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Add option to store all world states in information state tree #1074

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This PR adds a boolean flag to the constructor of the infostate tree to allow storing the corresponding world states and chance reach probability not just at the leaf nodes, but all infostate nodes (except filler nodes).

In particular, this change allows to attain an inverse mapping of info state to world states when traversing a player's infostate tree.

The changes are:

  • added boolean flag to InfostateTree class
  • change logic in building tree to account for the flag
  • adopt info state tree tests to account for the change
  • added is_filler_node() check to InfostateNode class to query node
  • extended child_at method of InfostateNode to choose to skip filler nodes via bool flag
  • exchange const std::string& with std::string_view in a couple of appropriate places in infostate_tree.(h|cpp)

An example output of traversing player 0's infostate tree of 2-player Kuhn Poker (skipping filler nodes):

Child-Sequence: []                           type: observation     #children: 1     states: []                   chance_reach_prob: []                       
Child-Sequence: [0]                          type: observation     #children: 3     states: []                   chance_reach_prob: ['1.000']                
Child-Sequence: [0, 2]                       type: observation     #children: 1     states: [2]                  chance_reach_prob: ['0.333']                
Child-Sequence: [0, 2, 0]                    type: decision        #children: 2     states: [2 0, 2 1]           chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 2, 0, 1]                 type: observation     #children: 1     states: [2 0 b, 2 1 b]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 2, 0, 1, 0]              type: observation     #children: 4     states: [2 0 b, 2 1 b]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 2, 0, 1, 0, 3]           type: terminal        #children: 0     states: [2 1 bb]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 2, 0, 1, 0, 2]           type: terminal        #children: 0     states: [2 1 bp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 2, 0, 1, 0, 1]           type: terminal        #children: 0     states: [2 0 bb]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 2, 0, 1, 0, 0]           type: terminal        #children: 0     states: [2 0 bp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 2, 0, 0]                 type: observation     #children: 1     states: [2 0 p, 2 1 p]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 2, 0, 0, 0]              type: observation     #children: 3     states: [2 0 p, 2 1 p]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 2, 0, 0, 0, 2]           type: terminal        #children: 0     states: [2 1 pp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 2, 0, 0, 0, 1]           type: decision        #children: 2     states: [2 0 pb, 2 1 pb]     chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 2, 0, 0, 0, 1, 1]        type: observation     #children: 2     states: [2 0 pbb, 2 1 pbb]   chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 2, 0, 0, 0, 1, 1, 1]     type: terminal        #children: 0     states: [2 1 pbb]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 2, 0, 0, 0, 1, 1, 0]     type: terminal        #children: 0     states: [2 0 pbb]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 2, 0, 0, 0, 1, 0]        type: observation     #children: 2     states: [2 0 pbp, 2 1 pbp]   chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 2, 0, 0, 0, 1, 0, 1]     type: terminal        #children: 0     states: [2 1 pbp]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 2, 0, 0, 0, 1, 0, 0]     type: terminal        #children: 0     states: [2 0 pbp]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 2, 0, 0, 0, 0]           type: terminal        #children: 0     states: [2 0 pp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1]                       type: observation     #children: 1     states: [1]                  chance_reach_prob: ['0.333']                
Child-Sequence: [0, 1, 0]                    type: decision        #children: 2     states: [1 0, 1 2]           chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 1, 0, 1]                 type: observation     #children: 1     states: [1 0 b, 1 2 b]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 1, 0, 1, 0]              type: observation     #children: 4     states: [1 0 b, 1 2 b]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 1, 0, 1, 0, 3]           type: terminal        #children: 0     states: [1 2 bb]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1, 0, 1, 0, 2]           type: terminal        #children: 0     states: [1 2 bp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1, 0, 1, 0, 1]           type: terminal        #children: 0     states: [1 0 bb]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1, 0, 1, 0, 0]           type: terminal        #children: 0     states: [1 0 bp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1, 0, 0]                 type: observation     #children: 1     states: [1 0 p, 1 2 p]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 1, 0, 0, 0]              type: observation     #children: 3     states: [1 0 p, 1 2 p]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 1, 0, 0, 0, 2]           type: terminal        #children: 0     states: [1 2 pp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1, 0, 0, 0, 1]           type: decision        #children: 2     states: [1 0 pb, 1 2 pb]     chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 1, 0, 0, 0, 1, 1]        type: observation     #children: 2     states: [1 0 pbb, 1 2 pbb]   chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 1, 0, 0, 0, 1, 1, 1]     type: terminal        #children: 0     states: [1 2 pbb]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1, 0, 0, 0, 1, 1, 0]     type: terminal        #children: 0     states: [1 0 pbb]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1, 0, 0, 0, 1, 0]        type: observation     #children: 2     states: [1 0 pbp, 1 2 pbp]   chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 1, 0, 0, 0, 1, 0, 1]     type: terminal        #children: 0     states: [1 2 pbp]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1, 0, 0, 0, 1, 0, 0]     type: terminal        #children: 0     states: [1 0 pbp]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 1, 0, 0, 0, 0]           type: terminal        #children: 0     states: [1 0 pp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0]                       type: observation     #children: 1     states: [0]                  chance_reach_prob: ['0.333']                
Child-Sequence: [0, 0, 0]                    type: decision        #children: 2     states: [0 1, 0 2]           chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 0, 0, 1]                 type: observation     #children: 1     states: [0 1 b, 0 2 b]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 0, 0, 1, 0]              type: observation     #children: 4     states: [0 1 b, 0 2 b]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 0, 0, 1, 0, 3]           type: terminal        #children: 0     states: [0 2 bb]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0, 0, 1, 0, 2]           type: terminal        #children: 0     states: [0 2 bp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0, 0, 1, 0, 1]           type: terminal        #children: 0     states: [0 1 bb]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0, 0, 1, 0, 0]           type: terminal        #children: 0     states: [0 1 bp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0, 0, 0]                 type: observation     #children: 1     states: [0 1 p, 0 2 p]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 0, 0, 0, 0]              type: observation     #children: 3     states: [0 1 p, 0 2 p]       chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 0, 0, 0, 0, 2]           type: terminal        #children: 0     states: [0 2 pp]             chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0, 0, 0, 0, 1]           type: decision        #children: 2     states: [0 1 pb, 0 2 pb]     chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 0, 0, 0, 0, 1, 1]        type: observation     #children: 2     states: [0 1 pbb, 0 2 pbb]   chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 0, 0, 0, 0, 1, 1, 1]     type: terminal        #children: 0     states: [0 2 pbb]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0, 0, 0, 0, 1, 1, 0]     type: terminal        #children: 0     states: [0 1 pbb]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0, 0, 0, 0, 1, 0]        type: observation     #children: 2     states: [0 1 pbp, 0 2 pbp]   chance_reach_prob: ['0.167', '0.167']       
Child-Sequence: [0, 0, 0, 0, 0, 1, 0, 1]     type: terminal        #children: 0     states: [0 2 pbp]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0, 0, 0, 0, 1, 0, 0]     type: terminal        #children: 0     states: [0 1 pbp]            chance_reach_prob: ['0.167']                
Child-Sequence: [0, 0, 0, 0, 0, 0]           type: terminal        #children: 0     states: [0 1 pp]             chance_reach_prob: ['0.167']                

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