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I'm not clear if you want the solution of the case: 3 coworkers with the following allocation of chocolates:

( 1 3 1123834 )

OR

the case 5 coworkes with the allocation (1 3 1 123 834).

Assume it's the first case. If it's the second just follow below steps closely.

First we find min { 1, 3, 1123834 } = 1. We have two cases and we need to try both and check which has less steps.

Case 1: target = (1 1 1)

delta = (1 3 1123834) - (1 1 1) = (0 2 1123833)

We next find min number of -5, -2 and -1 steps to get from (1 3 1123834) to (1 1 1)

0 = 0 * 5 + 0 * 2 + 0 * 1

2 = 0 * 5 + 1 * 2 + 0 * 1

1123833 = 224766 * 5 + 1 * 2 + 1 * 1

Total # of steps: (# of steps to make 0 -> 1) + (# of steps to make 2 -> 1) + (# of steps to make 1123833 -> 1) = (0 + 0 + 0) + (0 + 1 + 0) + (224766 + 1 + 1) = 224769

Case 2: target = (0 0 0)

delta = (1 3 1123834) - (0 0 0) = (1 3 1123834)

We next find min number of -5, -2 and -1 steps to get from (1 3 1123834) to (0 0 0)

1 = 0 * 5 + 0 * 2 + 1 * 1

3 = 0 * 5 + 1 * 2 + 1 * 1

1123834 = 224766 * 5 + 2 * 2 + 0 * 1

Total # of steps: (# of steps to make 1 -> 0) + (# of steps to make 3 -> 0) + (# of steps to make 1123834 -> 0) = (0 + 0 + 1) + (0 + 1 + 1) + (224766 + 2 + 0) = 224771

We see that case 1 requires fewer steps so min number of steps is 224769.

## Equal

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I'm not clear if you want the solution of the case: 3 coworkers with the following allocation of chocolates:

( 1 3 1123834 )

OR

the case 5 coworkes with the allocation (1 3 1 123 834).

Assume it's the first case. If it's the second just follow below steps closely.

First we find min { 1, 3, 1123834 } = 1. We have two cases and we need to try both and check which has less steps.

Case 1: target = (1 1 1)

delta = (1 3 1123834) - (1 1 1) = (0 2 1123833)

We next find min number of -5, -2 and -1 steps to get from (1 3 1123834) to (1 1 1)

0 = 0 * 5 + 0 * 2 + 0 * 1

2 = 0 * 5 + 1 * 2 + 0 * 1

1123833 = 224766 * 5 + 1 * 2 + 1 * 1

Total # of steps: (# of steps to make 0 -> 1) + (# of steps to make 2 -> 1) + (# of steps to make 1123833 -> 1) = (0 + 0 + 0) + (0 + 1 + 0) + (224766 + 1 + 1) = 224769

Case 2: target = (0 0 0)

delta = (1 3 1123834) - (0 0 0) = (1 3 1123834)

We next find min number of -5, -2 and -1 steps to get from (1 3 1123834) to (0 0 0)

1 = 0 * 5 + 0 * 2 + 1 * 1

3 = 0 * 5 + 1 * 2 + 1 * 1

1123834 = 224766 * 5 + 2 * 2 + 0 * 1

Total # of steps: (# of steps to make 1 -> 0) + (# of steps to make 3 -> 0) + (# of steps to make 1123834 -> 0) = (0 + 0 + 1) + (0 + 1 + 1) + (224766 + 2 + 0) = 224771

We see that case 1 requires fewer steps so min number of steps is 224769.

Thanku very much....ur explanation is very helpful to solve this problem efficiently..:)

could you explain for 1 123 834 please

if u consider the case of 1 4 1123834. You need to consider (-1,-1,-1) as well to get the ans.

case 1:(1,4,1123834)->(1,1,1)=(0,3,1123833) steps (0,2,224768), Total = 224770

case 2:(1,4,1123834)->(0,0,0)=(1,4,1123834) steps (1,2,224768) Total = 224771

case 2:(1,4,1123834)->(-1,-1,-1)=(2,5,1123835) steps (1,1,224767) Total = 224769

ans = min(224770,224771,224769) = 224769.