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# Check if item can be measured using a scale and some weights in Python

Suppose we have some weights like a^0, a^1, a^2, …, a^100, here 'a' is an integer, and we also have a weighing scale where weights can be put on both the sides of that scale. We have to check whether a particular item of weight W can be measured using these weights or not.

So, if the input is like a = 4, W = 17, then the output will be True the weights are a^0 = 1, a^1 = 4, a^2 = 16, we can get 16 + 1 = 17.

To solve this, we will follow these steps −

- found := False
- Define a function util() . This will take idx, itemWt, weights, N
- if found is true, then
- return

- if itemWt is same as 0, then
- found := True
- return

- if idx > N, then
- return

- util(idx + 1, itemWt, weights, N)
- util(idx + 1, itemWt + weights[idx], weights, N)
- util(idx + 1, itemWt - weights[idx], weights, N)
- From the main method do the following −
- if a is either 2 or 3, then
- return True

- weights := a list of size 100 and fill with 0
- total_weights := 0
- weights[0] := 1, i := 1
- Do the following infinitely, do
- weights[i] := weights[i - 1] * a
- total_weights := total_weights + 1
- if weights[i] > 10^7
- come out from loop

- i := i + 1

- util(0, W, weights, total_weights)
- if found true, then
- return True

- return False

## Example

Let us see the following implementation to get better understanding −

found = False def util(idx, itemWt, weights, N): global found if found: return if itemWt == 0: found = True return if idx > N: return util(idx + 1, itemWt, weights, N) util(idx + 1, itemWt + weights[idx], weights, N) util(idx + 1, itemWt - weights[idx], weights, N) def solve(a, W): global found if a == 2 or a == 3: return True weights = [0] * 100 total_weights = 0 weights[0] = 1 i = 1 while True: weights[i] = weights[i - 1] * a total_weights += 1 if weights[i] > 10**7: break i += 1 util(0, W, weights, total_weights) if found: return True return False a = 4 W = 17 print(solve(a, W))

## Input

4, 17

## Output

True

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