{"id":"sort-pair-greedy-optimal-1d-assignment","text":"Sorting both arrays and pairing by index yields the minimum total absolute displacement for 1D assignment problems, by the rearrangement inequality.","truth_value":"IN","source":"entries/2026/06/06/minimum-number-of-moves-to-seat-everyone-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"sort-pair-greedy-optimal-1d-assignment","truth_value":"IN","reason":"premise"}]}}