function $\color{Blue}\text{TREE-CSP-SOLVER}$($\color{Yellow}csp$) returns a solution, or a failure $\quad$ inputs: $\color{Yellow}csp$, a CSP with components $\color{Yellow}X, D, C$ $\quad$ $\color{Green}n$ $\leftarrow$ number of variables in $\color{Yellow}X$ $\quad$ $\color{Green}assignment$ $\leftarrow$ an empty assignment $\quad$ $\color{Green}root$ $\leftarrow$ any variable in $\color{Yellow}X$ $\quad$ $\color{Purple}X$ $\leftarrow$ $\color{Purple}\text{TOPOLOGICAL-SORT(\color{Yellow}{X}, \color{Green}{root})}$ $\quad$ for $j = \color{Green}n$ down to 2 do $\qquad$ $\color{Purple}{\text{MAKE-ARC-CONSISTENT}}$($\color{Purple}\text{PARENT}$($\color{Yellow}X_j$), $\color{Yellow}X_j$) $\qquad$ if it cannot be made consistent then return failure $\quad$ for $i = 1$ to $n$ do $\qquad$ $\color{Green}assignment[$$\color{Yellow}{X_i}$$] \leftarrow$ any consistent value from $\color{Yellow}D_i$ $\qquad$ if there is no consistent value then return $\text{failure}$ $\quad$ return $assignment$