% matrix C gives link costs (time, money, ...)
% C(i,j) is cost to go from j to i.
% V is col vector that stores the min-cost-to-go info
% V(i) is min cost to get to node 1 from node i
% i.e. node 1 is target
%
% DP says V(j) = min_i (C(i,j)+V(i)) for i>1
% and V(1)=0

% define C:

C=[
     0    11     5    31    13    28    46    52     5    49;
    19    26     1    42    70    25    59    18    49    24;
    25    33    27    26    63    25    10    16    42    24;
    71    28    21    26    41    56     6    25    70    12;
    14    27    28     7    48    47     4    48    22    37;
     9    40    51    44    62    54    58    40    10    11;
    53    41    52    16    34     4    19     0    52    71;
    66     2    21     9    31    94    23    33    54     1;
     2    33    29    10    34    31    12    47    14    13;
    19    78     4    50    26     2    41    31    53    23];

% the following two lines does one iteration of the DP equation:

n = size(C,1);
V = min(C+V*ones(1,n))';
V(1)=0;