Problem Statement

An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices.

For example, in a sequence

A

{\displaystyle A}

: 3   is an equilibrium index, because: 6   is also an equilibrium index, because: (sum of zero elements is zero) 7   is not an equilibrium index, because it is not a valid index of sequence

A

{\displaystyle A}

.

Write a function that, given a sequence, returns its equilibrium indices (if any). Assume that the sequence may be very long.

Let's start with the solution:

proc listEquilibria {list} {
    set after 0
    foreach item $list {incr after $item}
    set result {}
    set idx 0
    set before 0
    foreach item $list {
	incr after [expr {-$item}]
	if {$after == $before} {
	    lappend result $idx
	}
	incr before $item
	incr idx
    }
    return $result
}


set testData {-7 1 5 2 -4 3 0}
puts Equilibria=[join [listEquilibria $testData] ", "]