# What’s the minimum number of weights required to count between 1 to 121 pounds ?

Find the minimum number of weights required to count anything between 1 to 121 pounds ?

This type of problems have a standard formula to compute the minimum number of weights and it’s given by Ceiling of the log to the base 2 of the maximum weight to be counted.

Thus, the formula would be where W is the max weight which is 121 pounds in this case which would give a value of **7. **

Hence the minimum number of weights required for this would be 7 and those weights would be powers of 2 from 0 until N where N will be the value such that 2^N doesn’t exceed 121, which gives the weights as [1, 2, 4, 8, 16, 32, 64]

Below is an algorithm to count all possible weights from 1 to 121 pounds using binary search.

init(); function init() { var output = []; var weights = [1, 2, 4, 8, 16, 32, 64]; var maxWeightToCount = 121; for (var i = 1; i <= maxWeightToCount; i++) { searchWeights(weights, i, output); console.log('Sequence of minimum number of weights with sum equal = ', i, 'pounds from the given list of available weights ', weights, '=', output); output = []; } } function searchWeights(arr, value, result) { var val = binSearch(arr, value); if (value - val === 0) { result.push(val); return; } if (val === -1) { val = getNearestValue(arr, value); result.push(val); } searchWeights(arr, value - val, result); } function binSearch(arr, W, bounds=[]) { var l = 0, r = arr.length - 1; while (l <= r) { var m = Math.floor(l + (r - l) / 2); // Check if W is present at mid if (arr[m] == W) return arr[m]; // If W is greater, ignore left half if (arr[m] < W) l = m + 1; // If W is smaller, ignore right half else r = m - 1; } bounds[0] = l, bounds[1] = r; return -1; } function getNearestValue(a, value) { var bounds = []; if(value < a[0]) { return a[0]; } if(value > a[a.length-1]) { return a[a.length-1]; } var retVal = binSearch(a, value, bounds); var lo = bounds[0], hi = bounds[1]; if (retVal === -1) { retVal = (a[lo] - value) < (value - a[hi] && a[lo] < value) ? a[lo] : a[hi]; } return retVal; }

**Explanation:-**

**Use binary search to find if the weight to be counted is there in the available list of weights. If a match is found, push it to the output array and return.****If the previous step fails, find the closest possible value from the given set of weights which is lower than the weight to be counted and push that to an array.****Compute the difference between, intended weight to be counted and the closest possible lower value obtained in step 2 and repeat steps 1 & 2.****Repeat step 3 until the difference obtained in step 3 is zero.**

Here is the demo of the above algorithm:- http://code.golibrary.co/EjXBOJn1O72e