HDU 4939 stupid tower defense

 

Stupid tower defense

Time Limit: 12000/6000 MS (Java/others) memory limit: 131072/131072 K (Java/Others)
Total submission (s): 1589 accepted submission (s): 452

Problem descriptionfsf is addicted to a stupid tower defense game. the goal of tower Defense Games is to try to stop enemies from crossing a map by building traps to slow them down and towers which shoot at them as they pass.

The map is a line, which has n unit length. we can build only one tower on each unit length. the enemy takes t seconds on each unit length. and there are 3 kinds of tower in this game: The Red Tower, the Green Tower and the blue tower.

The Red Tower damage on the enemy X points per second when he passes through the tower.

The Green Tower damage on the enemy y points per second after he passes through the tower.

The blue tower let the enemy go slower than before (that is, the enemy takes more Z second to pass an unit length, also, after he passes through the tower .)

Of course, if you are already pass through M green towers, you shoshould have got M * y damage per second. the same, if you are already pass through K blue towers, the enemy shoshould have took T + K * z seconds every unit length.

FSF now wants to know the maximum damage the enemy can get.

 

Inputthere are multiply test cases.

The first line contains an integer T (t <= 100), indicates the number of cases.

Each test only contain 5 integers n, x, y, z, T (2 <= n <= 1500,0 <= x, y, z <= 60000,1 <= T <= 3)

 

Outputfor each case, You shoshould output "case # C:" First, where C indicates the case number and counts from 1. then output the answer. for each test only one line which have one integer, the answer to this question.

 

Sample input12 4 3 2 1

 

Sample outputcase #1: 12 Hint For the first sample, the first tower is blue tower, and the second is Red Tower. So, the total damage is 4*(1 + 2) = 12 damage points.

 

The question is a straight line with a length of N. You can build a tower on a unit with a length of 1.

There are three types of towers

Color Effect

When red passes through this tower, it receives X (D/S) damage.

Green suffered sustained damage from Y (D/S) after passing through the tower.

After the bule passes through this tower, the time for passing through one tower is increased by Z seconds.

 

The question requires that N Towers be placed in a straight line to maximize the damage after a straight line.

 

Then we can imagine that no matter how many colors are red. In the end, it must be correct, because the blue overlay time can be obtained, and the damage effect is as big as possible.

The rest is blue and green.

At this time, we need to use DP.

DP [I] [J]... It indicates the maximum damage caused by I + J (<= N) and I put green and J put blue.

 

Transfer is just like this.

DP [I] [J] = max (DP [I-1] [J] + (J * z + T) * y * (I-1 ), DP [I] [J-1] + (J-1) * z + T) * y * I );

 

Note the boundary.

Then, the answer is to add the damage to the Red Tower ~

 

#include <cstdio>#include <iostream>#include <cstring>using namespace std;typedef long long ll;const int N = 1550 ;ll dp[N][N];   // i = green , j = blue ...int main(){    ll _ , n , x , y , z , t , cas = 1;    #ifdef LOCAL        freopen("in","r",stdin);    #endif    cin >> _ ;    while( _ -- ){        cin >> n >> x >> y >> z >> t ;        cout << "Case #"<< cas++ <<": ";        memset(dp,0,sizeof dp);        for( int i = 1 ; i <= n ; ++i ){            for( int j = 0 ; j <= i ; ++j ){                    int k = i - j ;                    ll temp = 0 ;                    if( j > 0 ) temp = max( temp , dp[j-1][k] + ( k * z  + t ) * y * ( j - 1 )  );                    if( k > 0 ) temp = max( temp , dp[j][k-1] + ( ( k - 1 ) * z + t ) * y * j ) ;                    dp[j][k] = temp ;            }        }        ll ans = 0 ;        for( int i = 0 ; i <= n ; ++i ){            for( int j = 0 ; j + i <= n ; ++j ){                ans = max ( ans , dp[i][j] + ( n - i - j ) * ( x * ( t + z * j ) + i * y * ( t + z * j ) ) );            }        }        cout << ans << endl ;    }    return 0;}

 

HDU 4939 stupid tower defense