Added Award Budget cut problem

Author: ignacio-chiazzo

LeetcodeProblems/Award_Budget_Cuts.js

@@ -0,0 +1,73 @@
+/*
+Award Budget Cuts
+The awards committee of your alma mater (i.e. your college/university) asked for your assistance with a budget allocation problem they’re facing. Originally, 
+the committee planned to give N research grants this year. However, due to spending cutbacks, 
+the budget was reduced to newBudget dollars and now they need to reallocate the grants. 
+The committee made a decision that they’d like to impact as few grant recipients as possible by applying a maximum cap on all grants. 
+Every grant initially planned to be higher than cap will now be exactly cap dollars. Grants less or equal to cap, obviously, won’t be impacted.
+
+Given an array grantsArray of the original grants and the reduced budget newBudget, write a function findGrantsCap that finds in the most efficient manner a cap such that the least number of recipients is impacted and that the new budget constraint is met (i.e. sum of the N reallocated grants equals to newBudget).
+
+Analyze the time and space complexities of your solution.
+
+Example:
+
+input:  grantsArray = [2, 100, 50, 120, 1000], newBudget = 190
+
+output: 47 # and given this cap the new grants array would be
+           # [2, 47, 47, 47, 47]. Notice that the sum of the
+           # new grants is indeed 190
+Constraints:
+
+[time limit] 5000ms
+
+[input] array.double grantsArray
+
+0 ≤ grantsArray.length ≤ 20
+0 ≤ grantsArray[i]
+[input] double newBudget
+
+[output] double
+*/
+
+var cutAwardBadges = function(nums, newBadge) {
+  var currentBadge = 0;
+  for(var i = 0; i < nums.length; i++)
+    currentBadge += nums[i];
+
+  if(currentBadge < newBadge)
+    return;
+
+  const cap = findCap(nums, currentBadge, newBadge);
+
+  var iter = 0;
+  while(iter >= 0 && nums[iter] > cap) {
+    nums[iter] = cap;
+    iter++;
+  }
+
+  return nums;
+}
+
+var findCap = function(nums,  currentBadge, newBadge) {
+  nums.sort(function(a, b) { return b - a });
+  if(nums[nums.length - 1] * nums.length > newBadge)
+    return newBadge / nums.length;
+
+  var diff = currentBadge - newBadge;
+  var iter = 0;
+  while(iter < nums.length - 1 && diff > 0) {
+    const substraction = nums[iter] - nums[iter + 1]
+    diff -= (iter + 1)  * substraction;
+    iter++;
+  }
+
+  return nums[iter] + (-diff) / iter;
+}
+
+var main = function() {
+  console.log(cutAwardBadges([2, 100, 50, 120, 1000], 190));
+  console.log(cutAwardBadges([2, 100, 50, 120, 1000], 5));  
+}
+
+module.exports.main = main;