# C++ Reference: class IntegerSumLE

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A really basic implementation of an upper-bounded sum of integer variables. The complexity is in O(num_variables) at each propagation.Note that we assume that there can be NO integer overflow. This must be checked at model validation time before this is even created.

TODO(user): If one has many such constraint, it will be more efficient to propagate all of them at once rather than doing it one at the time.

TODO(user): Explore tree structure to get a log(n) complexity.

TODO(user): When the variables are Boolean, use directly the pseudo-Boolean constraint implementation. But we do need support for enforcement literals there.

Method | |
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`IntegerSumLE` | Arguments: If refied_literal is kNoLiteralIndex then this is a normal constraint, otherwise we enforce the implication refied_literal => constraint is true. Note that we don't do the reverse implication here, it is usually done by another IntegerSumLE constraint on the negated variables. |

`Propagate` | Return type: We propagate: - If the sum of the individual lower-bound is > upper_bound, we fail. - For all i, upper-bound of i <= upper_bound - Sum {individual lower-bound excluding i). |

`PropagateAtLevelZero` | Return type: Same as Propagate() but only consider current root level bounds. This is mainly useful for the LP propagator since it can find relevant optimal really late in the search tree. |

`RegisterWith` | Return type: Arguments: |