How to find cumulative sum from from-to matrix?

If A is from-to matrix and B is route

A =[0 10 20 30; 40 0 50 60; 70 80 0 90; 100 110 120 0],

B = [1 2 3 4;2 4 3 1]

How to find cumulative sum

C = [0 (0+10) (0+10+50) (0+10+50+90); 0 (0+60) (0+60+120) (0+60+120+70)]

C = [0 10 60 150; 0 60 180 250]

Answer 1

[DGM]

From the other comment:

A = [0 10 20 30; 40 0 50 60; 70 80 0 90; 100 110 120 0];
B = [1 2 3 4;2 4 3 1];
%     x (1,2)  (2,3)     (3,4)         x (2,4)  (4,3)      (3,1)
%C = [0 (0+10) (0+10+50) (0+10+50+90); 0 (0+60) (0+60+120) (0+60+120+70)]
%C = [0 10 60 150; 0 60 180 250]

% each column of BB is a row,col subscript pair into A
% each page of BB corresponds to each row of B
BB = repelem(B,1,2);
BB = reshape(permute(BB(:,2:end-1),[3 2 1]),2,[],size(B,1));
% convert to linear indices
BB = permute(sub2ind(size(A),BB(1,:,:),BB(2,:,:)),[3 2 1]);

% do sum and pad
C = cumsum(A(BB),2);
C = [zeros(size(C,1),1) C]

C = 2×4

0 10 60 150 0 60 180 250