // 64
 // https://www.khanacademy.org/computing/computer-science/algorithms/recursive-algorithms/a/computing-powers-of-a-number
-var exponent = function(base, exp) {
+var exponent = function (base, exp) {
     // if(exp === 1){
     //     return base;
     // }
     // if(exp === 0){
     //     return 1; 
     // }
-    if(exp === 0){
+    if (exp === 0) {
         return 1;
     }
-    if(exp < 0){
+    if (exp < 0) {
         return 1 / exponent(base, -exp)
     }
-    if(exp === 1){
+    if (exp === 1) {
         return base;
     } else {
         return base *= exponent(base, exp - 1);
@@ -123,58 +123,60 @@ var exponent = function(base, exp) {
 // powerOfTwo(1); // true
 // powerOfTwo(16); // true
 // powerOfTwo(10); // false
-var powerOfTwo = function(n) {
+var powerOfTwo = function (n) {
     //2^n     
-    if(n <= 0){
+    if (n <= 0) {
         return false;
-    }else if(n === 1 || n === 0) {
+    } else if (n === 1 || n === 0) {
         return true;
-    }else if(n % 2 === 1){
+    } else if (n % 2 === 1) {
         return false;
-    }else{
-        return powerOfTwo(n/2);
+    } else {
+        return powerOfTwo(n / 2);
     }
 };
 
 // 9. Write a function that accepts a string a reverses it.
 var reverse = function (startString, string = "", newString = '', arr = []) {
-    if (startString.length === 0){
+    if (startString.length === 0) {
         return string;
-    } else if(startString.length > 0){
+    } else if (startString.length > 0) {
         for (let i = startString.length - 1; i >= 0; i--) {
             arr.push(startString[i]);
             newString += arr[0];
             arr.shift();
         }
     }
-    return (reverse(string, newString ,arr))
+    return (reverse(string, newString, arr));
 };
 
 // 10. Write a function that determines if a string is a palindrome.
-var palindrome = function(string) {
-    if (string != string.split("").reverse().join("")){
-        return true;
-    }else if(string.length){
-        if (string[0] == string.split("").reverse().join("")[0]) {
-            return palindrome(string.substring(1));
-        }else{
-            return false;
-        }
+var palindrome = function (string) {
+    if (string.length <= 1) { return true; }
+    if (string[0].toLowerCase() !== string[string.length - 1].toLowerCase()) {
+        return false;
     }
+    string = string.substr(1, string.length - 2);
+    string = string.replace(' ', '');
+    return palindrome(string);
 };
 
+/*
+*
+*/
+
 
 // 11. Write a function that returns the remainder of x divided by y without using the
 // modulo (%) operator.
 // modulo(5,2) // 1
 // modulo(17,5) // 2
 // modulo(22,6) // 4
-var modulo = function(x, y) {
+var modulo = function (x, y) {
 };
 
 // 12. Write a function that multiplies two numbers without using the * operator  or
 // JavaScript's Math object.
-var multiply = function(x, y) {
+var multiply = function (x, y) {
     if (x === 0 || y === 0) {
         return 0;
     } else if (y < 0) {
@@ -186,7 +188,7 @@ var multiply = function(x, y) {
 
 // 13. Write a function that divides two numbers without using the / operator  or
 // JavaScript's Math object.
-var divide = function(x, y) {
+var divide = function (x, y) {
 };
 
 // 14. Find the greatest common divisor (gcd) of two positive numbers.  The GCD of two
@@ -194,7 +196,7 @@ var divide = function(x, y) {
 // Example:  gcd(4,36);  // 4
 // http://www.cse.wustl.edu/~kjg/cse131/Notes/Recursion/recursion.html
 // https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/the-euclidean-algorithm
-var gcd = function(x, y) {
+var gcd = function (x, y) {
 };
 
 // 15. Write a function that compares each character of two strings and returns true if
@@ -202,27 +204,27 @@ var gcd = function(x, y) {
 // compareStr('house', 'houses') // false
 // compareStr('', '') // true
 // compareStr('tomato', 'tomato') // true
-var compareStr = function(str1, str2) {
-    if(str1.length === 0 && str2.length === 0){
+var compareStr = function (str1, str2) {
+    if (str1.length === 0 && str2.length === 0) {
         return true;
     }
-    if(str1.charAt(0) === str2.charAt(0)){
+    if (str1.charAt(0) === str2.charAt(0)) {
         return compareStr(str1.slice(1), str2.slice(1));
     }
-    
-    
-    if(str1.charAt(0) !== str2.charAt(0)){
+
+
+    if (str1.charAt(0) !== str2.charAt(0)) {
         return false;
     }
 };
 
 // 16. Write a function that accepts a string and creates an array where each letter
 // occupies an index of the array.
-var createArray = function(str, i = 0, arr = []){
-    if(i >= str.length){
+var createArray = function (str, i = 0, arr = []) {
+    if (i >= str.length) {
         return arr;
     }
-    else{
+    else {
         arr.push(str[i]);
     }
     i++;
@@ -231,9 +233,9 @@ var createArray = function(str, i = 0, arr = []){
 
 // 17. Reverse the order of an array
 var reverseArr = function (array, array2 = [], num = 1) {
-    if (num >= array.length + 1){
+    if (num >= array.length + 1) {
         return array2;
-    }else{
+    } else {
         array2.push(array[array.length - num]);
     }
     num++
@@ -243,36 +245,36 @@ var reverseArr = function (array, array2 = [], num = 1) {
 // 18. Create a new array with a given value and length.
 // buildList(0,5) // [0,0,0,0,0]
 // buildList(7,3) // [7,7,7]
-var buildList = function(value, length, array = [], i = 0) {
-    if(i >= length){
+var buildList = function (value, length, array = [], i = 0) {
+    if (i >= length) {
         return array;
-    }else {
+    } else {
         array.push(value);
-    }i++
+    } i++
     return buildList(value, length, array, i);
 };
 
 // 19. Count the occurrence of a value inside a list.
 // countOccurrence([2,7,4,4,1,4], 4) // 3
 // countOccurrence([2,'banana',4,4,1,'banana'], 'banana') // 2
-var countOccurrence = function(array, value, i = 0, sum = 0) {
-    if(i >= array.length){
-        return sum; 
+var countOccurrence = function (array, value, i = 0, sum = 0) {
+    if (i >= array.length) {
+        return sum;
     }
-    if(array[i] === value){
+    if (array[i] === value) {
         sum += 1;
     }
-    
+
     i++;
     return countOccurrence(array, value, i, sum);
 };
 
 // 20. Write a recursive version of map.
 // rMap([1,2,3], timesTwo); // [2,4,6]
-var rMap = function(array, callback, i = 0, newArray = []) {
-    if(i >= array.length){
+var rMap = function (array, callback, i = 0, newArray = []) {
+    if (i >= array.length) {
         return newArray;
-    }else{
+    } else {
         newArray.push(callback(array[i]));
     }
     i++;
@@ -283,19 +285,19 @@ var rMap = function(array, callback, i = 0, newArray = []) {
 // var testobj = {'e': {'x':'y'}, 't':{'r': {'e':'r'}, 'p': {'y':'r'}},'y':'e'};
 // countKeysInObj(testobj, 'r') // 1
 // countKeysInObj(testobj, 'e') // 2
-var countKeysInObj = function(obj, key) {
+var countKeysInObj = function (obj, key) {
 };
 
 // 22. Write a function that counts the number of times a value occurs in an object.
 // var testobj = {'e': {'x':'y'}, 't':{'r': {'e':'r'}, 'p': {'y':'r'}},'y':'e'};
 // countValuesInObj(testobj, 'r') // 2
 // countValuesInObj(testobj, 'e') // 1
-var countValuesInObj = function(obj, value) {
+var countValuesInObj = function (obj, value) {
 };
 
 // 23. Find all keys in an object (and nested objects) by a provided name and rename
 // them to a provided new name while preserving the value stored at that key.
-var replaceKeysInObj = function(obj, key, newKey) {
+var replaceKeysInObj = function (obj, key, newKey) {
 };
 
 // 24. Get the first n Fibonacci numbers.  In the Fibonacci Sequence, each subsequent
@@ -303,7 +305,7 @@ var replaceKeysInObj = function(obj, key, newKey) {
 // Example:  0, 1, 1, 2, 3, 5, 8, 13, 21, 34.....
 // fibonacci(5);  // [0, 1, 1, 2, 3, 5]
 // Note:  The 0 is not counted.
-var fibonacci = function(n) {
+var fibonacci = function (n) {
 };
 
 // 25. Return the Fibonacci number located at index n of the Fibonacci sequence.
@@ -311,14 +313,14 @@ var fibonacci = function(n) {
 // nthFibo(5); // 5
 // nthFibo(7); // 13
 // nthFibo(3); // 2
-var nthFibo = function(n) {
+var nthFibo = function (n) {
     if (n === 0) {
         return 0;
     }
     if (n === 1) {
         return 1;
     }
-    if(n < 0){
+    if (n < 0) {
         return null;
     }
 
@@ -328,26 +330,26 @@ var nthFibo = function(n) {
 // 26. Given an array of words, return a new array containing each word capitalized.
 // var words = ['i', 'am', 'learning', 'recursion'];
 // capitalizedWords(words); // ['I', 'AM', 'LEARNING', 'RECURSION']
-var capitalizeWords = function(input, i = 0, arr = []) {
-    if(i >= input.length){
+var capitalizeWords = function (input, i = 0, arr = []) {
+    if (i >= input.length) {
         return arr;
-    }else{
+    } else {
         arr.push(input[i].toUpperCase());
     }
     i++;
-    return capitalizeWords(input,i,arr);
+    return capitalizeWords(input, i, arr);
 };
 
 // 27. Given an array of strings, capitalize the first letter of each index.
 // capitalizeFirst(['car', 'poop', 'banana']); // ['Car', 'Poop', 'Banana']
-var capitalizeFirst = function(input, i = 0, arr = []) {
-    if(i >= input.length){
+var capitalizeFirst = function (input, i = 0, arr = []) {
+    if (i >= input.length) {
         return arr;
-    }else{
+    } else {
         arr.push(input[i][0].toUpperCase() + input[i].substring(1));
     }
     i++;
-    return capitalizeFirst(input,i,arr);
+    return capitalizeFirst(input, i, arr);
 };
 
 // 28. Return the sum of all even numbers in an object containing nested objects.
@@ -359,32 +361,30 @@ var capitalizeFirst = function(input, i = 0, arr = []) {
 //   e: {e: {e: 2}, ee: 'car'}
 // };
 // nestedEvenSum(obj1); // 10
-var nestedEvenSum = function(obj) {
+var nestedEvenSum = function (obj) {
 };
 
 // 29. Flatten an array containing nested arrays.
 // Example: flatten([1,[2],[3,[[4]]],5]); // [1,2,3,4,5]
-var flatten = function(arrays) {
+var flatten = function (arrays) {
 };
 
 // 30. Given a string, return an object containing tallies of each letter.
 // letterTally('potato'); // {'p':1, 'o':2, 't':2, 'a':1}
-var letterTally = function(str, obj, i = 0) {
-    if(str.length < i){
+var letterTally = function (str, obj = {}) {
+    if (str.length === 0) {
         return obj;
     }
-    if(str.length > i){
-        if(obj[i] === false){
-            // if i is not in obj then add it as a key and a value 1
-            obj.i = "1"
-
-        }else{
-            // if i is in obj then add it as a value of +1
 
+    if (obj.hasOwnProperty(str[0])) {
+        obj[str[0]] += 1;
+        return letterTally(str.slice(1), obj);
 
-        }
+    } else {
+        obj[str[0]] = 1;
     }
-    return letterTally(str, obj, i);
+    return letterTally(str.slice(1), obj);
+
 };
 
 // 31. Eliminate consecutive duplicates in a list.  If the list contains repeated
@@ -392,47 +392,59 @@ var letterTally = function(str, obj, i = 0) {
 // elements should not be changed.
 // Example: compress([1, 2, 2, 3, 4, 4, 5, 5, 5]) // [1, 2, 3, 4, 5]
 // Example: compress([1, 2, 2, 3, 4, 4, 2, 5, 5, 5, 4, 4]) // [1, 2, 3, 4, 2, 5, 4]
-var compress = function(list, i = 0, arr = []) {
-    if(i >= list.length){
+var compress = function (list, arr = []) {
+    if (list.length === 0) {
         return arr;
     }
-    if(list[i] - 1 === list[i] || list[i] + 1 === list[i]){
-        list.slice(list[i]);
-    }
-    if(arr.indexOf(list[i]) === -1){
-        arr.push(list[i]);
+
+    if (list[0] !== list[1]) {
+        arr.push(list[0]);
+        return compress(list.slice(1), arr);
     }
-    i++;
-    return compress(list, i, arr);
+
+    return compress(list.slice(1), arr);
 };
 
 // 32. Augment every element in a list with a new value where each element is an array
 // itself.
 // Example: augmentElements([[],[3],[7]], 5); // [[5],[3,5],[7,5]]
-var augmentElements = function(array, aug) {
+var augmentElements = function (array, aug) {
 };
 
 // 33. Reduce a series of zeroes to a single 0.
 // minimizeZeroes([2,0,0,0,1,4]) // [2,0,1,4]
 // minimizeZeroes([2,0,0,0,1,0,0,4]) // [2,0,1,0,4]
-var minimizeZeroes = function(array) {
+var minimizeZeroes = function (array, newArr = []) {
+    if (array.length === 0) { return newArr }
+
+    if (array[0] !== 0) {
+        newArr.push(array[0]);
+        return minimizeZeroes(array.slice(1), newArr);
+    }
+
+    if (array[0] !== array[1]) {
+        newArr.push(array[0]);
+        return minimizeZeroes(array.slice(1), newArr);
+    }
+    return minimizeZeroes(array.slice(1), newArr);
 };
 
+
 // 34. Alternate the numbers in an array between positive and negative regardless of
 // their original sign.  The first number in the index always needs to be positive.
 // alternateSign([2,7,8,3,1,4]) // [2,-7,8,-3,1,-4]
 // alternateSign([-2,-7,8,3,-1,4]) // [2,-7,8,-3,1,-4]
-var alternateSign = function(array, i = 0) {
-    if (i >= array.length){
-    array[0] = Math.abs(array[0]);
+var alternateSign = function (array, i = 0) {
+    if (i >= array.length) {
+        array[0] = Math.abs(array[0]);
         return array;
-    }else if(i % 2 !== 0 && array[i] >= 0){
-        array[i] = array[i]*-1;
-    }else if (i % 2 !== 0 && array[i] < 0){
+    } else if (i % 2 !== 0 && array[i] >= 0) {
+        array[i] = array[i] * -1;
+    } else if (i % 2 !== 0 && array[i] < 0) {
         array[i] = array[i];
-    }else if (i % 2 === 0 && array[i] < 0){
+    } else if (i % 2 === 0 && array[i] < 0) {
         array[i] = array[i] * -1;
-    }else if (i % 2 === 0 && array[i] >= 0) {
+    } else if (i % 2 === 0 && array[i] >= 0) {
         array[i] = array[i];
     }
 
@@ -443,26 +455,26 @@ var alternateSign = function(array, i = 0) {
 // 35. Given a string, return a string with digits converted to their word equivalent.
 // Assume all numbers are single digits (less than 10).
 // numToText("I have 5 dogs and 6 ponies"); // "I have five dogs and six ponies"
-var numToText = function(str) {
+var numToText = function (str) {
 };
 
 // *** EXTRA CREDIT ***
 
 // 36. Return the number of times a tag occurs in the DOM.
-var tagCount = function(tag, node) {
+var tagCount = function (tag, node) {
 };
 
 // 37. Write a function for binary search.
 // Sample array:  [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
 // console.log(binarySearch(5)) will return '5'
 
-var binarySearch = function(array, target, min, max) {
+var binarySearch = function (array, target, min, max) {
 };
 
 // 38. Write a merge sort function.
 // Sample array:  [34,7,23,32,5,62]
 // Sample output: [5,7,23,32,34,62]
-var mergeSort = function(array) {
+var mergeSort = function (array) {
 };