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reasoning_image_9
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reasoning_image_11
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reasoning_image_12
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reasoning_image_13
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reasoning_image_14
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reasoning_image_15
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reasoning_image_16
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reasoning_image_17
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Shortest path from 3 to 1? [problem_image_1]
"Algorithm: Finding shortest path from 3 to 1 using Dijkstra's algorithm.\nDijkstra's algorithm find(...TRUNCATED)
Length=9; path=[3, 0, 1]
shortest_path_00000
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3iV5f0//jtA2HuPAA4EV1249x5YV1trtUOtWpV(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hcZb0/8N+mN9J7ltAJTSmhSu+9qYjYEBEpyhW(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hcZb0/8N+mN9J7ltAJTSmhSu+9qYjYEBEpyhW(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5icZb028P+27Kb3XqgSegKhI9K7IBZsR0VFRTh(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3idZd0/8F/apnvvEcqmLFlliiB7TxURNyICVRT(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hcdbk/8HdbdtN734QqobfQe6+CWLA3REX467X(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3zddbk/8CerSWdautu0ZUnZq2xky1D2qLgREBD(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hcdbk/8HdbdtN732xo0nvoHekEUBRUrhVQEa4(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hU9bk/8HcrvTcBAVEC9oa99xqNKd70qDFq9J9(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3iV5f038F+AQBBkg4yAW5x14Ky17j2qba3drbV(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3iV5f038F+AQBBkg4yAW5x14Ky17j2qba3drbV(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hcdbk/8HdbNr2QnmxCld4TEhARECkKIogIXgu(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hcdbk/8HdbNr2QnmxCld4TEhARECkKIogIXgu(...TRUNCATED)
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Is the undirected graph connected? [problem_image_1]
"Algorithm: Checking connectivity via breadth-first traversal starting at node 0. In a connected gra(...TRUNCATED)
Yes
connectivity_00001
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3iUZfYH7AOhgyAgKthRsKxd11WxKx17Ad39u7p(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdBZiVZfo/8BuGBkFAVFBsMNbGtWPVFSTsQN1d1w6(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3iUZfYH7AOhgyAgKthRsKxd11WxKx17Ad39u7p(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5SU5fUH4Lvs0hEpogJ2xdhRMRawG0VAjR1L/om(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3iUZfY/7hMSOiJFVFAsCNjFtjZQV11FwN5Qt+n(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5iU5fU34LPs0hEpooJiBTtiSyygRo0goMYOav6(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3iUZdo/7CuNLlVQUFBR7Ipt1wLqqisIqGtH3X1(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5iU5fU34LONLgIKCooFxa6omFiwG0VAEzu2f2J(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5iU5dU/4LONLk0BQUFFsQsqGgt2IwhoYseWYuw(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB3SVVfY34B2S0EWKqBS7OHZUrGB3FAF17FjmP2M(...TRUNCATED)
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Provide a valid topological order. [problem_image_1]
"Algorithm: Finding a topological ordering using Kahn's algorithm.\nA topological sort of a directed(...TRUNCATED)
0-1-2-3-4-6-5
topological_sort_00002
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACnOElEQVR4nOzdCZTVZf348Q87KIooioi7gLuoqLmbW2ou5JJbuee(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACmzUlEQVR4nOzdB5hU5b348d/SQQRRFBUbUtRYEMHYxRo1tlhiS1T(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACm20lEQVR4nOzdB5RV1dn44XfoIIoIioqKKGAXEewFjRp7N7bEHhU(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACma0lEQVR4nOzdB5RV1bnA8W/ogyigKCoqomCJBRGMXTRqjLHFElu(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACmKElEQVR4nOzdB5SdVb3/4e+kJ9RAIHQIUqUESJDeBFQEVIo0G0U(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACmQUlEQVR4nOzdB5SdVb3/4e+kJ9RAIHQIUqUESJDeBFQEVIo0G0U(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAClMElEQVR4nOzdB5SdVb3/4e+kJ9RAIHQIUqUESJDeBFQEVIo0G0U(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAClMElEQVR4nOzdB5SdVb3/4e+kJ9RAIHQIUqUESJDeBFQEVIo0G0U(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACHJElEQVR4nOzdBZjsVfkH8FcR6ZIuke5ukG5p9C8t3QiIgGACCoK(...TRUNCATED)
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Is the undirected graph connected? [problem_image_1]
"Algorithm: Checking connectivity via breadth-first traversal starting at node 0. In a connected gra(...TRUNCATED)
No
connectivity_00003
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADCmElEQVR4nOzdCZRW5Zng8QdkFReCoihxgcYNRRFcRkPHSVzamGh(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADDNUlEQVR4nOzdCbiWdZn48fsg2xFRQ1GKNGG0REUR0EajzHXUstx(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADFrUlEQVR4nOzdCZRW5Zng8QdkFReCoihxgcYNRRFcRkPHSVzamGh(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADFmUlEQVR4nOzdCbiWdZ3w8d9hR0QJRUnShNxQUQS116LMXFLLcmF(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADGtUlEQVR4nOzdCbjWdZn4//vAYRNBQhGSNHE0RUFRUH8Waa5ji+W(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADIX0lEQVR4nOzdCXTW5Znw/yshBCKCiGyKWGGwsosCWi1qXXCsLa1(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADKWUlEQVR4nOzdCXTW5Znw/yshBCKCiGyKWGGwsosCWi1qXXCsLa1(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADDYUlEQVR4nOzdCbiWdZn48fsg2xFRQ1GKNGG0REUR0EajzHXUstx(...TRUNCATED)
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Is the undirected graph connected? [problem_image_1]
"Algorithm: Checking connectivity via breadth-first traversal starting at node 0. In a connected gra(...TRUNCATED)
No
connectivity_00004
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACgtklEQVR4nOzdeZjWdbn48XvYQRRxwVxwA5IUREHcBSRTM1vMzHI(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACgVklEQVR4nOzdeZiV9Xn4/3vYQRRxwbjgBigqiIK4C0iMGmMWY40(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACiRklEQVR4nOzdeZjWdbn48XvYQRRxwVxwA5IUREHcBSRTM1vMzHI(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACiSklEQVR4nOzdeZTedXnw/2uybxASIMgSICRIWEIgIewkYYrgQlV(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACjfElEQVR4nOzdeZjddXn4/XuybxISIMgSliRACISEhLBDwqigSBV(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACkkklEQVR4nOzdeZSdZZno7bsq8yAhISRMYUqAGBICCTOEhIigYDs(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACfl0lEQVR4nOzde5jWdZn48Xs4nxRBxDzgCUxEEQXxLOBkauZWVuZ(...TRUNCATED)
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Provide a valid topological order. [problem_image_1]
"Algorithm: Finding a topological ordering using Kahn's algorithm.\nA topological sort of a directed(...TRUNCATED)
0-1-2-3
topological_sort_00005
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAC37UlEQVR4nOzdeZRddZno77fmqsxzmCEkTAFBBEVEBhEQWrEVVEB(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAC3vUlEQVR4nOzdeZRddZno77fmqsxzmCEkTAFBBEVEBhEQWrEVVEB(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAC2cUlEQVR4nOzdd5iddZ3w/8+0zEx6QkjoEEINSDFRZKmyiKDig2C(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAC2YElEQVR4nOzdd5iddZ3w/8+0zEx6QkjoEEINSDFRZKmyiKDig2C(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAC2YElEQVR4nOzdd5iddZ3w/8+0zEx6QkjoEEINSDFRZKmyiKDig2C(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAABuiklEQVR4nOzdB5hsVZU/7I0OQYJkSQMIiEQJAgYMiIOgRMVRclY(...TRUNCATED)
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Provide a valid topological order. [problem_image_1]
"Algorithm: Finding a topological ordering using Kahn's algorithm.\nA topological sort of a directed(...TRUNCATED)
1-2-3-5-6-7-4-0
topological_sort_00006
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdBZhc5fk34DcJEFyDhuAOwbVYcdriTqG4WwsUL0V(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdBZhc5fk34DcJEFyDhuAOwbVYcdriTqG4WwsUL0V(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdBZhc5fk34DcJEFyDhuAOwbVYcdriTqG4WwsUL0V(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hcZfUH4JOE0LuhhtB770WaCIrSQZrSUYo0/6B(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hcZfUH4JOEAKH3Egi9916UKghIFQVE6UhH8S+(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hcZfUH4JOEAKH3Egi9916UKghIFQVE6UhH8S+(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hU1fkH4A8QBBQFBAuIir0X1KiJvccaY4mJGnv(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hU1fkH4A+QagMEFRAVey+IURN7iYk9sUQTexd(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdB5hU1fkH4A+QagMEFRAVey+IURN7iYk9sUQTexd(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAACaOUlEQVR4nOzdB5RrVfUH4G1BEAFRbPQmqBSlIyK9WQDpValKBxU(...TRUNCATED)
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Total weight of a minimum spanning tree? [problem_image_1]
"Algorithm: Finding a Minimum Spanning Tree (MST) using Kruskal's algorithm.\nKruskal's algorithm bu(...TRUNCATED)
19
mst_00007
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADlQUlEQVR4nOzdB5xV9Zk//mcYhi4gEFDsDaMoomiisaAmdizJ2o0(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADoW0lEQVR4nOzdB5hV5bk+7ndm6E1BEBUVKyp2sWvsPdZEjRo1nlg(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADnQ0lEQVR4nOzdB3zV9fU//pOEsAUZQVx1AnUPtFVQHK2Ke1tHnXU(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADprUlEQVR4nOzdB5icddU/7jNbs+ltE3onSC8BRDooVYr6iiJIUWk(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADpU0lEQVR4nOzdB5icddU/7jNbs+ltE3onSC8BRDooVYr6iiJIUWk(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADoUUlEQVR4nOzdB5icddU/7jPbN71tQu8E6SWAKB2lStNXFEEQlZa(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADpFUlEQVR4nOzdB5icddU/7jPbN71tQu8E6SWAKB2lStNXFEEQlZa(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADk3ElEQVR4nOzdB5hcddUH4DPbN9n0bBJ6B+mBBKUjqBQFwUKXXlN(...TRUNCATED)
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Is the undirected graph connected? [problem_image_1]
"Algorithm: Checking connectivity via breadth-first traversal starting at node 0. In a connected gra(...TRUNCATED)
Yes
connectivity_00008
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAD8JElEQVR4nOzdB5hU5fk/7pfeVVQsWEApimID7BXsIZoYEo1dojH(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAD7o0lEQVR4nOzdB5TU5dUH4EtvoqJiFAsoRVFsYI0lllgSotGQTxN(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAD+RUlEQVR4nOzdCVhU9ffH8cMuKCoqargrYiSmiblUmksuZfrLLCu(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAD/sElEQVR4nOzdCXhM9/fH8ZNdEkEQKnYiqFijltop1Wq1qj9t0ZZ(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAD/TUlEQVR4nOzdCXhM9/fH8ZNdEkEQS+xEULFG0Vpa1NJqtao/bdG(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdCZyNdfvH8e/sBmPfsu9LRmGUilRKm/JUelRIixb(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdC3zO9fvH8Wtn2wzDRs6HGTLHKcohlEMpHfRTIRF(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdC3zO9fvH8Wtn2wzDRs6HGTLHKcohlEMpHfRTIRF(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAEAAElEQVR4nOzdCZzN9ffH8TP7wmAwQ/Z1kLGOoiyJSImSfiokRSU(...TRUNCATED)
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAAD4sklEQVR4nOzdB5SU5fUH4EsvioqKBRtKUSI2wBaNsURjJBqNiUa(...TRUNCATED)
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Provide a valid topological order. [problem_image_1]
"Algorithm: Finding a topological ordering using Kahn's algorithm.\nA topological sort of a directed(...TRUNCATED)
1-2-0-3-4
topological_sort_00009
"iVBORw0KGgoAAAANSUhEUgAABa8AAAWmCAYAAACP8lxYAADM30lEQVR4nOzdB3RVdfY/7E0vUgVsoCJiAxUVFcWu6Ni7IPaGvY2(...TRUNCATED)
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