Need help: weights problem

You are given N weights, the first weighs 1 pound, the second 2 pounds, and so on (the N weight weighs N pounds)ץ

You are given an N-binary-word that's formed by L's and R's and scales.

You need to provide an algorithm of N steps, which in each step puts a weight on on of the scales (the left or the right one), and that in the i-th step the scales will lean left if the i-th letter in the word is L and will lean right if it's R.

for example: if N=3 and the word is LLR then the algorithm should say:

1. put 2 on the left scale

2. put 1 on the right scale (the scales will still lean to the left)

3. put 3 on the right scale

Re: Need help: weights problem

I have no algorithm more sophisticated than trying the combinations and seeing what happens.

Here are the results for 7 weights that minimize the amount of imbalance in the scale.

Note that negative numbers represent a weight placed in the left pan; positives go on the right.

To get the combinations where the scale tips right first, reverse the signs.

LLLLLLL -7 6 -5 4 1 -3 2

LLLLLLR -6 5 -3 2 1 -4 7

LLLLLRL -5 4 -3 2 1 6 -7

LLLLLRR -6 5 -3 2 -4 7 1

LLLLRLL -5 4 -3 2 7 -6 -1

LLLLRLR -4 3 -2 1 6 -7 5

LLLLRRL -5 4 -1 -2 6 3 -7

LLLLRRR -6 5 -3 2 7 -4 1

LLLRLLL -5 4 -2 6 -7 3 -1

LLLRLLR -4 3 -2 7 -6 -1 5

LLLRLRL -3 2 -1 6 -7 5 -4

LLLRLRR -4 3 -2 6 -7 5 1

LLLRRLL -5 4 -3 6 2 -7 1

LLLRRLR -4 3 -2 5 1 -7 6

LLLRRRL -5 4 -2 6 -1 3 -7

LLLRRRR -6 5 -4 7 2 -3 1

LLRLLLL -5 4 6 -7 1 -3 2

LLRLLLR -4 3 5 -7 1 -2 6

LLRLLRL -2 1 4 -7 3 5 -6

LLRLLRR -4 3 5 -7 1 6 -2

LLRLRLL -3 2 5 -7 6 -4 -1

LLRLRLR -2 1 5 -7 6 -4 3

LLRLRRL -2 1 5 -7 4 3 -6

LLRLRRR -4 3 5 -7 6 -2 1

LLRRLLR -5 4 6 -2 -7 3 -1

LLRRLLR -1 -3 5 4 -7 -2 6

LLRRLRL -1 -2 4 3 -7 6 -5

LLRRLRR -4 2 6 -3 -5 7 -1

LLRRRLL -5 3 7 -4 2 -6 1

LLRRRLR -4 3 5 -2 1 -7 6

LLRRRRL -5 3 6 -2 -1 4 -7

LLRRRRR -6 5 7 -4 2 -3 1

LRLLLLL -5 7 -6 2 1 -4 3

LRLLLLR -4 7 -5 -1 2 -3 6

LRLLLRL -1 4 -7 3 -2 6 -5

LRLLLRR -4 7 -6 2 -3 5 1

LRLLRLL -4 6 -3 -2 7 -5 -1

LRLLRLR -1 4 -7 3 2 -5 6

LRLLRRL -4 7 -5 1 2 3 -6

LRLLRRR -4 7 -6 2 5 -3 1

LRLRLLL -2 6 -7 4 -5 3 -1

LRLRLLR -1 4 -7 6 -5 2 3

LRLRLRL -1 5 -7 6 -4 2 -3

LRLRLRR -2 6 -7 5 -4 3 1

LRLRRLL -2 6 -7 4 3 -5 -1

LRLRRLR -1 4 -5 3 2 -7 6

LRLRRRL -3 7 -6 4 -1 2 -5

LRLRRRR -4 7 -5 6 -3 2 -1

LRRLLLL -5 6 4 -7 1 -3 2

LRRLLLR -4 6 1 -7 3 -2 5

LRRLLRL -4 7 -2 -3 1 5 -6

LRRLLRR -4 6 1 -7 3 5 -2

LRRLRLL -4 5 2 -7 6 -3 -1

LRRLRLR -1 2 3 -7 6 -5 4

LRRLRRL -4 5 2 -7 6 -1 -3

LRRLRRR -4 5 3 -7 6 -2 1

LRRRLLL -5 6 3 -2 -7 4 -1

LRRRLLR -4 7 -2 3 -6 -1 5

LRRRLRL -2 4 -1 3 -7 6 -5

LRRRLRR -4 7 -2 3 -6 5 -1

LRRRRLL -5 7 2 -3 4 -6 -1

LRRRRLR -4 6 1 -2 3 -7 5

LRRRRRL -5 6 1 2 -3 4 -7

LRRRRRR -6 7 5 -4 2 -3 1