cap4 examples

cap4/common.go

@@ -0,0 +1,10 @@
+package cap4
+
+func _makeMatrix(m, n int) [][]int {
+    matrix := make([][]int, m)
+    for i := 0; i < m; i++ {
+        matrix[i] = make([]int, n)
+    }
+
+    return matrix
+}

cap4/ex15.go

@@ -0,0 +1,15 @@
+package cap4
+
+// Ex15 最大子段和
+func Ex15(nums []int) int {
+    result := nums[0]
+    currMaxSum := nums[0]
+    n := len(nums)
+    for i := 1; i < n; i++ {
+        num := nums[i]
+        currMaxSum = max(currMaxSum+num, num)
+        result = max(result, currMaxSum)
+    }
+
+    return result
+}

cap4/ex24.go

@@ -0,0 +1,22 @@
+package cap4
+
+// Ex24 树塔问题
+func Ex24(nums [][]int) (int, []int) {
+	steps := make([]int, 0)
+
+	dp := make([][]int, len(nums))
+	for i, layer := range nums {
+		dp[i] = make([]int, len(layer))
+		copy(dp[i], layer)
+	}
+
+	for i := len(nums) - 2; i >= 0; i-- {
+		layer := nums[i]
+		for j := range layer {
+			// 取最大的两个来源（下层同位置和下层同位置+1）
+			dp[i][j] += max(dp[i+1][j], dp[i+1][j+1])
+		}
+	}
+
+	return dp[0][0], steps
+}

cap4/ex25.go

@@ -0,0 +1,41 @@
+package cap4
+
+// Ex25 项目资源分配，项目数，资源数，收益表（第i个项目可得到的利润）
+func Ex25(m, n int, income []float64) ([]int, float64) {
+	dp := make([]float64, n)
+	tmp := make([]float64, n)
+
+	a := _makeMatrix(m, n)
+
+	for i := 0; i < n; i++ {
+		a[0][i] = i
+	}
+
+	copy(dp, income)
+	copy(tmp, income)
+
+	// 前i个项目
+	for i := 1; i < m; i++ {
+		// 资源数限制在j时
+		for j := 0; j < n; j++ {
+			// 第i个项目可分配k个资源
+			for k := 0; k < j; k++ {
+				if dp[j-k]+income[k] > tmp[j] {
+					tmp[j] = dp[j-k] + income[k]
+					a[i][j] = k
+				}
+			}
+		}
+
+		copy(dp, tmp)
+	}
+
+	rest := n
+	gain := make([]int, m+1)
+	for i := m - 1; i > 0; i-- {
+		gain[i] = a[i][rest]
+		rest -= gain[i]
+	}
+
+	return gain, dp[n]
+}

cap4/ex26.go

@@ -0,0 +1,31 @@
+package cap4
+
+import (
+	"math"
+)
+
+// Ex26 矩阵连乘，p为矩阵链，p[0],p[1]代表第一个矩阵的行数和列数，p[1],p[2]代表第二个矩阵的行数和列数
+func Ex26(p []int) (int, [][]int) {
+	length := len(p)
+
+	m, s := _makeMatrix(length, length), _makeMatrix(length, length)
+
+	for i := 1; i < length; i++ {
+		m[i][i] = 0
+	}
+
+	n := length - 1
+	for l := 2; l <= n; l++ {
+		for i := 1; i <= n-l+1; i++ {
+			j := i + l - 1
+			m[i][j] = math.MaxInt32
+			for k := i; k <= j-1; k++ {
+				q := m[i][k] + m[k+1][j] + p[i-1]*p[k]*p[j]
+				if q < m[i][j] {
+					m[i][j], s[i][j] = q, k
+				}
+			}
+		}
+	}
+	return m[1][length-1], s
+}

cap4/ex27.go

@@ -0,0 +1,22 @@
+package cap4
+
+import "strings"
+
+// Ex27 最长公共子序列
+func Ex27(str1, str2 []rune) (int, string) {
+	dp := _makeMatrix(len(str1)+1, len(str2)+1)
+	subStr := strings.Builder{}
+	for i := 1; i <= len(str1); i++ {
+		for j := 1; j <= len(str2); j++ {
+			a, b := str1[i], str2[j]
+			if a == b {
+				dp[i][j] = dp[i-1][j-1] + 1
+				subStr.WriteRune(a)
+			} else {
+				dp[i][j] = max(dp[i-1][j], dp[i][j-1])
+			}
+		}
+	}
+
+	return dp[len(str1)][len(str2)], subStr.String()
+}

cap4/ex28.go

@@ -0,0 +1,17 @@
+package cap4
+
+// Ex28 最长不下降子序列
+func Ex28(nums []int) int {
+	dp := make([]int, len(nums))
+
+	for i := 0; i < len(nums); i++ {
+		dp[i] = 1
+		for j := 0; j < len(nums); j++ {
+			if nums[i] > nums[j] {
+				dp[i] = max(dp[i], dp[j]+1)
+			}
+		}
+	}
+
+	return dp[len(dp)-1]
+}

cap4/example_test.go

@@ -0,0 +1,44 @@
+package cap4
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestEx14(t *testing.T) {
+	result := Ex15([]int{-1})
+	println(result)
+}
+
+func TestEx24(t *testing.T) {
+	nums := [][]int{
+		{9},
+		{12, 15},
+		{10, 6, 8},
+		{2, 18, 9, 5},
+		{19, 7, 10, 4, 16},
+	}
+	result, steps := Ex24(nums)
+	println(result)
+	for _, step := range steps {
+		fmt.Printf("%d ", step)
+	}
+	println()
+}
+
+func TestEx28(t *testing.T) {
+	nums := []int{3, 18, 7, 14, 10, 12, 23, 41, 16, 24}
+	result := Ex28(nums)
+	fmt.Println(result)
+}
+
+func PrintEx26Answer(s [][]int, i, j int) {
+	if i == j {
+		fmt.Printf("A%d", i)
+	} else {
+		fmt.Print("(")
+		PrintEx26Answer(s, i, s[i][j])
+		PrintEx26Answer(s, s[i][j]+1, j)
+		fmt.Print(")")
+	}
+}

cap5/ex1.go

@@ -0,0 +1 @@
+package cap5