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    <p>This problem reduces to finding a <a href="http://en.wikipedia.org/wiki/Maximum_flow_problem" rel="nofollow noreferrer">maximum flow</a> in a flow network.</p> <p>Here's the idea:</p> <ol> <li><p>For each type of resource (A, B, ...) a node with an incoming edge from the <strong>source</strong> node (the source node has nothing to do with the sources from the problem, it's a common label used in network flow theory, usually marked <strong>s</strong>) with capacity equal to the required quantity of the given resource. For example if you need <em>2B</em>, the capacity would be 2.</p></li> <li><p>For each <em>source</em> (by this I mean a source as defined by the problem description), you create a node with an outgoing edge to the sink (usually marked <strong>t</strong>) with capacity 1.</p></li> <li><p>From each node from step 1. add an outgoing edge to each of the nodes from step 2. that provide that can provide the required type of resource.</p></li> </ol> <p>For example, the graph for your situation would look like this:</p> <p><img src="https://i.stack.imgur.com/ltpln.png" alt="flow graph"></p> <p>Now a maximal S-T flow in this network will give you the answer. Basically saturated edges between the <em>type</em> nodes (A, B, C) and the <em>source</em> nodes (src1, src2, src3) will tell you which <em>source</em> should supply which <em>type</em> of resource.</p> <p>The maximum flow can be found using any of the classical algorithms, such as <strong>augmenting path</strong> (<em>Ford-Fulkerson</em>, <em>Dinic's</em>, etc.) or one of the <strong>push-relabel</strong> methods (<em>Goldberg-Tarjan</em>, <em>Relabel-to-Front</em>, etc.).</p> <p>This particular application of maximum flow can also be viewed as a sort of generalized <a href="http://en.wikipedia.org/wiki/Matching_(graph_theory)#Maximum_matchings_in_bipartite_graphs" rel="nofollow noreferrer">bipartite matching</a>, where you're matching each type of resource to possibly multiple sources, but each source can handle only one resource. The idea is easily extended to the case where a source may handle more than one type (by simply changing the <strong>src - T</strong> edge capacities from 1 to the ones desired).</p>
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    1. POAlgorithm for searching the disjoint union on dependency graph
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    1. USgus
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    1. COThanks, will check this more in depth
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