Old Top Coder riddle: Making a number by inserting +

Question

I am thinking about this topcoder problem.

Given a string of digits, find the minimum number of additions required for the string to equal some target n

Answer 1

Seems to be too late .. but just read some comments and answers here which say no to dp approach . But it is a very straightforward dp similar to rod-cutting problem:

To get the essence:

int val[N][N];
int dp[N][T];

val[i][j]: numerical value of s[i..j] including both i and j

val[i][j] can be easily computed using dynamic programming approach in O(N^2) time

dp[i][j] : Minimum no of '+' symbols to be inserted in s[0..i] to get the required sum j

dp[i][j] = min( 1+dp[k][j-val[k+1][j]] ) over all k such that 0<=k<=i and val[k][j]>0

In simple terms , to compute dp[i][j] you assume the position k of last '+' symbol and then recur for s[0..k]