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In recursion method, a method calls itself until a condition becomes true and returned back. In mystery(), at first time, first is 0 and last is 4. Condition is checked and 0!=4 so else part is executed in which again mystery is called with first as 1 and last 4. This will go again and again until first=4.
When first=4 it is also equal to last so if part is executed and alpha[4] is returned which is 9, now it comes alpha[3] +9 which is 8+9 =17 .
It is returning values to its previous calls that is why it will reduce to alpha[0]+alpha[1]+alpha[2]+17 which is nothing but sum of all elements of a alpha
