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feat(csharp): add csharp code for unbounded knapsack (#596)

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hpstory 2023-07-13 15:49:40 +08:00 committed by GitHub
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71
codes/csharp/chapter_dynamic_programming/coin_change.cs Normal file
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/**
* File: coin_change.cs
* Created Time: 2023-07-12
* Author: hpstory (hpstory1024@163.com)
*/
namespace hello_algo.chapter_dynamic_programming;
public class coin_change {
/* 零钱兑换：动态规划 */
public int coinChangeDP(int[] coins, int amt) {
int n = coins.Length;
int MAX = amt + 1;
// 初始化 dp 表
int[,] dp = new int[n + 1, amt + 1];
// 状态转移：首行首列
for (int a = 1; a <= amt; a++) {
dp[0, a] = MAX;
}
// 状态转移：其余行列
for (int i = 1; i <= n; i++) {
for (int a = 1; a <= amt; a++) {
if (coins[i - 1] > a) {
// 若超过背包容量，则不选硬币 i
dp[i, a] = dp[i - 1, a];
} else {
// 不选和选硬币 i 这两种方案的较小值
dp[i, a] = Math.Min(dp[i - 1, a], dp[i, a - coins[i - 1]] + 1);
}
}
}
return dp[n, amt] != MAX ? dp[n, amt] : -1;
}
/* 零钱兑换：状态压缩后的动态规划 */
public int coinChangeDPComp(int[] coins, int amt) {
int n = coins.Length;
int MAX = amt + 1;
// 初始化 dp 表
int[] dp = new int[amt + 1];
Array.Fill(dp, MAX);
dp[0] = 0;
// 状态转移
for (int i = 1; i <= n; i++) {
for (int a = 1; a <= amt; a++) {
if (coins[i - 1] > a) {
// 若超过背包容量，则不选硬币 i
dp[a] = dp[a];
} else {
// 不选和选硬币 i 这两种方案的较小值
dp[a] = Math.Min(dp[a], dp[a - coins[i - 1]] + 1);
}
}
}
return dp[amt] != MAX ? dp[amt] : -1;
}
[Test]
public void Test() {
int[] coins = { 1, 2, 5 };
int amt = 4;
// 动态规划
int res = coinChangeDP(coins, amt);
Console.WriteLine("凑到目标金额所需的最少硬币数量为 " + res);
// 状态压缩后的动态规划
res = coinChangeDPComp(coins, amt);
Console.WriteLine("凑到目标金额所需的最少硬币数量为 " + res);
}
}

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codes/csharp/chapter_dynamic_programming/coin_change_ii.cs Normal file
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/**
* File: coin_change_ii.cs
* Created Time: 2023-07-12
* Author: hpstory (hpstory1024@163.com)
*/
namespace hello_algo.chapter_dynamic_programming;
public class coin_change_ii {
/* 零钱兑换 II：动态规划 */
public int coinChangeIIDP(int[] coins, int amt) {
int n = coins.Length;
// 初始化 dp 表
int[,] dp = new int[n + 1, amt + 1];
// 初始化首列
for (int i = 0; i <= n; i++) {
dp[i, 0] = 1;
}
// 状态转移
for (int i = 1; i <= n; i++) {
for (int a = 1; a <= amt; a++) {
if (coins[i - 1] > a) {
// 若超过背包容量，则不选硬币 i
dp[i, a] = dp[i - 1, a];
} else {
// 不选和选硬币 i 这两种方案之和
dp[i, a] = dp[i - 1, a] + dp[i, a - coins[i - 1]];
}
}
}
return dp[n, amt];
}
/* 零钱兑换 II：状态压缩后的动态规划 */
public int coinChangeIIDPComp(int[] coins, int amt) {
int n = coins.Length;
// 初始化 dp 表
int[] dp = new int[amt + 1];
dp[0] = 1;
// 状态转移
for (int i = 1; i <= n; i++) {
for (int a = 1; a <= amt; a++) {
if (coins[i - 1] > a) {
// 若超过背包容量，则不选硬币 i
dp[a] = dp[a];
} else {
// 不选和选硬币 i 这两种方案之和
dp[a] = dp[a] + dp[a - coins[i - 1]];
}
}
}
return dp[amt];
}
[Test]
public void Test() {
int[] coins = { 1, 2, 5 };
int amt = 5;
// 动态规划
int res = coinChangeIIDP(coins, amt);
Console.WriteLine("凑出目标金额的硬币组合数量为 " + res);
// 状态压缩后的动态规划
res = coinChangeIIDPComp(coins, amt);
Console.WriteLine("凑出目标金额的硬币组合数量为 " + res);
}
}

64
codes/csharp/chapter_dynamic_programming/unbounded_knapsack.cs Normal file
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/**
* File: unbounded_knapsack.cs
* Created Time: 2023-07-12
* Author: hpstory (hpstory1024@163.com)
*/
namespace hello_algo.chapter_dynamic_programming;
public class unbounded_knapsack {
/* 完全背包：动态规划 */
public int unboundedKnapsackDP(int[] wgt, int[] val, int cap) {
int n = wgt.Length;
// 初始化 dp 表
int[,] dp = new int[n + 1, cap + 1];
// 状态转移
for (int i = 1; i <= n; i++) {
for (int c = 1; c <= cap; c++) {
if (wgt[i - 1] > c) {
// 若超过背包容量，则不选物品 i
dp[i, c] = dp[i - 1, c];
} else {
// 不选和选物品 i 这两种方案的较大值
dp[i, c] = Math.Max(dp[i - 1, c], dp[i, c - wgt[i - 1]] + val[i - 1]);
}
}
}
return dp[n, cap];
}
/* 完全背包：状态压缩后的动态规划 */
public int unboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {
int n = wgt.Length;
// 初始化 dp 表
int[] dp = new int[cap + 1];
// 状态转移
for (int i = 1; i <= n; i++) {
for (int c = 1; c <= cap; c++) {
if (wgt[i - 1] > c) {
// 若超过背包容量，则不选物品 i
dp[c] = dp[c];
} else {
// 不选和选物品 i 这两种方案的较大值
dp[c] = Math.Max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);
}
}
}
return dp[cap];
}
[Test]
public void Test() {
int[] wgt = { 1, 2, 3 };
int[] val = { 5, 11, 15 };
int cap = 4;
// 动态规划
int res = unboundedKnapsackDP(wgt, val, cap);
Console.WriteLine("不超过背包容量的最大物品价值为 " + res);
// 状态压缩后的动态规划
res = unboundedKnapsackDPComp(wgt, val, cap);
Console.WriteLine("不超过背包容量的最大物品价值为 " + res);
}
}