feat(cses): range queries

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cses/range-queries/rui

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+
+
+basically allows for answering queries of a range [l, r]
+
+and updating values/ranges in O(lg(n))
+
+
+so, for example, finding the minimum of elements in range [l, r]
+can be answered in log(n) rather than r - l + 1
+
+
+basically, you divide up the array into pieces:
+
+
+this is the segtree
+for each "segment" you store the answer for the query
+[--------------- + x]
+[------ + x][-------]
+[--][-- + x][--][---]
+[-][-][x][-][-][-]
+
+usually way too advanced
+
+its super powerful b/c you can, for example
+find min/max/sum/gcd over ranges, while updating those values OR 
+
+updating a [l, r] range of values, all in O(lgn)
+
+so, for example:
+
+- sum from l to r
+- update at index i
+- increase indices [l, r] by x
+
+^ all in log(n)
+(pretty insane)
+
+yes, but i alr knew it before
+
+adv algos is tuff 
+
+say i update something to x
+then i need to go back UP and update each segment
+
+so it takes: O(lg(n)) time too
+
+the problem: intervals don't cleanly overlap
+
+so if i do sum[0:n/2+2]
+
+i first get sum[0:n/2], then combine with sum[n/2:n/2+2]
+the "height" is O(log(n)), so in worst-case you traverse down
+the entire depth to combine the sum
+
+last thing: updating a value