Counts paths from a point to reach Origin | DP based function to count number of paths ; $dp [ $n + 1 ] [ $m + 1 ] ; Fill entries in bottommost row and leftmost columns ; Fill DP in bottom up manner ; Driver Code
< ? php function countPaths ( $ n , $ m ) { for ( $ i = 0 ; $ i <= $ n ; $ i ++ ) $ dp [ $ i ] [ 0 ] = 1 ; for ( $ i = 0 ; $ i <= $ m ; $ i ++ ) $ dp [ 0 ] [ $ i ] = 1 ; for ( $ i = 1 ; $ i <= $ n ; $ i ++ ) for ( $ j = 1 ; $ j <= $ m ; $ j ++ ) $ dp [ $ i ] [ $ j ] = $ dp [ $ i - 1 ] [ $ j ] + $ dp [ $ i ] [ $ j - 1 ] ; return $ dp [ $ n ] [ $ m ] ; } $ n = 3 ; $ m = 2 ; echo " ▁ Number ▁ of ▁ Paths ▁ " , countPaths ( $ n , $ m ) ; ? >