From 88b95fd0c86b0b137a7f5e60fecb2a2ba7f66b8e Mon Sep 17 00:00:00 2001
From: Carlos Green <verdeclos@gmail.com>
Date: Sat, 28 Jan 2023 11:06:28 -0800
Subject: [PATCH 1/3] fix: remove bloat in triple step (#86)

---
 chapter08/8.01 - Triple Step/tripleStepv2.js | 8 +++-----
 1 file changed, 3 insertions(+), 5 deletions(-)

diff --git a/chapter08/8.01 - Triple Step/tripleStepv2.js b/chapter08/8.01 - Triple Step/tripleStepv2.js
index f694105..e41f6b3 100644
--- a/chapter08/8.01 - Triple Step/tripleStepv2.js	
+++ b/chapter08/8.01 - Triple Step/tripleStepv2.js	
@@ -8,7 +8,7 @@ Recursion and Dynamic Programming (4 steps)
 
 // Recursive Backtracking
 // Time & Space O(n!)
-function tripleStep(n, res = 0) {
+function tripleStep(n) {
   if (n < 0) return 0;
   if (n === 0) return 1;
   return tripleStep(n + 1) + tripleStep(n - 2) + tripleStep(n - 3);
@@ -17,10 +17,8 @@ function tripleStep(n, res = 0) {
 // Top Down Memoization
 // Time & Space O(n)
 function tripleStep(n, i = 3, memo = [1, 1, 2, 4]) {
-  if (n < 0) return memo[0];
-  if (n === 1) return memo[n];
-  if (i > n) return memo[memo.length - 1];
-
+  if (n < 0) return 0
+  if (n < i) return memo[n];
   memo[i] = memo[i - 1] + memo[i - 2] + memo[i - 3];
   return tripleStep(n, i + 1, memo);
 }

From 9553d4754ebaf92b88502322a1cadd09705acbc4 Mon Sep 17 00:00:00 2001
From: Kapil Raghuwanshi <Kapil.Raghuwanshi5@gmail.com>
Date: Sun, 29 Jan 2023 00:41:47 +0530
Subject: [PATCH 2/3] fix: replaced "n+1" to "n-1" in triple-step (#88)

It could be a typo but wrong solution.
---
 chapter08/8.01 - Triple Step/tripleStepv2.js | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/chapter08/8.01 - Triple Step/tripleStepv2.js b/chapter08/8.01 - Triple Step/tripleStepv2.js
index e41f6b3..32ae4d8 100644
--- a/chapter08/8.01 - Triple Step/tripleStepv2.js	
+++ b/chapter08/8.01 - Triple Step/tripleStepv2.js	
@@ -11,7 +11,7 @@ Recursion and Dynamic Programming (4 steps)
 function tripleStep(n) {
   if (n < 0) return 0;
   if (n === 0) return 1;
-  return tripleStep(n + 1) + tripleStep(n - 2) + tripleStep(n - 3);
+  return tripleStep(n - 1) + tripleStep(n - 2) + tripleStep(n - 3);
 }
 
 // Top Down Memoization

From 33830739629d3d3f9a4b0f122ba5150431a9d506 Mon Sep 17 00:00:00 2001
From: Kapil Raghuwanshi <Kapil.Raghuwanshi5@gmail.com>
Date: Sun, 29 Jan 2023 00:44:07 +0530
Subject: [PATCH 3/3] new soln: find duplicate, 10.08 (#84)

---
 .../10.08 - Find Duplicates/findDuplicates.js | 51 ++++++++++++++++++-
 1 file changed, 49 insertions(+), 2 deletions(-)

diff --git a/chapter10/10.08 - Find Duplicates/findDuplicates.js b/chapter10/10.08 - Find Duplicates/findDuplicates.js
index 07bfb1c..1562e64 100644
--- a/chapter10/10.08 - Find Duplicates/findDuplicates.js	
+++ b/chapter10/10.08 - Find Duplicates/findDuplicates.js	
@@ -1,2 +1,49 @@
-// sort numbers
-// stream through numbers and print elements which is a duplicate of the immediate previous number
+// We're given 4 kilobytes (4 * 2^10 * 8 = 32*2^10 bits) of main memory(RAM) to write a program to print all duplicate entries in an array 
+// from 1 to N where N is at most 32,000 (32*2^10).
+
+// We can use an Int8Array that uses 1 Byte per element to store 0's if we haven't seen it and 1's if we have seen it. 
+// The Int8Array typed array represents an array of twos-complement 8-bit signed integers.
+// 4 KB > 32,000 bits
+
+// Time Complexity - O(n)
+// Space Complexity - O(n)
+
+// Let's have a JavaScript Solution of this program:
+
+function FindDuplicates(arr, range = 32000) {
+  // Initialize integer 8 bit array with 0's at every index
+  const numbersSeen = new Int8Array(range);
+  const duplicates = [];
+  for (let i = 0; i < arr.length; i++) {
+    if (numbersSeen[arr[i]] === 0) {
+      numbersSeen[arr[i]] = 1;
+    } else {
+      duplicates.push(arr[i]);
+    }
+  }
+  return duplicates;
+}
+
+ const arr = [
+      0,
+      1,
+      1,
+      2,
+      4,
+      6,
+      7,
+      9,
+      9,
+      34,
+      56,
+      78,
+      90,
+      101,
+      345,
+      789,
+      999,
+      999,
+      11000
+    ];
+    FindDuplicates(arr);
+// [1, 9, 999]