Richelle - dynamic programming assignment

lib/max_subarray.js

@@ -1,9 +1,29 @@
 
-// Time Complexity:
-// Space Complexity:
+// Time Complexity: O(n)
+// Space Complexity: O(1) constant
 
 function maxSubArray(nums) {
-  throw new Error("Function not implemented yet...")
+  let maxSoFar = Number.NEGATIVE_INFINITY;
+  // or should I init maxSoFar as nums[0] but that would assume the array is not empty
+  // would need to check if nums is empty & return here in that case
+  let maxEndingHere = 0;
+
+  nums.forEach(num => { //O(n)
+    maxEndingHere = maxEndingHere + num;
+
+    if(maxEndingHere > maxSoFar) {
+      maxSoFar = maxEndingHere;
+    }
+
+    if(maxEndingHere < 0) {
+      // reset maxEndingHere, so that it doesn't accumulate
+      // negative nums,  any single negative num would be greater
+      maxEndingHere = 0
+    }
+  })
+
+  if (maxSoFar == Number.NEGATIVE_INFINITY) return null;
+  return maxSoFar;
 }
 
 module.exports = {

lib/newman_conway.js

@@ -1,9 +1,27 @@
 
-// Time Complexity:
-// Space Complexity:
+// Time Complexity: O(n) where n = num
+// Space Complexity: O(n) - technically my in 2n because of the .slice
+
+// P(1) = 1
+// P(2) = 1
+// for all n > 2
+// P(n) = P(P(n - 1)) + P(n - P(n - 1))
 
 function newmanConway(num) {
-  throw new Error("Function not implemented yet...")
+  if (num < 1) throw new Error;
+
+  let solutions = [0, 1];
+
+  if (num > 1) {
+    solutions.push(1);
+
+    for (let i = 3; i <= num; i++) {
+      solutions.push(
+        solutions[solutions[i -1]] + solutions[i - solutions[i -1]])
+    }
+  }
+
+  return solutions.slice(1).join(" ");
 }
 
 module.exports = {