From dd3ff4886cd3c631cdb46df0ddcf4f7e7ecdad99 Mon Sep 17 00:00:00 2001
From: hunter nguyen <hunterh.nguyen@gmail.com>
Date: Thu, 20 Sep 2018 15:52:12 -0500
Subject: [PATCH 01/10] working on recursion

---
 src/recursion.js | 32 +++++++++++++++++++++++++++++++-
 1 file changed, 31 insertions(+), 1 deletion(-)

diff --git a/src/recursion.js b/src/recursion.js
index 12ca0a3d7..173d07a43 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -4,27 +4,57 @@
 // 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) {
+    
+    if(i<0){
+        return null;
+    }else if(i === 0){
+        return total;
+    }
+    total = total * i;
+    i--;
+    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) {
+    if(array.length === 0){
+        return 0;
+    }
+    if(array.length === 1){
+        return array[0];
+    }
+    for(let i = 0;i<array.length;i++){
+        let x = array[i];
+        i++;
+        x + array[i];
+        return x;
+    }
+
 };
 
 // 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) {
+    if(n/2 === n*2){
+        return true;
+    }else{
+        return false;
+    }
 };
 
 // 5. Sum all integers below a given integer.
 // sumBelow(10); // 45
 // sumBelow(7); // 21
 var sumBelow = function(n) {
+    return n;
 };
 
 // 6. Get the integers in range (x, y).

From 9bd56375ff0c2109734c33b07b4822a30a531bdf Mon Sep 17 00:00:00 2001
From: hunter nguyen <hunterh.nguyen@gmail.com>
Date: Thu, 20 Sep 2018 22:02:46 -0600
Subject: [PATCH 02/10] recursion work

---
 src/recursion.js | 65 +++++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 62 insertions(+), 3 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 173d07a43..f934d6a47 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -43,11 +43,14 @@ var arraySum = function(array) {
 
 // 4. Check if a number is even.
 var isEven = function(n) {
-    if(n/2 === n*2){
-        return true;
-    }else{
+    if(n & 1){
         return false;
+    }else{
+        return true;
     }
+    //do something
+
+    
 };
 
 // 5. Sum all integers below a given integer.
@@ -60,6 +63,10 @@ var sumBelow = function(n) {
 // 6. Get the integers in range (x, y).
 // Example:  range(2, 9);  // [3, 4, 5, 6, 7, 8]
 var range = function(x, y) {
+    let arr = [];
+    
+
+    return arr;
 };
 
 // 7. Compute the exponent of a number.
@@ -68,6 +75,15 @@ 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) {
+    let num;
+    if(exp === 0){
+        return 1;
+    }
+    if(exp === 1){
+        return base;
+    }
+    num = base * base; //exponent times
+    return num;
 };
 
 // 8. Determine if a number is a power of two.
@@ -75,14 +91,24 @@ var exponent = function(base, exp) {
 // powerOfTwo(16); // true
 // powerOfTwo(10); // false
 var powerOfTwo = function(n) {
+    // if(n*n === answer){
+    //     return true
+    // }
 };
 
 // 9. Write a function that accepts a string a reverses it.
 var reverse = function(string) {
+    let str = ""
+    for(let i = string.length-1; i>=0;i--){
+        str = str + string[i];
+    }
+
+    return str;
 };
 
 // 10. Write a function that determines if a string is a palindrome.
 var palindrome = function(string) {
+    //use reverse
 };
 
 // 11. Write a function that returns the remainder of x divided by y without using the
@@ -96,6 +122,9 @@ 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) {
+    let num;
+    num = x + y; //x +x by y times
+    return num;
 };
 
 // 13. Write a function that divides two numbers without using the / operator  or
@@ -117,15 +146,26 @@ var gcd = function(x, y) {
 // compareStr('', '') // true
 // compareStr('tomato', 'tomato') // true
 var compareStr = function(str1, str2) {
+    // if(str1.charAt() === str2.charAt){
+    //     return true;
+    // }
 };
 
 // 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){
+    let arr =[];
+    arr.push(str.split(""));
+    return arr;
 };
 
 // 17. Reverse the order of an array
 var reverseArr = function (array) {
+    let arr = [];
+    for(let i = array.length-1;i>=0;i--){
+        arr.push(array[i]);
+    }
+    return arr;
 };
 
 // 18. Create a new array with a given value and length.
@@ -138,6 +178,18 @@ var buildList = function(value, length) {
 // countOccurrence([2,7,4,4,1,4], 4) // 3
 // countOccurrence([2,'banana',4,4,1,'banana'], 'banana') // 2
 var countOccurrence = function(array, value) {
+    let num;
+    let arr = [];
+    for(let i = 0; i<array.length;i++){
+        array[i];
+        if(array[i]===value){
+            arr.push(value);
+        }
+    
+    }
+
+
+    return arr.length;
 };
 
 // 20. Write a recursive version of map.
@@ -184,6 +236,13 @@ var nthFibo = function(n) {
 // var words = ['i', 'am', 'learning', 'recursion'];
 // capitalizedWords(words); // ['I', 'AM', 'LEARNING', 'RECURSION']
 var capitalizeWords = function(input) {
+   
+    // for(let i = 0; i<input.length;i++){
+    //    input[i].toUpperCase();
+
+    // }
+    
+    return input;
 };
 
 // 27. Given an array of strings, capitalize the first letter of each index.

From ec26f4d708a25941c729b67168e79bfa1c35dd37 Mon Sep 17 00:00:00 2001
From: hunter nguyen <hunterh.nguyen@gmail.com>
Date: Fri, 21 Sep 2018 15:55:48 -0500
Subject: [PATCH 03/10] recursion work

---
 src/recursion.js | 110 ++++++++++++++++++++++++++++++++++++++---------
 1 file changed, 89 insertions(+), 21 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 173d07a43..0a37ecbbd 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -19,19 +19,13 @@ 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) {
-    if(array.length === 0){
-        return 0;
-    }
-    if(array.length === 1){
-        return array[0];
-    }
-    for(let i = 0;i<array.length;i++){
-        let x = array[i];
-        i++;
-        x + array[i];
-        return x;
+var sum = function(array, total = 0, i = 0) {
+    if(i >= array.length){
+        return total;
     }
+    total += array[i];
+    i++;
+    return sum(array, total, i);
 
 };
 
@@ -43,23 +37,73 @@ var arraySum = function(array) {
 
 // 4. Check if a number is even.
 var isEven = function(n) {
-    if(n/2 === n*2){
-        return true;
-    }else{
-        return false;
-    }
+    // if(n & 1){
+    //     return false;
+    // }
+if (n === 0) {
+    return true;
+}
+else if (n === 1) {
+    return false;
+}
+if(n<0){
+    n = n+2;
+}
+else if(n>0){
+    n = n-2;
+}
+      return isEven(n);       
+
+    
 };
 
 // 5. Sum all integers below a given integer.
 // sumBelow(10); // 45
 // sumBelow(7); // 21
-var sumBelow = function(n) {
-    return n;
+var sumBelow = function(n, total = 0, i = n) {
+    if(i === 0){
+        return total;
+    }
+    if(n  > 0 ){
+        i--;
+        total = total + i;
+        
+    }
+    else if( n < 0){
+        i++;
+        total  = total +i;
+    }
+    
+    return sumBelow(n, total, i);
 };
 
 // 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 = [], i =x) {
+    
+    
+   
+    if(x === y || x === y+1 ){
+        return arr;
+    }
+    if(x > y){
+        i--;
+    }
+    else if(x < y){
+        i++;
+    }
+    if (i === y) {
+        return arr;
+    }
+
+    arr.push(i);
+
+    
+
+    return range(x,y, arr, i);
+
+
+    
 };
 
 // 7. Compute the exponent of a number.
@@ -67,7 +111,28 @@ var range = function(x, y) {
 // 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, i= exp, total=1) {
+    if(exp === 0){
+        return 1;
+    }
+    if(exp === 1){
+        return base;
+    }
+    if(i === 0){
+        return total;
+    }
+    if(exp<0){
+        total = total/base;
+        i++
+
+    }else if(exp>0){
+        total *=base
+        i--
+    }
+
+    
+    return exponent(base, exp, i,total);
+
 };
 
 // 8. Determine if a number is a power of two.
@@ -75,6 +140,9 @@ var exponent = function(base, exp) {
 // powerOfTwo(16); // true
 // powerOfTwo(10); // false
 var powerOfTwo = function(n) {
+
+
+    //return powerOfTwo(n);
 };
 
 // 9. Write a function that accepts a string a reverses it.

From 6727addc047b20c2472305a24da579f543fe9649 Mon Sep 17 00:00:00 2001
From: hunter nguyen <hunterh.nguyen@gmail.com>
Date: Mon, 24 Sep 2018 15:59:16 -0500
Subject: [PATCH 04/10] recursion work

---
 src/recursion.js | 66 +++++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 63 insertions(+), 3 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 0a37ecbbd..610289952 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -139,18 +139,60 @@ var exponent = function(base, exp, i= exp, total=1) {
 // powerOfTwo(1); // true
 // powerOfTwo(16); // true
 // powerOfTwo(10); // false
-var powerOfTwo = function(n) {
+var powerOfTwo = function(n, total = n) {
+    if(n === 0){
+        return false;
+    }
+    if(n === 1){
+        return true;
+    }
+    if(n< 0){
+        return false;
+    }
+    if(n === 2){
+        return true;
+    }
+    
+    if(total === 2){
+        return true;
+    }else if(total < 2){
+        return false;
+    }
 
+    total  = total/2;
 
-    //return powerOfTwo(n);
+
+    return powerOfTwo(n, total);
 };
 
 // 9. Write a function that accepts a string a reverses it.
 var reverse = function(string) {
+    if(string === ''){
+        return '';
+    }else{
+       return reverse (string.substring(1)) +string.charAt(0);
+       
+    }
+    
+    
 };
 
 // 10. Write a function that determines if a string is a palindrome.
 var palindrome = function(string) {
+    string = string[0].toLowerCase();
+    console.log('hello');
+    string = string.split('');
+    console.log(string);
+    
+    if(string[0] == string[string.length-1]){
+    string = string.splice(0,1);
+    string = string.splice(string.length-1,1);
+    console.log(string);
+    return true;
+    }
+
+
+    return palindrome(string);
 };
 
 // 11. Write a function that returns the remainder of x divided by y without using the
@@ -163,7 +205,25 @@ 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, i=0, total) {
+    if(x === 0 || y===0){
+        return 0;
+    }
+    if(x<0 && y<0){
+        total = (x - x) ;
+        //increment or decrement
+    }
+    if(x<0 || y< 0){
+        total = x - x;
+        //increment or decrement
+    }
+    if(y === i){
+      return total;
+    }
+    total = x + x;
+    i++;
+
+    return multiply(x,y,i, total);
 };
 
 // 13. Write a function that divides two numbers without using the / operator  or

From 6c1767b16a85ca45320f5c06eadc68ecfb9c2825 Mon Sep 17 00:00:00 2001
From: hunter nguyen <hunterh.nguyen@gmail.com>
Date: Tue, 25 Sep 2018 15:53:06 -0500
Subject: [PATCH 05/10] recursion work

---
 src/recursion.js | 88 ++++++++++++++++++++++++++++--------------------
 1 file changed, 52 insertions(+), 36 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 7b3382ae1..23cb8a2fb 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -177,22 +177,16 @@ var reverse = function(string) {
 };
 
 // 10. Write a function that determines if a string is a palindrome.
-var palindrome = function(string) {
+var palindrome = function(string, value = false) {
     string = string[0].toLowerCase();
-    //console.log('hello');
-    string = string.split('');
-    //console.log(string);
     
-    if(string === undefined){
+    string = string.split('');
     
     return true;
-    }
-    
-    string = string.splice(0, 1);
-    string = string.splice(string.length - 1, 1);
 
+    //return palindrome(string);
 
-    return palindrome(string);
+    
 };
 
 // 11. Write a function that returns the remainder of x divided by y without using the
@@ -245,50 +239,75 @@ var gcd = function(x, y) {
 // compareStr('', '') // true
 // compareStr('tomato', 'tomato') // true
 var compareStr = function(str1, str2) {
-    // if(str1.charAt() === str2.charAt){
-    //     return true;
-    // }
+    
+
+
+    //return compareStr(str1, str2)
 };
 
 // 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){
-    let arr =[];
-    arr.push(str.split(""));
-    return arr;
+var createArray = function(str, arr = [], num = 0){
+
+    if(num === str.length){
+        return arr;
+    }
+
+    arr.push(str.charAt(num));
+    num++;
+
+    return createArray(str,arr, num);
 };
 
 // 17. Reverse the order of an array
-var reverseArr = function (array) {
-    let arr = [];
-    for(let i = array.length-1;i>=0;i--){
-        arr.push(array[i]);
+var reverseArr = function (array, arr = []) {
+    
+    if(array.length === 0){
+        return arr;
     }
-    return arr;
+    
+    if(array.length > 0 ){
+        arr.push(array[array.length-1]);
+    }
+
+    array.splice(array.length-1,1);
+
+    return reverseArr(array, arr);
 };
 
 // 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, arr = []) {
+
+    if(value === length){
+        return arr;
+    }
+
+    if(value !== length){
+        arr.push(value);
+    }
+
+    
+
+    return buildList(value, length, arr);
 };
 
 // 19. Count the occurence 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) {
-    let num;
-    let arr = [];
-    for(let i = 0; i<array.length;i++){
-        array[i];
-        if(array[i]===value){
-            arr.push(value);
-        }
+var countOccurrence = function(array, value, count = 0, i = 0) {
     
+    if(array.length === 0){
+        return count;
     }
 
+    if(array[i] === value){
+        count++;
+    }
+    array.splice(0,1);
 
-    return arr.length;
+    return countOccurrence(array, value, count)
 };
 
 // 20. Write a recursive version of map.
@@ -336,10 +355,7 @@ var nthFibo = function(n) {
 // capitalizedWords(words); // ['I', 'AM', 'LEARNING', 'RECURSION']
 var capitalizeWords = function(input) {
    
-    // for(let i = 0; i<input.length;i++){
-    //    input[i].toUpperCase();
-
-    // }
+    
     
     return input;
 };

From b57da53bffb9289977956b2030dc80b15f845612 Mon Sep 17 00:00:00 2001
From: hunter nguyen <hunterh.nguyen@gmail.com>
Date: Wed, 26 Sep 2018 15:56:26 -0500
Subject: [PATCH 06/10] almost done recursion

---
 src/recursion.js | 118 ++++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 102 insertions(+), 16 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 23cb8a2fb..e42cb1c82 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -238,11 +238,27 @@ var gcd = function(x, y) {
 // compareStr('house', 'houses') // false
 // compareStr('', '') // true
 // compareStr('tomato', 'tomato') // true
-var compareStr = function(str1, str2) {
+var compareStr = function(str1, str2,  i = 0) {
+
+    if(str1[i] !== str2[i]){
+        return false;
+    }
+
+    if (i === str1.length && i === str2.length) {
+        return true;
+    }
+    
+
+    if(str1[i] === str2[i]){
+        i++;
+    }
     
 
 
-    //return compareStr(str1, str2)
+    return compareStr(str1, str2, i);
+
+
+    
 };
 
 // 16. Write a function that accepts a string and creates an array where each letter
@@ -278,19 +294,24 @@ var reverseArr = function (array, arr = []) {
 // 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, arr = []) {
+var buildList = function (value, length, arr = [], i = 0) {
+
 
-    if(value === length){
+    if (value === undefined) {
+        return [undefined];
+    }
+    if (i === length) {
         return arr;
     }
 
-    if(value !== length){
+    if (arr[i] !== value) {
         arr.push(value);
+
     }
+    i++;
 
-    
 
-    return buildList(value, length, arr);
+    return buildList(value, length, arr, i);
 };
 
 // 19. Count the occurence of a value inside a list.
@@ -313,6 +334,7 @@ var countOccurrence = function(array, value, count = 0, i = 0) {
 // 20. Write a recursive version of map.
 // rMap([1,2,3], timesTwo); // [2,4,6]
 var rMap = function(array, callback) {
+
 };
 
 // 21. Write a function that counts the number of times a key occurs in an object.
@@ -347,22 +369,68 @@ var fibonacci = function(n) {
 // nthFibo(5); // 5
 // nthFibo(7); // 13
 // nthFibo(3); // 2
-var nthFibo = function(n) {
+var nthFibo = function(n, next = 0, arr = [0], i = 1) {
+    if(n<0){
+        return null;
+    }
+
+    if(arr[n]){
+        return arr[n];
+    }
+
+    
+
+    next = next+ i;
+    i=next;
+
+    arr.push(next);
+
+    return nthFibo(n, next, arr,i);
 };
 
 // 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;
+    }
     
+    // if(input.length > 0 ){
+    //     input[i].toUpperCase();
+    // }
+
+    // i++;
+
+    arr.push(input[i].toUpperCase());
+    i++;
+
+    return capitalizeWords(input, i, arr);
     
-    return input;
 };
 
 // 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(array, i = 0, arr = [],n = 1,x,y,z) {
+    if(i === array.length){
+        return arr;
+    }
+
+
+    // x = array[i].charAt(0).toUpperCase();
+    x = array[i].slice(0,1).toUpperCase();
+    y = array[i].slice(1);
+    //concat/join it together
+
+    z = x.concat(y);
+    arr.push(z);
+    i++;
+    n++;
+
+    //access element in array then charAt(0).touppercase
+    //increment up 
+
+    return capitalizeFirst(array, i, arr, n,x,y,z);
 };
 
 // 28. Return the sum of all even numbers in an object containing nested objects.
@@ -384,7 +452,18 @@ 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, object = {}, tally = 1) {
+    
+    // if(letter is not in object){
+    //     object.letter = tally;
+    //    
+    // }
+    //tally++ only if letter is seen again
+
+
+    return object;
+
+    //return letterTally(str, obj,object,tally);
 };
 
 // 31. Eliminate consecutive duplicates in a list.  If the list contains repeated
@@ -392,7 +471,8 @@ 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, arr = []) {
+    return arr;
 };
 
 // 32. Augment every element in a list with a new value where each element is an array
@@ -404,14 +484,20 @@ 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, arr = []) {
+    return arr;
 };
 
 // 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) {
+var alternateSign = function(array, arr = []) {
+    return arr;
+
+
+
+
 };
 
 // 35. Given a string, return a string with digits converted to their word equivalent.

From e93a745da34f9247598e1f33d3b52e87d3c43b09 Mon Sep 17 00:00:00 2001
From: hunter nguyen <hunterh.nguyen@gmail.com>
Date: Thu, 27 Sep 2018 15:55:49 -0500
Subject: [PATCH 07/10] 8 more to go in recursion

---
 src/recursion.js | 69 ++++++++++++++++++++++++++++++++++++++----------
 1 file changed, 55 insertions(+), 14 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index e42cb1c82..00b4d55b1 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -334,6 +334,12 @@ var countOccurrence = function(array, value, count = 0, i = 0) {
 // 20. Write a recursive version of map.
 // rMap([1,2,3], timesTwo); // [2,4,6]
 var rMap = function(array, callback) {
+    if (array.length === 1) {
+        return callback(array);
+    }
+    else {
+        return [callback(array[0])].concat(rMap(array.slice(1), callback))
+    }
 
 };
 
@@ -452,18 +458,26 @@ 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, object = {}, tally = 1) {
-    
-    // if(letter is not in object){
-    //     object.letter = tally;
-    //    
-    // }
-    //tally++ only if letter is seen again
+var letterTally = function(str, obj = {}, tally = 0, i = 0) {
 
+    let letters = str.split('');
+  
+    
+    let arrOfObjKeys = Object.keys(obj);
 
-    return object;
+    if (i === letters.length) {
+        
+        return obj;
+    }
+    
 
-    //return letterTally(str, obj,object,tally);
+    if (!obj[letters[i]]){
+        obj[letters[i]] = 1;
+    }else{
+        obj[letters[i]] += 1;
+    }
+    i++;
+    return letterTally(str, obj, tally, i);
 };
 
 // 31. Eliminate consecutive duplicates in a list.  If the list contains repeated
@@ -471,8 +485,17 @@ var letterTally = function(str, obj, object = {}, tally = 1) {
 // 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, arr = []) {
-    return arr;
+var compress = function(list, arr = [],i = 0) {
+
+    if(i === list.length){
+        return arr;
+    }
+    if(list[i]  ){
+        arr.push(list[i]);
+    }
+
+    i++;
+    return compress(list, arr, i)
 };
 
 // 32. Augment every element in a list with a new value where each element is an array
@@ -484,19 +507,37 @@ 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, arr = []) {
-    return arr;
+var minimizeZeroes = function(array, arr = [], i= 0, n =1) {
+
+    if(i === array.length){
+        return arr;
+    }
+    
+    if(array[i] !== array[n]){
+        arr.push(array[i]);
+    }
+    
+
+    
+    i++;
+    n++;
+
+    return minimizeZeroes(array, arr, i , n)
 };
 
 // 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, arr = []) {
+var alternateSign = function(array, arr = [], i = 0) {
     return arr;
 
 
+    // arr.push(array[i]);
+    // i++;
+
 
+    //return alternateSign(array, arr,i);
 
 };
 

From a557b5f117f0f7e23cd05afc83f959c071542afa Mon Sep 17 00:00:00 2001
From: hunter nguyen <hunterh.nguyen@gmail.com>
Date: Fri, 28 Sep 2018 15:55:04 -0500
Subject: [PATCH 08/10] 3 more tests

---
 src/recursion.js | 90 +++++++++++++++++++++++++++++++++---------------
 1 file changed, 62 insertions(+), 28 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 00b4d55b1..817f304be 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -177,14 +177,25 @@ var reverse = function(string) {
 };
 
 // 10. Write a function that determines if a string is a palindrome.
-var palindrome = function(string, value = false) {
-    string = string[0].toLowerCase();
+var palindrome = function(string) {
     
-    string = string.split('');
+    if (string.length === undefined) {
+        return false;
+    }
+
+    if (string[0].toLowerCase() === string[string.length - 1].toLowerCase()) {
+        return true;
+    }
+
     
-    return true;
+    
+    
+    
+    string = string.slice(0,1);
+    string = string.slice(string.length-1,1)
+
 
-    //return palindrome(string);
+    return palindrome(string);
 
     
 };
@@ -203,17 +214,25 @@ var multiply = function(x, y, i=0, total) {
     if(x === 0 || y===0){
         return 0;
     }
+    if (i === y) {
+        return total;
+    }
+    if(x === 1){
+        return y;
+    }
+    if(y ===1){
+        return x;
+    }
     if(x<0 && y<0){
         total = (x - x) ;
-        //increment or decrement
+        i--;
     }
     if(x<0 || y< 0){
-        total = x - x;
-        //increment or decrement
-    }
-    if(y === i){
-      return total;
+        total = x + x;
+        i++;
     }
+    
+
     total = x + x;
     i++;
 
@@ -375,23 +394,25 @@ var fibonacci = function(n) {
 // nthFibo(5); // 5
 // nthFibo(7); // 13
 // nthFibo(3); // 2
-var nthFibo = function(n, next = 0, arr = [0], i = 1) {
-    if(n<0){
+var nthFibo = function (n, fibSeq = [0, 1]) {
+    let nexnum = fibSeq[fibSeq.length - 1] + fibSeq[fibSeq.length - 2];
+    fibSeq.push(nexnum);
+
+
+    if (n < 0) {
         return null;
     }
-
-    if(arr[n]){
-        return arr[n];
+    if (!n) {
+        return 0;
     }
 
-    
-
-    next = next+ i;
-    i=next;
 
-    arr.push(next);
+    if (fibSeq.length - 2 === n) {
+        return fibSeq[n];
+    } else {
+        return nthFibo(n, fibSeq);
+    }
 
-    return nthFibo(n, next, arr,i);
 };
 
 // 26. Given an array of words, return a new array containing each word capitalized.
@@ -490,7 +511,7 @@ var compress = function(list, arr = [],i = 0) {
     if(i === list.length){
         return arr;
     }
-    if(list[i]  ){
+    if(list[i] !== arr[arr.length-1]){
         arr.push(list[i]);
     }
 
@@ -529,16 +550,29 @@ var minimizeZeroes = function(array, arr = [], i= 0, n =1) {
 // 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, arr = [], i = 0) {
-    return arr;
+var alternateSign = function (array, i = 0) {
+    i++;
+    var el = array[i];
 
+    if (i === array.length) {
+        return array;
+    }
 
-    // arr.push(array[i]);
-    // i++;
+    if (array[0] < 0) {
+        array[0] *= -1;
+    }
+
+
+    if (el > 0 && i % 2 === 1) {
+        array[i] = array[i] * -1;
+    }
+    if (el < 0 && i % 2 === 0) {
+        array[i] *= -1;
+    }
 
 
-    //return alternateSign(array, arr,i);
 
+    return alternateSign(array, i);
 };
 
 // 35. Given a string, return a string with digits converted to their word equivalent.

From e03d39dfea0645845f8535317f50dba72971c884 Mon Sep 17 00:00:00 2001
From: Half Day <halfday@Macbooks-MacBook-Pro-45.local>
Date: Sat, 6 Oct 2018 09:04:27 -0700
Subject: [PATCH 09/10] done with palindrome

---
 src/recursion.js | 20 +++++++++-----------
 1 file changed, 9 insertions(+), 11 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index 817f304be..c591984f0 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -179,22 +179,18 @@ var reverse = function(string) {
 // 10. Write a function that determines if a string is a palindrome.
 var palindrome = function(string) {
     
-    if (string.length === undefined) {
-        return false;
+    if (string.length <= 1) {
+        return true;
     }
 
-    if (string[0].toLowerCase() === string[string.length - 1].toLowerCase()) {
-        return true;
+    if (string[0].toLowerCase() !== string[string.length - 1].toLowerCase()) {
+        return false;
+        
     }
 
+    string = string.substr(1,string.length-2);
+    string = string.replace(' ' , '');
     
-    
-    
-    
-    string = string.slice(0,1);
-    string = string.slice(string.length-1,1)
-
-
     return palindrome(string);
 
     
@@ -223,6 +219,7 @@ var multiply = function(x, y, i=0, total) {
     if(y ===1){
         return x;
     }
+
     if(x<0 && y<0){
         total = (x - x) ;
         i--;
@@ -232,6 +229,7 @@ var multiply = function(x, y, i=0, total) {
         i++;
     }
     
+    
 
     total = x + x;
     i++;

From a3d7524fdb4135ce1ad74b580ce0b39793f2d67b Mon Sep 17 00:00:00 2001
From: Half Day <halfday@Macbooks-MacBook-Pro-42.local>
Date: Fri, 26 Oct 2018 15:36:45 -0500
Subject: [PATCH 10/10] DONE

---
 src/recursion.js | 25 ++++++++-----------------
 1 file changed, 8 insertions(+), 17 deletions(-)

diff --git a/src/recursion.js b/src/recursion.js
index c591984f0..bf851dbba 100644
--- a/src/recursion.js
+++ b/src/recursion.js
@@ -206,35 +206,26 @@ 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, i=0, total) {
+var multiply = function(x, y) {
     if(x === 0 || y===0){
         return 0;
     }
-    if (i === y) {
-        return total;
+    if (y === 1) {
+        return x;
     }
     if(x === 1){
         return y;
     }
-    if(y ===1){
+    if(y === 1){
         return x;
     }
-
-    if(x<0 && y<0){
-        total = (x - x) ;
-        i--;
-    }
-    if(x<0 || y< 0){
-        total = x + x;
-        i++;
+    if(y<0){
+        return -multiply(x, -y);
     }
-    
-    
 
-    total = x + x;
-    i++;
+    y--;
 
-    return multiply(x,y,i, total);
+    return x + multiply(x, y);
 };
 
 // 13. Write a function that divides two numbers without using the / operator  or