Problem:
Score : 100 points

Problem Statement

There are N items, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Item i has a weight of w_i and a value of v_i.

Taro has decided to choose some of the N items and carry them home in a knapsack.
The capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.

Find the maximum possible sum of the values of items that Taro takes home.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq W \leq 10^9

1 \leq w_i \leq W

1 \leq v_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N W
w_1 v_1
w_2 v_2
:
w_N v_N

Output

Print the maximum possible sum of the values of items that Taro takes home.

Sample Input 1

3 8
3 30
4 50
5 60

Sample Output 1

90

Items 1 and 3 should be taken.
Then, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.

Sample Input 2

1 1000000000
1000000000 10

Sample Output 2

10

Sample Input 3

6 15
6 5
5 6
6 4
6 6
3 5
7 2

Sample Output 3

17

Items 2, 4 and 5 should be taken.
Then, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.Writer;
import java.io.BufferedWriter;
import java.io.OutputStreamWriter;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.math.*;

public class Main{
  static class pair{
    int val, idx;
    pair(int a, int b){
      val=a;
      idx=b;
    }
    public String toString(){
      return "(val: "+val+" idx: "+idx+")";
    }
  }

  static class ProblemSolver{
    static int MAX=10000;
    public void solveTheProblem(InputReader in,OutputWriter out, NumberTheory nt){
      int test=1;//in.nextInt();
      while(test-- >0){
        int n;
        n=in.nextInt();
        int w=in.nextInt();
        int ar[]= new int[n];
        int val[]= new int[n];
        int sum=0;
        for(int i=0;i<n;i++){
          ar[i]=in.nextInt();
          val[i]=in.nextInt();
          sum+=val[i];
        }
        //earlier: dp[i][j]== given weight w and taking upto ith element in the array, what is the max possible value that can be generated
        //Here we took all weights from 0 to w
        //it gave the value
        //now: dp[i][j]== given value v and taking weight of only a subset of array elements what is the
        // dp[i][v]= the min weight subset of array required to get atleast v value. Weight of min number of elements present in the array such that their total value is atleast V
        //it will give the weight.
        long ans=0;
        MAX=sum+10;
        long dp[][]= new long[n+1][sum+1];
        for(int i=0;i<=n;i++){
          Arrays.fill(dp[i], Integer.MAX_VALUE);
          dp[i][0]=0; //if I want value to be 0, the min weight required is 0
        }
        for(int i=1;i<=n;i++){
          for(int j=1;j<=sum;j++){
              dp[i][j]=Math.min(dp[i-1][Math.max(0, j-val[i-1])]+ar[i-1], dp[i-1][j]);
            if(dp[i][j]<=w){
              ans=Math.max(ans, j);
            }
          }
        }
        out.println(ans);
      }
    }
  }

  public static void main(String[] args){
    InputStream inputStream=System.in;
    OutputStream outputStream=System.out;
    InputReader in=new InputReader(inputStream);
    OutputWriter out=new OutputWriter(outputStream);
    NumberTheory nt= new NumberTheory();
    ProblemSolver problemSolver=new ProblemSolver();
    problemSolver.solveTheProblem(in,out, nt);
    out.flush();
    out.close();
  }

  static class InputReader {
    private boolean finished = false;

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public InputReader(InputStream stream) {
      this.stream = stream;
    }

    public int read() {
      if (numChars == -1) {
        throw new InputMismatchException();
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          throw new InputMismatchException();
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar++];
    }

    public int peek() {
      if (numChars == -1) {
        return -1;
      }
      if (curChar >= numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch (IOException e) {
          return -1;
        }
        if (numChars <= 0) {
          return -1;
        }
      }
      return buf[curChar];
    }

    public int nextInt() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      int res = 0;
      do {
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public long nextLong() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      long res = 0;
      do {
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      } while (!isSpaceChar(c));
      return res * sgn;
    }

    public String nextLine() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      StringBuilder res = new StringBuilder();
      do {
        if (Character.isValidCodePoint(c)) {
          res.appendCodePoint(c);
        }
        c = read();
      } while (!isSpaceChar(c));
      return res.toString();
    }

    public boolean isSpaceChar(int c) {
      if (filter != null) {
        return filter.isSpaceChar(c);
      }
      return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
      StringBuilder buf = new StringBuilder();
      int c = read();
      while (c != '\n' && c != -1) {
        if (c != '\r') {
          buf.appendCodePoint(c);
        }
        c = read();
      }
      return buf.toString();
    }

    public String readLine() {
      String s = readLine0();
      while (s.trim().length() == 0) {
        s = readLine0();
      }
      return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
      if (ignoreEmptyLines) {
        return readLine();
      } else {
        return readLine0();
      }
    }

    public BigInteger readBigInteger() {
      try {
        return new BigInteger(nextLine());
      } catch (NumberFormatException e) {
        throw new InputMismatchException();
      }
    }

    public char nextCharacter() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      return (char) c;
    }

    public double nextDouble() {
      int c = read();
      while (isSpaceChar(c)) {
        c = read();
      }
      int sgn = 1;
      if (c == '-') {
        sgn = -1;
        c = read();
      }
      double res = 0;
      while (!isSpaceChar(c) && c != '.') {
        if (c == 'e' || c == 'E') {
          return res * Math.pow(10, nextInt());
        }
        if (c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c - '0';
        c = read();
      }
      if (c == '.') {
        c = read();
        double m = 1;
        while (!isSpaceChar(c)) {
          if (c == 'e' || c == 'E') {
            return res * Math.pow(10, nextInt());
          }
          if (c < '0' || c > '9') {
            throw new InputMismatchException();
          }
          m /= 10;
          res += (c - '0') * m;
          c = read();
        }
      }
      return res * sgn;
    }

    public boolean isExhausted() {
      int value;
      while (isSpaceChar(value = peek()) && value != -1) {
        read();
      }
      return value == -1;
    }

    public String next() {
      return nextLine();
    }

    public SpaceCharFilter getFilter() {
      return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
      this.filter = filter;
    }

    public interface SpaceCharFilter {
      public boolean isSpaceChar(int ch);
    }
    public int[] nextIntArray(int n){
      int[] array=new int[n];
      for(int i=0;i<n;++i)array[i]=nextInt();
      return array;
    }
    public int[] nextSortedIntArray(int n){
      int array[]=nextIntArray(n);
      Arrays.sort(array);
      return array;
    }
    public ArrayList<Integer> nextIntArrayList(int n){
      ArrayList<Integer> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
      ar.add(nextInt());
      return ar;
    }
    public ArrayList<Long> nextLongArrayList(int n){
      ArrayList<Long> ar= new ArrayList<>();
      for(int i=0;i<n;i++)
      ar.add(nextLong());
      return ar;
    }

    public int[] nextSumIntArray(int n){
      int[] array=new int[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextLongArray(int n){
      long[] array=new long[n];
      for(int i=0;i<n;++i)array[i]=nextLong();
      return array;
    }
    public long[] nextSumLongArray(int n){
      long[] array=new long[n];
      array[0]=nextInt();
      for(int i=1;i<n;++i)array[i]=array[i-1]+nextInt();
      return array;
    }
    public long[] nextSortedLongArray(int n){
      long array[]=nextLongArray(n);
      Arrays.sort(array);
      return array;
    }
    public int[][] nextIntMatrix(int n,int m){
      int[][] matrix=new int[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextInt();
      return matrix;
    }

    public int[][] nextIntMatrix(int n){
      return nextIntMatrix(n,n);
    }

    public long[][] nextLongMatrix(int n,int m){
      long[][] matrix=new long[n][m];
      for(int i=0;i<n;++i)
      for(int j=0;j<m;++j)
      matrix[i][j]=nextLong();
      return matrix;
    }

    public long[][] nextLongMatrix(int n){
      return nextLongMatrix(n,n);
    }

    public char[][] nextCharMatrix(int n,int m){
      char[][] matrix=new char[n][m];
      for(int i=0;i<n;++i)
      matrix[i]=next().toCharArray();
      return matrix;
    }

    public char[][] nextCharMatrix(int n){
      return nextCharMatrix(n,n);
    }
  }

  static class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
      writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
      this.writer = new PrintWriter(writer);
    }

    // public void print(char[] array) {
    //     writer.print(array);
    // }

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void print(int[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(double[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(long[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(char[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(String[] array) {
      for (int i = 0; i < array.length; i++) {
        if (i != 0) {
          writer.print(' ');
        }
        writer.print(array[i]);
      }
    }

    public void print(int[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(double[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(long[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(char[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void print(String[][] matrix){
      for(int i=0;i<matrix.length;++i){
        println(matrix[i]);
      }
    }

    public void println(int[] array) {
      print(array);
      writer.println();
    }

    public void println(double[] array) {
      print(array);
      writer.println();
    }

    public void println(long[] array) {
      print(array);
      writer.println();
    }

    // public void println(char[] array) {
    //     print(array);
    //     writer.println();
    // }

    public void println(String[] array) {
      print(array);
      writer.println();
    }

    public void println() {
      writer.println();
    }

    public void println(Object... objects) {
      print(objects);
      writer.println();
    }

    public void print(char i) {
      writer.print(i);
    }

    public void println(char i) {
      writer.println(i);
    }

    public void println(char[] array) {
      writer.println(array);
    }

    public void printf(String format, Object... objects) {
      writer.printf(format, objects);
    }

    public void close() {
      writer.close();
    }

    public void flush() {
      writer.flush();
    }

    public void print(long i) {
      writer.print(i);
    }

    public void println(long i) {
      writer.println(i);
    }

    public void print(int i) {
      writer.print(i);
    }

    public void println(int i) {
      writer.println(i);
    }

    public void separateLines(int[] array) {
      for (int i : array) {
        println(i);
      }
    }
  }
  static class NumberTheory{

    /**
    * Modular Arithmetic:
    *  1. (a+b)%c=(a%c+b%c)%c
    *  2. (a*b)%c=(a%c*b%c)%c
    *  3. (a-b)%c=(a%c-b%c+c)%c
    *  4. (a/b)%c=(a%c*(b^-1)%c)%c -- (b^-1 is multiplicative modulo inverse)
    */
    //Modular Addition
    public int modularAddition(int a,int b,int MOD){
      return (a%MOD+b%MOD)%MOD;
    }
    public long modularAddition(long a,long b,long MOD){
      return (a%MOD+b%MOD)%MOD;
    }
    //Modular Multiplication
    public int modularMultiplication(int a,int b,int MOD){
      return ((a%MOD)*(b%MOD))%MOD;
    }
    public long modularMultiplication(long a,long b,long MOD){
      return ((a%MOD)*(b%MOD))%MOD;
    }
    //Modular Subtraction
    public int modularSubtraction(int a,int b,int MOD){
      return (a%MOD-b%MOD+MOD)%MOD;
    }
    public long modularSubtraction(long a,long b,long MOD){
      return (a%MOD-b%MOD+MOD)%MOD;
    }

    /**
    * Binary Exponentiation
    */
    public int binaryExponentiation(int x,int n){
      if(n==0)return 1;
      else if(n%2==0)return binaryExponentiation(x*x,n/2);
      else return x*binaryExponentiation(x*x,(n-1)/2);
    }
    public long binaryExponentiation(long x,long n){
      long result=1;
      while(n>0){
        if(n%2==1)result*=x;
        x=x*x;
        n/=2;
      }
      return result;
    }

    /**
    * Modular Exponentiation
    */
    public int modularExponentiation(int x,int n,int MOD){
      if(n==0)return 1%MOD;
      else if(n%2==0)return modularExponentiation(modularMultiplication(x,x,MOD),n/2,MOD);
      else return modularMultiplication(x,modularExponentiation(modularMultiplication(x,x,MOD),(n-1)/2,MOD),MOD);
    }
    public long modularExponentiation(long x,long n,long MOD){
      long result=1;
      while(n>0){
        if(n%2==1)result=modularMultiplication(result,x,MOD);
        x=modularMultiplication(x,x,MOD);
        n/=2;
      }
      return result;
    }

    /**
    * Factorial of a number
    */
    public long factorials(long n){
      if(n==0)return 1;
      return n*factorials(n-1);
    }

    /**
    * Prime factors of a number
    */
    public ArrayList<Integer> distinctPrimeFactors(int n){
      ArrayList<Integer> factorials=new ArrayList<>();
      int limit=(int)Math.sqrt(n);
      if(n%2==0){
        factorials.add(2);
        while(n%2==0)n/=2;
      }
      for(int i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    public ArrayList<Long> distinctPrimeFactors(long n){
      ArrayList<Long> factorials=new ArrayList<>();
      long limit=(long)Math.sqrt(n);
      if(n%2==0){
        factorials.add((long)2);
        while(n%2==0)n/=2;
      }
      for(long i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    public ArrayList<Integer> primeFactors(int n){
      ArrayList<Integer> factorials=new ArrayList<>();
      int limit=(int)Math.sqrt(n);
      if(n%2==0){
        factorials.add(2);
        while(n%2==0)n/=2;
      }
      for(int i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    public ArrayList<Long> primeFactors(long n){
      ArrayList<Long> factorials=new ArrayList<>();
      long limit=(long)Math.sqrt(n);
      if(n%2==0){
        factorials.add((long)2);
        while(n%2==0)n/=2;
      }
      for(long i=3;i<=limit;i+=2){
        if(n%i==0){
          factorials.add(i);
          while(n%i==0)n/=i;
        }
      }
      if(n>2)factorials.add(n);
      return factorials;
    }

    /**
    * Combination: nCr
    */
    //Naive version
    //(n,r)=(n-1,r-1)+(n-1,r) for r!=0 or r!=n
    //(n,0)=(n,n)=1
    public int binomialCoefficientRecursive(int n,int k){
      if(k==0 || k==n)return 1;//base case
      return binomialCoefficientRecursive(n-1,k-1)+binomialCoefficientRecursive(n-1,k);//recursion
    }

    //Dynamic Programming version(Uses bottom up approach to fill the table)
    //Time complexity: O(n*k)
    //Space complexity: O(n*k)
    public long binomialCoefficientIterative(int n,int k){
      long[][] C=new long[n+1][k+1];
      for(int i=0;i<=n;++i){
        for(int j=0;j<=Math.min(n,k);++j){
          if(j==0 || j==i)C[i][j]=1;
          else C[i][j]=C[i-1][j-1]+C[i-1][j];
        }
      }
      return C[n][k];
    }

    //Pascal's Triangle version(Space efficient program)
    //Time complexity: O(n*k)
    //Space complexity: O(k)
    public long nCr(int n,int r){
      int[] C=new int[r+1];
      C[0]=1;//nC0=1
      for(int i=1;i<=n;++i)
      for(int j=Math.min(i,r);j>0;--j)
      C[j]=C[j]+C[j-1];
      return C[r];
    }

    /**
    * Catlan number:
    *  - Time complexity: O(n*n)
    *  - Auxiliary space: O(n)
    *
    *  NOTE: Time complexity could be reduced to O(n) but it is
    *        possible if and only if n is small or else there is
    *        a chance of getting an overflow. To decrease the time
    *        complexity to O(n) just remember nCr=nCn-r
    */
    public long catlanNumber(int n){
      long[] catlan=new long[n+1];
      catlan[0]=catlan[1]=1;
      for(int i=2;i<=n;++i)
      for(int j=0;j<i;++j)
      catlan[i]+=catlan[j]*catlan[i-1-j];

      return catlan[n];
    }

    /**
    * Greatest Common Divisor(GCD)
    *  - It is also known as Highest Common Factor(HCF)
    *  - Time complexity: log(min(a,b))
    *  - Auxiliary Space: O(1)
    */
    public int gcd(int a,int b){
      if(b==0)return a;
      return gcd(b,a %b);
    }

    public long gcd(long a,long b){
      if(b==0)return a;
      return gcd(b,a%b);
    }

    /**
    * Extended Euclid's Algorithm:
    *  - ax+by=gcd(a,b)
    *  - Time complexity:
    *  -
    */


    /**
    * Least Common Multiple(LCM):
    *  - Time complexity: log(min(a,b))
    *  - Auxiliary Space: O(1)
    */
    public long lcm(long a,long b){
      return (a*b)/gcd(a,b);
    }

  }
}
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//            "I8,      "I8,      "I8        .,mmmI8888888m,.
//              I8,      "I8,      I8,  .mI8I88"""". .. "I8888
//              "I8,      "I8      mI8I88"". . . . . .,m8"   "8
//               I8m,  __ ;I8   ,II88" . . . . .,;miI88"
//               "I88I8I88I88,,I88" . . . ,mmiiI8888"
//                ,I8". . ."I8I8". . . mi888888888"
//              ,I8 . . . .,I88I. . .i88888888888"
//             I8. . . .,mII88Ima. .i88888888888"
//            ,8"..,mI88I88I88I8Imi888888888888"
//            I8.,I8I"""        ""II88888888888
//           ;I8I8"                  ""I8888888
//           ""                         "I88888
//                                        "I888
//                                         "I88,
//                                          "I88
//                                           "88,
//                                            I88,              ______   __
//                           ______           "I88__        .mI88I88I88I88I88,
//                      .,mI88I88I88, ,mI88,   I88"""     ,mI8". . . . "I8,..8,
//                    ,I888' . . . "I88.\ "8,  I88      ,I8". . . .  / :;I8 \ 8,
//                  .mI8' . . .  / .:"I8.\ 88  "88,    ,8". . .  / .;mI8I8I8,\ 8
//                 ,I8'. . .  / . .:;,I8I8I888  I88   ,8". .  / .:mI8"'   "I8,:8
//                ,I8'. . . / . .:;,mI8"  `"I88 I88   I8. .  / .m8"         "I8I
//               ,I8 . .  / . .:;,mI8"      "I88888   88,.  / ,m8            "8'
//               I8'. .  / . .;,mI8"          "II888 ,I8I8,.,I8"
//               I8 . . / . .,mI8"              I8888888' """
//               `I8,.  / ;,mI8"                 II888
//                "I8I, /,mI8"                 __I888
//                  "I8888"                   """I88
//                    ""                         I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                               I88
//                                             __I88
//                                            """I88
//                                               I88
//                                               I88
//                                               I88__
//                                               I88"""
//                                               I88
//                                        BITSY  ___  CHUCK