Hdoj 2620 Bone Collector (0-1 backpack)

title Link:http://acm.hdu.edu.cn/showproblem.php?pid=2602

Thinking Analysis: The problem is a classic 0-1 knapsack problem; Assuming state Dp[i][v] indicates the maximum value that the first I item fits into a backpack with a capacity of V, then the DP recurrence formula can be deduced

Dp[i][v] = Max{dp[i-1][v], Dp[i-1][v–c[i]] + w[i]};c[i) indicates the capacity of the article I, w[i] denotes the value of article I items; the decision for each stage of the dynamic planning issue is whether to

Select the item I to put in the backpack, if I do not select the item I, then dp[i][v] = Dp[i-1][v], if you select the item I put into the backpack, then Dp[i][v] = Dp[i-1][v-c[i]], v-c[i] >= 0;

At the same time, you can use a one-dimensional array recursion, because recursion I, only need to use to the i-1 line of array elements, so can be pushed from V down to 0, recursive formula is as follows: dp[v] = MAX (Dp[v], dp[v-c[i] + w[i]),

(one-dimensional DP) code is as follows:

ImportJava.util.*; Public classMain {Static Final intMax_n = 1000 + 10; Static int[] Value =New int[Max_n]; Static int[] Volumn =New int[Max_n]; Static int[] DP =New int[Max_n];  Public Static intMax (intAintb) {returna > B?a:b; }     Public Static voidMain (string[] args) {Scanner in=NewScanner (system.in); intCase_times =In.nextint ();  while(case_times--! = 0) {            intN, V;  for(inti = 0; i < max_n; ++i) dp[i]= 0; N=In.nextint (); V=In.nextint ();  for(inti = 1; I <= N; ++i) value[i]=In.nextint ();  for(inti = 1; I <= N; ++i) volumn[i]=In.nextint ();  for(inti = 1; I <= N; ++i) { for(intv = v; V >= 0; --v) {if(V-volumn[i] >= 0) Dp[v]= Max (Dp[v], Dp[v-volumn[i]] +Value[i]);        }} System.out.println (Dp[v]); }    }}

The (two-dimensional DP) code is as follows:

ImportJava.util.*; Public classMain {Static Final intMax_n = 1000 + 10; Static int[] Value =New int[Max_n]; Static int[] Volumn =New int[Max_n]; Static int[] DP =New int[Max_n][max_n];  Public Static intMax (intAintb) {returna > B?a:b; }     Public Static voidMain (string[] args) {Scanner in=NewScanner (system.in); intCase_times =In.nextint ();  while(case_times--! = 0) {            intN, V;  for(inti = 0; i < max_n; ++i) { for(intj = 0; J < Max_n; ++j) Dp[i][j]= 0; } N=In.nextint (); V=In.nextint ();  for(inti = 1; I <= N; ++i) value[i]=In.nextint ();  for(inti = 1; I <= N; ++i) volumn[i]=In.nextint ();  for(inti = 1; I <= N; ++i) { for(intv = 0; V <= v; ++v) {if(V-volumn[i] >= 0) Dp[i][v]= Max (Dp[i-1][v], Dp[i-1][v-volumn[i]] +Value[i]); ElseDp[i][v]= Dp[i-1][v];        }} System.out.println (Dp[n][v]); }    }}

Hdoj 2620 Bone Collector (0-1 backpack)