Adding the data of different tables

Question

I have three tables of data say

t1 = {{1, 2}, {2, 3}, {3, 4}};
t2 = {{1, 3}, {2, 3}, {3, 5}};
t3 = {{1, 3}, {2, 3}};

First I want to add t1 and t2 such that first data in the brace remains same but the second data of the two tables are added up.

For an example:

tsum1 = {{1,5},{2,6},{3,9}};

How can I do it in Mathematica?

If I want to add t1, t2 and t3 (t3 has less number of data set than t1 and t2) such that first data points remain same but the second ones are added up.

For an example

tsum2 = {{1,8},{2,9},{3,9}};

How can I do it with Mathematica?

Answer 1

t1 = {{1, 2}, {2, 3}, {3, 4}};
t2 = {{1, 3}, {2, 3}, {3, 5}};
t3 = {{1, 3}, {2, 3}};

sum[x : (_?ArrayQ ..)] := Module[
  {maxLen, xp, yp},
  maxLen = Max[Length /@ {x}];
  xp = Select[{x}, Length[#] == maxLen &][[1, All, 1]];
  yp = Plus @@ (PadRight[#[[All, 2]], maxLen, 0] & /@ {x});
  Transpose[{xp, yp}]]

tsum1 = sum[t1, t2]

(*  {{1, 5}, {2, 6}, {3, 9}}  *)

tsum2 = sum[t1, t2, t3]

(*  {{1, 8}, {2, 9}, {3, 9}}  *)

EDIT: A more robust approach using ReplaceRepeated

sum2[x : (_?ArrayQ ..)] := (Join @@ {x}) //.
  {s___, {a_, b_}, m___, {a_, c_}, e___} :>
   {s, {a, b + c}, m, e}

tsum1 = sum2[t1, t2]

(*  {{1, 5}, {2, 6}, {3, 9}}  *)

tsum2 = sum2[t1, t2, t3]

(*  {{1, 8}, {2, 9}, {3, 9}}  *)

t4 = {{3, 5}, {1, 3}};

tsum3 = sum2[t1, t2, t4]

(*  {{1, 8}, {2, 6}, {3, 14}}  *)

Answer 2

A short one-liner, taking advantage of the second argument of Flatten to perform a ragged transpose:

{First@#1, Tr@#2} & @@@ Flatten[{t1, t2, t3}, {{2}, {3}}]

(Thank to Simon Woods for changing

Thread /@ Flatten[{t1, t2, t3}, {{2}}]

to

Flatten[{t1, t2, t3}, {{2}, {3}}] )

Answer 3

You may use GatherBy and Total. Or GroupBy and KeyValueMap with Total.

{#[[1, 1]], Total@#[[All, 2]]} & /@ GatherBy[Join @@ {t1, t2, t3}, First]

or

KeyValueMap[{#1, Total@#2[[All, 2]]} &]@GroupBy[Join @@ {t1, t2, t3}, First]

both give

{{1, 8}, {2, 9}, {3, 9}}

Hope this helps.