2025/04/05

Hard/815 Bus Routes.md

@@ -0,0 +1,78 @@
+# 815 Bus Routes
+
+## Intuition
+
+The problem can be modeled as a graph where:
+
+- Each bus route represents a set of connected stops
+- We need to find the minimum number of bus changes required to go from source to target
+- We can use BFS to explore all possible routes level by level, where each level represents one bus change
+
+## Approach
+
+1. First check if source and target are the same (return 0 if true)
+2. Create a map `stopToBus` to store which buses stop at each station
+3. Use BFS to explore all possible routes:
+   - Start from the source stop
+   - For each stop, check all buses that pass through it
+   - For each bus, check all stops it can reach
+   - If we reach the target, return the current number of bus changes
+   - Keep track of visited stops and buses to avoid cycles
+4. If we exhaust all possibilities without finding the target, return -1
+
+## Complexity
+
+- Time complexity: O(N + M), where N is the number of stops and M is the number of bus routes
+- Space complexity: O(N + M)
+
+## Keywords
+
+- BFS
+- Graph
+
+## Code
+
+```go
+func numBusesToDestination(routes [][]int, source int, target int) int {
+    if source == target {
+        return 0
+    }
+    ret, n, stopToBus := 0, 0, make(map[int][]int)
+    for i, route := range routes {
+        for _, stop := range route {
+            stopToBus[stop] = append(stopToBus[stop], i)
+        }
+    }
+
+    queue, stopRecord, busRecord := []int{source}, map[int]bool{source: true}, make(map[int]bool)
+    bfs := func(curStop int) bool {
+        for _, bus := range stopToBus[curStop] {
+            if busRecord[bus] {
+                continue
+            }
+            busRecord[bus] = true
+            for _, stop := range routes[bus] {
+                if stopRecord[stop] {
+                    continue
+                }
+                if stop == target {
+                    return true
+                }
+                queue, stopRecord[stop] = append(queue, stop), true
+            }
+        }
+        return false
+    }
+    for len(queue) != 0 {
+        ret, n = ret + 1, len(queue)
+        for _, curStop := range queue {
+            if bfs(curStop) {
+                return ret
+            }
+        }
+        queue = queue[n:]
+    }
+
+    return -1
+}
+```

Medium/322 Coin Change.md

@@ -0,0 +1,75 @@
+# 322. Coin Change
+
+## Intuition
+
+We can use dynamic programming to solve this problem by breaking it down into smaller subproblems. For each amount from 1 to the target amount, we can calculate the minimum number of coins needed by considering all possible coin denominations.
+
+## Approach
+
+1. First, handle edge cases:
+   - If amount is 0, return 0
+   - If any coin equals the amount, return 1
+   - If all coins are larger than the amount, return -1
+2. Initialize a DP array where dp[i] represents the minimum number of coins needed for amount i
+3. Set initial values:
+   - dp[0] = 0 (0 coins needed for amount 0)
+   - All other values initialized to a large number (math.MaxInt - 1)
+4. Sort the coins array for optimization
+5. For each amount from 1 to target amount:
+   - For each coin denomination:
+     - If the coin is less than or equal to the current amount
+     - Update dp[i] with the minimum of current value and (dp[i - coin] + 1)
+6. Return dp[amount] if it's not the initial large value, otherwise return -1
+
+## Complexity
+
+- Time complexity: O(n * m)
+- Space complexity: O(n)
+
+## Keywords
+
+- Dynamic Programming
+- Bottom-up Approach
+
+## Code
+
+```go
+func coinChange(coins []int, amount int) int {
+    if amount == 0 {
+        return 0
+    }
+    smallFlag := false
+    for _, coin := range coins {
+        if coin == amount {
+            return 1
+        } else if coin < amount {
+            smallFlag = true
+        }
+    }
+    if !smallFlag {
+        return -1
+    }
+
+    dp := make([]int, amount + 1)
+    for i := range dp {
+        dp[i] = math.MaxInt - 1
+    }
+    dp[0] = 0
+
+    sort.Ints(coins)
+
+    for i := 1; i <= amount ; i += 1 {
+        for _, coin := range coins {
+            if coin <= i {
+                dp[i] = min(dp[i], dp[i - coin] + 1)
+            } else {
+                break
+            }
+        }
+    }
+    if dp[amount] == math.MaxInt - 1 {
+        return -1
+    }
+    return dp[amount]
+}
+```

Medium/752 Open the Lock.md

@@ -0,0 +1,102 @@
+# 752 Open the Lock
+
+## Intuition
+
+The problem can be modeled as a graph traversal problem where each node represents a lock combination (4-digit number) and edges represent valid moves (turning one wheel up or down). We need to find the shortest path from "0000" to the target combination while avoiding deadends. This naturally leads to using BFS (Breadth-First Search) as it guarantees finding the shortest path in an unweighted graph.
+
+## Approach
+
+1. Start with the initial combination "0000"
+2. Use BFS to explore all possible combinations:
+   - For each digit in the current combination, try turning it up and down
+   - Skip combinations that are in the deadends list
+   - Keep track of visited combinations to avoid cycles
+   - Return the number of steps when the target is found
+3. If the queue becomes empty without finding the target, return -1
+
+## Complexity
+
+- Time complexity: O(N), where N is the number of possible combinations (10^4 = 10000)
+- Space complexity: O(N)
+
+## Keywords
+
+- BFS
+- Graph Traversal
+
+## Code
+
+```go
+func openLock(deadends []string, target string) int {
+    if "0000" == target {
+        return 0
+    }
+    dds, record, ret := make(map[string]bool, len(deadends)), make(map[string]bool), 0
+    for _, dd := range deadends {
+        dds[dd] = true
+    }
+    if dds["0000"] {
+        return -1
+    }
+    record[target] = true
+
+    newCurProcess := func(i int, destDigit byte, cur string, tmp *[]string) bool {
+        curByte := []byte(cur)
+        curByte[i] = destDigit
+        cur = string(curByte)
+        if dds[cur] {
+            return false
+        }
+        if cur == target {
+            return true
+        }
+        if _, found := record[cur]; !found {
+            *tmp, record[cur] = append(*tmp, cur), true
+        }
+        return false
+    }
+
+    getNext := func(cur string, tmp *[]string) bool {
+        for i := 0; i < 4; i += 1 {
+            switch cur[i] {
+            case '0':
+                if newCurProcess(i, '1', cur, tmp) {
+                    return true
+                }
+                if newCurProcess(i, '9', cur, tmp) {
+                    return true
+                }
+            case '9':
+                if newCurProcess(i, '0', cur, tmp) {
+                    return true
+                }
+                if newCurProcess(i, '8', cur, tmp) {
+                    return true
+                }
+            default:
+                if newCurProcess(i, cur[i] + 1, cur, tmp) {
+                    return true
+                }
+                if newCurProcess(i, cur[i] - 1, cur, tmp) {
+                    return true
+                }
+            }
+        }
+        return false
+    }
+
+    queue := []string{"0000"}
+    for len(queue) != 0 {
+        ret += 1
+        tmp := make([]string, 0)
+        for _, cur := range queue {
+            if getNext(cur, &tmp) {
+                return ret
+            }
+        }
+        queue = tmp
+    }
+
+    return -1
+}
+```

README.md

@@ -22,9 +22,12 @@
 | 140 | Word Break II | [go](/Hard/140%20Word%20Break%20II.md) | H |
 | 146 | LRU Cache | [go](/Medium/146%20LRU%20Cache.md) | M |
 | 239 | Sliding Window Maximum | [go](/Hard/239%20Sliding%20Window%20Maximum.md) | H |
+| 322 | Coin Change | [go](/Medium/322%20Coin%20Change.md) | M |
 | 460 | LFU Cache | [go](/Hard/460%20LFU%20Cache.md) | H |
 | 592 | Fraction Addition and Subtraction | [go](/Medium/592%20Fraction%20Addition%20and%20Subtraction.md) | M |
+| 752 | Open the Lock | [go](/Medium/752%20Open%20the%20Lock.md) | M |
 | 757 | Set Intersection Size At Least Two | [go](/Hard/757%20Set%20Intersection%20Size%20At%20Least%20Two.md) | H |
+| 815 | Bus Routes | [go](/Hard/815%20Bus%20Routes.md) | H |
 | 765 | Couples Holding Hands | [go](/Hard/765%20Couples%20Holding%20Hands.md) | H |
 | 840 | Magic Squares In Grid | [go](/Medium/840%20Magic%20Squares%20In%20Grid.md) | M |
 | 881 | Boats to Save People | [go](/Medium/881%20Boats%20to%20Save%20People.md) | M |

Week7/322 Coin Change.md

@@ -0,0 +1,75 @@
+# 322. Coin Change
+
+## Intuition
+
+We can use dynamic programming to solve this problem by breaking it down into smaller subproblems. For each amount from 1 to the target amount, we can calculate the minimum number of coins needed by considering all possible coin denominations.
+
+## Approach
+
+1. First, handle edge cases:
+   - If amount is 0, return 0
+   - If any coin equals the amount, return 1
+   - If all coins are larger than the amount, return -1
+2. Initialize a DP array where dp[i] represents the minimum number of coins needed for amount i
+3. Set initial values:
+   - dp[0] = 0 (0 coins needed for amount 0)
+   - All other values initialized to a large number (math.MaxInt - 1)
+4. Sort the coins array for optimization
+5. For each amount from 1 to target amount:
+   - For each coin denomination:
+     - If the coin is less than or equal to the current amount
+     - Update dp[i] with the minimum of current value and (dp[i - coin] + 1)
+6. Return dp[amount] if it's not the initial large value, otherwise return -1
+
+## Complexity
+
+- Time complexity: O(n * m)
+- Space complexity: O(n)
+
+## Keywords
+
+- Dynamic Programming
+- Bottom-up Approach
+
+## Code
+
+```go
+func coinChange(coins []int, amount int) int {
+    if amount == 0 {
+        return 0
+    }
+    smallFlag := false
+    for _, coin := range coins {
+        if coin == amount {
+            return 1
+        } else if coin < amount {
+            smallFlag = true
+        }
+    }
+    if !smallFlag {
+        return -1
+    }
+
+    dp := make([]int, amount + 1)
+    for i := range dp {
+        dp[i] = math.MaxInt - 1
+    }
+    dp[0] = 0
+
+    sort.Ints(coins)
+
+    for i := 1; i <= amount ; i += 1 {
+        for _, coin := range coins {
+            if coin <= i {
+                dp[i] = min(dp[i], dp[i - coin] + 1)
+            } else {
+                break
+            }
+        }
+    }
+    if dp[amount] == math.MaxInt - 1 {
+        return -1
+    }
+    return dp[amount]
+}
+```