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krahets
2023-10-08 01:43:28 +08:00
parent 3d2d669b43
commit baac2d11a7
52 changed files with 999 additions and 625 deletions
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zh/chapter_dynamic_programming/dp_problem_features.md
+46 -7
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@@ -104,7 +104,7 @@ $$
```csharp title="min_cost_climbing_stairs_dp.cs"
/* 爬楼梯最小代价：动态规划 */
int minCostClimbingStairsDP(int[] cost) {
int MinCostClimbingStairsDP(int[] cost) {
int n = cost.Length - 1;
if (n == 1 || n == 2)
return cost[n];
@@ -130,6 +130,12 @@ $$
if n == 1 || n == 2 {
return cost[n]
}
min := func(a, b int) int {
if a < b {
return a
}
return b
}
// 初始化 dp 表，用于存储子问题的解
dp := make([]int, n+1)
// 初始状态：预设最小子问题的解
@@ -137,7 +143,7 @@ $$
dp[2] = cost[2]
// 状态转移：从较小子问题逐步求解较大子问题
for i := 3; i <= n; i++ {
dp[i] = int(math.Min(float64(dp[i-1]), float64(dp[i-2]+cost[i])))
dp[i] = min(dp[i-1], dp[i-2]) + cost[i]
}
return dp[n]
}
@@ -252,7 +258,22 @@ $$
=== "C"
```c title="min_cost_climbing_stairs_dp.c"
[class]{}-[func]{minCostClimbingStairsDP}
/* 爬楼梯最小代价：动态规划 */
int minCostClimbingStairsDP(int cost[], int costSize) {
int n = costSize - 1;
if (n == 1 || n == 2)
return cost[n];
// 初始化 dp 表，用于存储子问题的解
int dp[n + 1];
// 初始状态：预设最小子问题的解
dp[1] = cost[1];
dp[2] = cost[2];
// 状态转移：从较小子问题逐步求解较大子问题
for (int i = 3; i <= n; i++) {
dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];
}
return dp[n];
}
```
=== "Zig"
@@ -339,7 +360,7 @@ $$
```csharp title="min_cost_climbing_stairs_dp.cs"
/* 爬楼梯最小代价：空间优化后的动态规划 */
int minCostClimbingStairsDPComp(int[] cost) {
int MinCostClimbingStairsDPComp(int[] cost) {
int n = cost.Length - 1;
if (n == 1 || n == 2)
return cost[n];
@@ -362,12 +383,18 @@ $$
if n == 1 || n == 2 {
return cost[n]
}
min := func(a, b int) int {
if a < b {
return a
}
return b
}
// 初始状态：预设最小子问题的解
a, b := cost[1], cost[2]
// 状态转移：从较小子问题逐步求解较大子问题
for i := 3; i <= n; i++ {
tmp := b
b = int(math.Min(float64(a), float64(tmp+cost[i])))
b = min(a, tmp) + cost[i]
a = tmp
}
return b
@@ -468,7 +495,19 @@ $$
=== "C"
```c title="min_cost_climbing_stairs_dp.c"
[class]{}-[func]{minCostClimbingStairsDPComp}
/* 爬楼梯最小代价：空间优化后的动态规划 */
int minCostClimbingStairsDPComp(int cost[], int costSize) {
int n = costSize - 1;
if (n == 1 || n == 2)
return cost[n];
int a = cost[1], b = cost[2];
for (int i = 3; i <= n; i++) {
int tmp = b;
b = min(a, tmp) + cost[i];
a = tmp;
}
return b;
}
```
=== "Zig"
@@ -605,7 +644,7 @@ $$
```csharp title="climbing_stairs_constraint_dp.cs"
/* 带约束爬楼梯：动态规划 */
int climbingStairsConstraintDP(int n) {
int ClimbingStairsConstraintDP(int n) {
if (n == 1 || n == 2) {
return 1;
}