算法导论15章动态规划

钢条切割问题

public class Main {int n = 10;int[] p = new int[]{1,5,8,9,10,17,17,20,24,30};int[] r = new int[n+1];int[] s = new int[n+1];int solve(int n,int[] s,int c){if(n==0) return 0;if(r[n]>=0) return r[n];else{int max = -10000;for(int i=1;i<=n;i++){int t = p[i-1]+solve(n-i,s,c)-c;if(t>max){max = t;s[n] = i;}}r[n] = max;return max;}}void solve2(int n){Arrays.fill(r, -1);r[0] = 0;for(int i=1;i<=n;i++){int max = 0;for(int j=1;j<=i;j++){if(max<p[j-1]+r[i-j]){max = p[j-1]+r[i-j];s[i] = j;}}r[i] = max;}System.out.println("最大价值为"+r[n]);System.out.println("切割方式：");while(n>0){System.out.println(s[n]);n = n-s[n];}}public static void main(String[] args) {Main m = new Main();Arrays.fill(m.r, -1);System.out.println(m.solve(7,m.s,1));System.out.println(Arrays.toString(m.s));int n = 7;while(n>0){System.out.println(m.s[n]);n = n-m.s[n];}}}

矩阵链乘

public class Main {int n = 6;int[][] m = new int[n][n];int[][] s = new int[n][n];int solve(int[] p){for(int i=0;i<n;i++){m[i][i] = 0;}for(int l=1;l<n;l++){//l-1为几个矩阵相乘for(int i=0;i<n-l;i++){//i为起始int j = i+l;//j为结束m[i][j] = 100000;for(int k=i;k<j;k++){//k为分割点if(m[i][j]>m[i][k]+m[k+1][j]+p[i]*p[k+1]*p[j+1]){m[i][j]=m[i][k]+m[k+1][j]+p[i]*p[k+1]*p[j+1];s[i][j] = k;}}}}return m[0][n-1];}int solve(int[] p,int i,int j){if(m[i][j]>0) return m[i][j];if(i==j) return 0;m[i][j] = 100000;for(int k=i;k<j;k++){int t = solve(p, i, k)+solve(p,k+1,j)+p[i]*p[k+1]*p[j+1];if(m[i][j]>t){m[i][j] = t;s[i][j] = k;}}return m[i][j];}void print(int[][] s,int i,int j){if(i==j){System.out.print("A"+i);}else{System.out.print('(');print(s, i, s[i][j]);print(s, s[i][j]+1,j);System.out.print(')');}}public static void main(String[] args) {Main m = new Main();//System.out.println(m.solve(new int[]{5,10,3,12,5,50,6}));//m.print(m.s,0,5);System.out.println(m.solve(new int[]{5,10,3,12,5,50,6},0,5));m.print(m.s,0,5);}}

最长公共子序列

public class Main {void solve(char[] x,char[] y){int m = x.length;int n = y.length;int c[][] = new int[m+1][n+1];for(int i=0;i<n;i++){c[0][i] = 0;}for(int i=0;i<m;i++){c[i][0] = 0;}for(int i=1;i<=m;i++){//i为子序列长度for(int j=1;j<=n;j++){//j为子序列长度if(x[i-1]==y[j-1]){c[i][j] = c[i-1][j-1]+1;}else{c[i][j] = Math.max(c[i][j-1], c[i-1][j]);}}}System.out.println(c[m][n]);print(c, m, n, x);}int solve2(int c[][],char[] x,char[] y,int i,int j){if(c[i][j]>0) return c[i][j];if(i==0||j==0) c[i][j] = 0;else{if(x[i-1]==y[j-1]){c[i][j] = solve2(c, x, y, i-1, j-1)+1;}else{c[i][j] = Math.max(solve2(c, x, y, i-1, j), solve2(c, x, y, i, j-1));}}return c[i][j];}void print(int[][] c,int m,int n,char[] x){if(m==0||n==0) return;if(c[m][n]==c[m-1][n-1]+1){System.out.println(x[m-1]);print(c, m-1, n-1, x);}else if(c[m][n]==c[m-1][n]){print(c, m-1, n, x);}else{print(c, m, n-1, x);}}public static void main(String[] args) {Main m = new Main();//m.solve("BDCABA".toCharArray(),"ABCBDAB".toCharArray());char[] a1 = "BDCABA".toCharArray();char[] a2 = "ABCBDAB".toCharArray();int[][] c = new int[a1.length+1][a2.length+1];int t = m.solve2(c, a1, a2, a1.length, a2.length);System.out.println(t);m.print(c, a1.length, a2.length, a1);}}

最长单调递增子序列

public class Main {void solve(int[] arr){int[] d = new int[arr.length];d[0] = 1;for(int i=0;i<arr.length;i++){d[i] = 1;for(int j=0;j<i;j++){if(arr[i]>arr[j]){if(d[j]+1>d[i]){d[i] = d[j]+1;}}}}System.out.println(d[arr.length-1]);}public static void main(String[] args) {Main m = new Main();m.solve(new int[]{1,1,2,3,4,1,2,7,5,7,1,3,4,8,9});}}