in problem zuma , why do we need a dp state like : as mentioned in tutorial

if(arr[i] == arr[i+1]) dp[i][j] = 1+dp[i+2][j]

i checked by removing this state and it gave WA .

why only these 2 dp states are not enough ! #@

dp[i][j] = 1+dp[i+1][j] and

dp[i][j] = dp[i+1][k-1] + dp[k+1][j]

CAN anyone clarify it more ? ! @